58.307 * [progress]: [Phase 1 of 3] Setting up.
0.001 * * * [progress]: [1/2] Preparing points
0.187 * * * [progress]: [2/2] Setting up program.
0.190 * [progress]: [Phase 2 of 3] Improving.
0.190 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.190 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.190 * * [simplify]: iteration 1: (13 enodes)
0.194 * * [simplify]: iteration 2: (31 enodes)
0.200 * * [simplify]: iteration 3: (62 enodes)
0.244 * * [simplify]: iteration 4: (124 enodes)
0.314 * * [simplify]: iteration 5: (330 enodes)
0.526 * * [simplify]: iteration 6: (831 enodes)
1.493 * * [simplify]: iteration 7: (1981 enodes)
8.449 * * [simplify]: Extracting #0: cost 1 inf + 0
8.449 * * [simplify]: Extracting #1: cost 118 inf + 0
8.452 * * [simplify]: Extracting #2: cost 496 inf + 1
8.457 * * [simplify]: Extracting #3: cost 580 inf + 50
8.463 * * [simplify]: Extracting #4: cost 537 inf + 17474
8.568 * * [simplify]: Extracting #5: cost 201 inf + 274545
8.732 * * [simplify]: Extracting #6: cost 0 inf + 448926
8.946 * * [simplify]: Extracting #7: cost 0 inf + 443910
9.200 * * [simplify]: Extracting #8: cost 0 inf + 443832
9.400 * [simplify]: Simplified to:
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
9.406 * * [progress]: iteration 1 / 4
9.406 * * * [progress]: picking best candidate
9.413 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))>
9.413 * * * [progress]: localizing error
9.441 * * * [progress]: generating rewritten candidates
9.441 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
9.456 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
9.486 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
9.511 * * * [progress]: generating series expansions
9.511 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
9.512 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
9.513 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
9.513 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
9.513 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
9.513 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
9.513 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.513 * [taylor]: Taking taylor expansion of 1/2 in k
9.513 * [backup-simplify]: Simplify 1/2 into 1/2
9.513 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.513 * [taylor]: Taking taylor expansion of 1 in k
9.513 * [backup-simplify]: Simplify 1 into 1
9.513 * [taylor]: Taking taylor expansion of k in k
9.513 * [backup-simplify]: Simplify 0 into 0
9.513 * [backup-simplify]: Simplify 1 into 1
9.513 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.513 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.513 * [taylor]: Taking taylor expansion of 2 in k
9.513 * [backup-simplify]: Simplify 2 into 2
9.513 * [taylor]: Taking taylor expansion of (* n PI) in k
9.513 * [taylor]: Taking taylor expansion of n in k
9.513 * [backup-simplify]: Simplify n into n
9.513 * [taylor]: Taking taylor expansion of PI in k
9.513 * [backup-simplify]: Simplify PI into PI
9.513 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.513 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.513 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.514 * [backup-simplify]: Simplify (- 0) into 0
9.514 * [backup-simplify]: Simplify (+ 1 0) into 1
9.515 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.515 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.515 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.515 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
9.515 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
9.515 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
9.515 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.515 * [taylor]: Taking taylor expansion of 1/2 in n
9.515 * [backup-simplify]: Simplify 1/2 into 1/2
9.515 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.515 * [taylor]: Taking taylor expansion of 1 in n
9.515 * [backup-simplify]: Simplify 1 into 1
9.515 * [taylor]: Taking taylor expansion of k in n
9.515 * [backup-simplify]: Simplify k into k
9.515 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.515 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.515 * [taylor]: Taking taylor expansion of 2 in n
9.515 * [backup-simplify]: Simplify 2 into 2
9.515 * [taylor]: Taking taylor expansion of (* n PI) in n
9.515 * [taylor]: Taking taylor expansion of n in n
9.516 * [backup-simplify]: Simplify 0 into 0
9.516 * [backup-simplify]: Simplify 1 into 1
9.516 * [taylor]: Taking taylor expansion of PI in n
9.516 * [backup-simplify]: Simplify PI into PI
9.516 * [backup-simplify]: Simplify (* 0 PI) into 0
9.517 * [backup-simplify]: Simplify (* 2 0) into 0
9.518 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.520 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.521 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.521 * [backup-simplify]: Simplify (- k) into (- k)
9.521 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.521 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.522 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.523 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
9.525 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
9.525 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
9.525 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
9.525 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
9.525 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.525 * [taylor]: Taking taylor expansion of 1/2 in n
9.525 * [backup-simplify]: Simplify 1/2 into 1/2
9.525 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.525 * [taylor]: Taking taylor expansion of 1 in n
9.525 * [backup-simplify]: Simplify 1 into 1
9.525 * [taylor]: Taking taylor expansion of k in n
9.525 * [backup-simplify]: Simplify k into k
9.525 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.525 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.525 * [taylor]: Taking taylor expansion of 2 in n
9.525 * [backup-simplify]: Simplify 2 into 2
9.525 * [taylor]: Taking taylor expansion of (* n PI) in n
9.525 * [taylor]: Taking taylor expansion of n in n
9.525 * [backup-simplify]: Simplify 0 into 0
9.525 * [backup-simplify]: Simplify 1 into 1
9.525 * [taylor]: Taking taylor expansion of PI in n
9.525 * [backup-simplify]: Simplify PI into PI
9.526 * [backup-simplify]: Simplify (* 0 PI) into 0
9.526 * [backup-simplify]: Simplify (* 2 0) into 0
9.528 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.529 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.530 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.530 * [backup-simplify]: Simplify (- k) into (- k)
9.530 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.530 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.532 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.533 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
9.534 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
9.534 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
9.534 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
9.534 * [taylor]: Taking taylor expansion of 1/2 in k
9.534 * [backup-simplify]: Simplify 1/2 into 1/2
9.534 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
9.534 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.534 * [taylor]: Taking taylor expansion of 1 in k
9.534 * [backup-simplify]: Simplify 1 into 1
9.535 * [taylor]: Taking taylor expansion of k in k
9.535 * [backup-simplify]: Simplify 0 into 0
9.535 * [backup-simplify]: Simplify 1 into 1
9.535 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
9.535 * [taylor]: Taking taylor expansion of (log n) in k
9.535 * [taylor]: Taking taylor expansion of n in k
9.535 * [backup-simplify]: Simplify n into n
9.535 * [backup-simplify]: Simplify (log n) into (log n)
9.535 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.535 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.535 * [taylor]: Taking taylor expansion of 2 in k
9.535 * [backup-simplify]: Simplify 2 into 2
9.535 * [taylor]: Taking taylor expansion of PI in k
9.535 * [backup-simplify]: Simplify PI into PI
9.535 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.537 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.537 * [backup-simplify]: Simplify (- 0) into 0
9.537 * [backup-simplify]: Simplify (+ 1 0) into 1
9.539 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.540 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
9.541 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
9.542 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.543 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.544 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.545 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.547 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.547 * [backup-simplify]: Simplify (- 0) into 0
9.548 * [backup-simplify]: Simplify (+ 0 0) into 0
9.548 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
9.550 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.551 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
9.553 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.553 * [taylor]: Taking taylor expansion of 0 in k
9.553 * [backup-simplify]: Simplify 0 into 0
9.553 * [backup-simplify]: Simplify 0 into 0
9.554 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.555 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.557 * [backup-simplify]: Simplify (+ 0 0) into 0
9.557 * [backup-simplify]: Simplify (- 1) into -1
9.558 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.560 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
9.562 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
9.564 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.565 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.566 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.567 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.569 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.569 * [backup-simplify]: Simplify (- 0) into 0
9.569 * [backup-simplify]: Simplify (+ 0 0) into 0
9.570 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
9.571 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.572 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.573 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.573 * [taylor]: Taking taylor expansion of 0 in k
9.573 * [backup-simplify]: Simplify 0 into 0
9.573 * [backup-simplify]: Simplify 0 into 0
9.573 * [backup-simplify]: Simplify 0 into 0
9.574 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.575 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.576 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.577 * [backup-simplify]: Simplify (+ 0 0) into 0
9.577 * [backup-simplify]: Simplify (- 0) into 0
9.577 * [backup-simplify]: Simplify (+ 0 0) into 0
9.578 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.580 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.582 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.585 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.593 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
9.594 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
9.594 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
9.594 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
9.594 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.594 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.594 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.594 * [taylor]: Taking taylor expansion of 1/2 in k
9.594 * [backup-simplify]: Simplify 1/2 into 1/2
9.594 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.594 * [taylor]: Taking taylor expansion of 1 in k
9.594 * [backup-simplify]: Simplify 1 into 1
9.594 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.594 * [taylor]: Taking taylor expansion of k in k
9.594 * [backup-simplify]: Simplify 0 into 0
9.594 * [backup-simplify]: Simplify 1 into 1
9.594 * [backup-simplify]: Simplify (/ 1 1) into 1
9.594 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.594 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.594 * [taylor]: Taking taylor expansion of 2 in k
9.594 * [backup-simplify]: Simplify 2 into 2
9.594 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.594 * [taylor]: Taking taylor expansion of PI in k
9.595 * [backup-simplify]: Simplify PI into PI
9.595 * [taylor]: Taking taylor expansion of n in k
9.595 * [backup-simplify]: Simplify n into n
9.595 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.595 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.595 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.595 * [backup-simplify]: Simplify (- 1) into -1
9.596 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.596 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.596 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.596 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
9.597 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
9.597 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.597 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.597 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.597 * [taylor]: Taking taylor expansion of 1/2 in n
9.597 * [backup-simplify]: Simplify 1/2 into 1/2
9.597 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.597 * [taylor]: Taking taylor expansion of 1 in n
9.597 * [backup-simplify]: Simplify 1 into 1
9.597 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.597 * [taylor]: Taking taylor expansion of k in n
9.597 * [backup-simplify]: Simplify k into k
9.597 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.597 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.597 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.597 * [taylor]: Taking taylor expansion of 2 in n
9.597 * [backup-simplify]: Simplify 2 into 2
9.597 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.597 * [taylor]: Taking taylor expansion of PI in n
9.597 * [backup-simplify]: Simplify PI into PI
9.597 * [taylor]: Taking taylor expansion of n in n
9.597 * [backup-simplify]: Simplify 0 into 0
9.597 * [backup-simplify]: Simplify 1 into 1
9.598 * [backup-simplify]: Simplify (/ PI 1) into PI
9.598 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.599 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.599 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.599 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.599 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.601 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.602 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
9.603 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.603 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
9.603 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.603 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.603 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.603 * [taylor]: Taking taylor expansion of 1/2 in n
9.603 * [backup-simplify]: Simplify 1/2 into 1/2
9.603 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.603 * [taylor]: Taking taylor expansion of 1 in n
9.603 * [backup-simplify]: Simplify 1 into 1
9.603 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.603 * [taylor]: Taking taylor expansion of k in n
9.603 * [backup-simplify]: Simplify k into k
9.603 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.603 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.603 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.603 * [taylor]: Taking taylor expansion of 2 in n
9.603 * [backup-simplify]: Simplify 2 into 2
9.603 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.603 * [taylor]: Taking taylor expansion of PI in n
9.603 * [backup-simplify]: Simplify PI into PI
9.603 * [taylor]: Taking taylor expansion of n in n
9.604 * [backup-simplify]: Simplify 0 into 0
9.604 * [backup-simplify]: Simplify 1 into 1
9.604 * [backup-simplify]: Simplify (/ PI 1) into PI
9.604 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.605 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.606 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.606 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.606 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.607 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.608 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
9.609 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.610 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
9.610 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
9.610 * [taylor]: Taking taylor expansion of 1/2 in k
9.610 * [backup-simplify]: Simplify 1/2 into 1/2
9.610 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
9.610 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.610 * [taylor]: Taking taylor expansion of 1 in k
9.610 * [backup-simplify]: Simplify 1 into 1
9.610 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.610 * [taylor]: Taking taylor expansion of k in k
9.610 * [backup-simplify]: Simplify 0 into 0
9.610 * [backup-simplify]: Simplify 1 into 1
9.610 * [backup-simplify]: Simplify (/ 1 1) into 1
9.610 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
9.610 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.610 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.610 * [taylor]: Taking taylor expansion of 2 in k
9.611 * [backup-simplify]: Simplify 2 into 2
9.611 * [taylor]: Taking taylor expansion of PI in k
9.611 * [backup-simplify]: Simplify PI into PI
9.611 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.612 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.612 * [taylor]: Taking taylor expansion of (log n) in k
9.612 * [taylor]: Taking taylor expansion of n in k
9.612 * [backup-simplify]: Simplify n into n
9.612 * [backup-simplify]: Simplify (log n) into (log n)
9.613 * [backup-simplify]: Simplify (- 1) into -1
9.613 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.613 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.614 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
9.615 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
9.616 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
9.617 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.619 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.620 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.620 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.622 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.622 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.623 * [backup-simplify]: Simplify (- 0) into 0
9.623 * [backup-simplify]: Simplify (+ 0 0) into 0
9.624 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
9.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.626 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.628 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.628 * [taylor]: Taking taylor expansion of 0 in k
9.628 * [backup-simplify]: Simplify 0 into 0
9.628 * [backup-simplify]: Simplify 0 into 0
9.628 * [backup-simplify]: Simplify 0 into 0
9.629 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.630 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.632 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.632 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.632 * [backup-simplify]: Simplify (- 0) into 0
9.633 * [backup-simplify]: Simplify (+ 0 0) into 0
9.633 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
9.634 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.635 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
9.636 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.636 * [taylor]: Taking taylor expansion of 0 in k
9.636 * [backup-simplify]: Simplify 0 into 0
9.636 * [backup-simplify]: Simplify 0 into 0
9.636 * [backup-simplify]: Simplify 0 into 0
9.636 * [backup-simplify]: Simplify 0 into 0
9.637 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.638 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.641 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.642 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.642 * [backup-simplify]: Simplify (- 0) into 0
9.642 * [backup-simplify]: Simplify (+ 0 0) into 0
9.643 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
9.644 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.645 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
9.647 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.647 * [taylor]: Taking taylor expansion of 0 in k
9.647 * [backup-simplify]: Simplify 0 into 0
9.647 * [backup-simplify]: Simplify 0 into 0
9.647 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
9.648 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
9.648 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
9.648 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
9.648 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
9.648 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
9.648 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
9.648 * [taylor]: Taking taylor expansion of 1/2 in k
9.648 * [backup-simplify]: Simplify 1/2 into 1/2
9.648 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.648 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.648 * [taylor]: Taking taylor expansion of k in k
9.648 * [backup-simplify]: Simplify 0 into 0
9.648 * [backup-simplify]: Simplify 1 into 1
9.648 * [backup-simplify]: Simplify (/ 1 1) into 1
9.648 * [taylor]: Taking taylor expansion of 1 in k
9.648 * [backup-simplify]: Simplify 1 into 1
9.648 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.648 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.648 * [taylor]: Taking taylor expansion of -2 in k
9.648 * [backup-simplify]: Simplify -2 into -2
9.648 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.648 * [taylor]: Taking taylor expansion of PI in k
9.648 * [backup-simplify]: Simplify PI into PI
9.648 * [taylor]: Taking taylor expansion of n in k
9.648 * [backup-simplify]: Simplify n into n
9.648 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.648 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.649 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.649 * [backup-simplify]: Simplify (+ 1 0) into 1
9.649 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.649 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.649 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
9.649 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
9.649 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
9.649 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
9.649 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.649 * [taylor]: Taking taylor expansion of 1/2 in n
9.649 * [backup-simplify]: Simplify 1/2 into 1/2
9.649 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.649 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.649 * [taylor]: Taking taylor expansion of k in n
9.649 * [backup-simplify]: Simplify k into k
9.649 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.649 * [taylor]: Taking taylor expansion of 1 in n
9.649 * [backup-simplify]: Simplify 1 into 1
9.650 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.650 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.650 * [taylor]: Taking taylor expansion of -2 in n
9.650 * [backup-simplify]: Simplify -2 into -2
9.650 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.650 * [taylor]: Taking taylor expansion of PI in n
9.650 * [backup-simplify]: Simplify PI into PI
9.650 * [taylor]: Taking taylor expansion of n in n
9.650 * [backup-simplify]: Simplify 0 into 0
9.650 * [backup-simplify]: Simplify 1 into 1
9.650 * [backup-simplify]: Simplify (/ PI 1) into PI
9.650 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.651 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.651 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.651 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.652 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.652 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
9.653 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.653 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
9.653 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
9.653 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
9.653 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
9.653 * [taylor]: Taking taylor expansion of 1/2 in n
9.653 * [backup-simplify]: Simplify 1/2 into 1/2
9.653 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
9.653 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.653 * [taylor]: Taking taylor expansion of k in n
9.653 * [backup-simplify]: Simplify k into k
9.653 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.653 * [taylor]: Taking taylor expansion of 1 in n
9.653 * [backup-simplify]: Simplify 1 into 1
9.653 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.653 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.653 * [taylor]: Taking taylor expansion of -2 in n
9.653 * [backup-simplify]: Simplify -2 into -2
9.653 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.654 * [taylor]: Taking taylor expansion of PI in n
9.654 * [backup-simplify]: Simplify PI into PI
9.654 * [taylor]: Taking taylor expansion of n in n
9.654 * [backup-simplify]: Simplify 0 into 0
9.654 * [backup-simplify]: Simplify 1 into 1
9.654 * [backup-simplify]: Simplify (/ PI 1) into PI
9.654 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.655 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.655 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
9.655 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
9.656 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.656 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
9.657 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.657 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
9.657 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
9.657 * [taylor]: Taking taylor expansion of 1/2 in k
9.657 * [backup-simplify]: Simplify 1/2 into 1/2
9.657 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
9.657 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
9.657 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.657 * [taylor]: Taking taylor expansion of k in k
9.657 * [backup-simplify]: Simplify 0 into 0
9.657 * [backup-simplify]: Simplify 1 into 1
9.658 * [backup-simplify]: Simplify (/ 1 1) into 1
9.658 * [taylor]: Taking taylor expansion of 1 in k
9.658 * [backup-simplify]: Simplify 1 into 1
9.658 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
9.658 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
9.658 * [taylor]: Taking taylor expansion of (* -2 PI) in k
9.658 * [taylor]: Taking taylor expansion of -2 in k
9.658 * [backup-simplify]: Simplify -2 into -2
9.658 * [taylor]: Taking taylor expansion of PI in k
9.658 * [backup-simplify]: Simplify PI into PI
9.658 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.659 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.659 * [taylor]: Taking taylor expansion of (log n) in k
9.659 * [taylor]: Taking taylor expansion of n in k
9.659 * [backup-simplify]: Simplify n into n
9.659 * [backup-simplify]: Simplify (log n) into (log n)
9.659 * [backup-simplify]: Simplify (+ 1 0) into 1
9.659 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.660 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
9.660 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
9.661 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
9.662 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.663 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
9.664 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.665 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.666 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
9.667 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.667 * [backup-simplify]: Simplify (+ 0 0) into 0
9.668 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
9.669 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.670 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
9.671 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.671 * [taylor]: Taking taylor expansion of 0 in k
9.671 * [backup-simplify]: Simplify 0 into 0
9.671 * [backup-simplify]: Simplify 0 into 0
9.671 * [backup-simplify]: Simplify 0 into 0
9.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.673 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.674 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
9.675 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.675 * [backup-simplify]: Simplify (+ 0 0) into 0
9.675 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
9.676 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.677 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
9.678 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.678 * [taylor]: Taking taylor expansion of 0 in k
9.679 * [backup-simplify]: Simplify 0 into 0
9.679 * [backup-simplify]: Simplify 0 into 0
9.679 * [backup-simplify]: Simplify 0 into 0
9.679 * [backup-simplify]: Simplify 0 into 0
9.679 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.680 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.683 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
9.683 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.684 * [backup-simplify]: Simplify (+ 0 0) into 0
9.685 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
9.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.687 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
9.689 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.689 * [taylor]: Taking taylor expansion of 0 in k
9.689 * [backup-simplify]: Simplify 0 into 0
9.689 * [backup-simplify]: Simplify 0 into 0
9.689 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
9.690 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
9.690 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
9.690 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
9.690 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.690 * [taylor]: Taking taylor expansion of 2 in n
9.690 * [backup-simplify]: Simplify 2 into 2
9.690 * [taylor]: Taking taylor expansion of (* n PI) in n
9.690 * [taylor]: Taking taylor expansion of n in n
9.690 * [backup-simplify]: Simplify 0 into 0
9.690 * [backup-simplify]: Simplify 1 into 1
9.690 * [taylor]: Taking taylor expansion of PI in n
9.690 * [backup-simplify]: Simplify PI into PI
9.690 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.690 * [taylor]: Taking taylor expansion of 2 in n
9.690 * [backup-simplify]: Simplify 2 into 2
9.690 * [taylor]: Taking taylor expansion of (* n PI) in n
9.690 * [taylor]: Taking taylor expansion of n in n
9.690 * [backup-simplify]: Simplify 0 into 0
9.690 * [backup-simplify]: Simplify 1 into 1
9.690 * [taylor]: Taking taylor expansion of PI in n
9.690 * [backup-simplify]: Simplify PI into PI
9.691 * [backup-simplify]: Simplify (* 0 PI) into 0
9.691 * [backup-simplify]: Simplify (* 2 0) into 0
9.691 * [backup-simplify]: Simplify 0 into 0
9.692 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.693 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.693 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.694 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.695 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.695 * [backup-simplify]: Simplify 0 into 0
9.697 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.698 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.698 * [backup-simplify]: Simplify 0 into 0
9.699 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.700 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
9.700 * [backup-simplify]: Simplify 0 into 0
9.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.702 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
9.702 * [backup-simplify]: Simplify 0 into 0
9.703 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.705 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
9.705 * [backup-simplify]: Simplify 0 into 0
9.707 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
9.709 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
9.709 * [backup-simplify]: Simplify 0 into 0
9.710 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
9.711 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
9.711 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
9.711 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.711 * [taylor]: Taking taylor expansion of 2 in n
9.711 * [backup-simplify]: Simplify 2 into 2
9.711 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.711 * [taylor]: Taking taylor expansion of PI in n
9.711 * [backup-simplify]: Simplify PI into PI
9.711 * [taylor]: Taking taylor expansion of n in n
9.711 * [backup-simplify]: Simplify 0 into 0
9.711 * [backup-simplify]: Simplify 1 into 1
9.711 * [backup-simplify]: Simplify (/ PI 1) into PI
9.712 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.712 * [taylor]: Taking taylor expansion of 2 in n
9.712 * [backup-simplify]: Simplify 2 into 2
9.712 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.712 * [taylor]: Taking taylor expansion of PI in n
9.712 * [backup-simplify]: Simplify PI into PI
9.712 * [taylor]: Taking taylor expansion of n in n
9.712 * [backup-simplify]: Simplify 0 into 0
9.712 * [backup-simplify]: Simplify 1 into 1
9.712 * [backup-simplify]: Simplify (/ PI 1) into PI
9.713 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.713 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.714 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.715 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.715 * [backup-simplify]: Simplify 0 into 0
9.716 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.717 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.717 * [backup-simplify]: Simplify 0 into 0
9.718 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.719 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.719 * [backup-simplify]: Simplify 0 into 0
9.720 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.722 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.722 * [backup-simplify]: Simplify 0 into 0
9.723 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.724 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.724 * [backup-simplify]: Simplify 0 into 0
9.725 * [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
9.727 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.727 * [backup-simplify]: Simplify 0 into 0
9.728 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
9.728 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
9.728 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
9.728 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.728 * [taylor]: Taking taylor expansion of -2 in n
9.728 * [backup-simplify]: Simplify -2 into -2
9.728 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.728 * [taylor]: Taking taylor expansion of PI in n
9.728 * [backup-simplify]: Simplify PI into PI
9.728 * [taylor]: Taking taylor expansion of n in n
9.728 * [backup-simplify]: Simplify 0 into 0
9.728 * [backup-simplify]: Simplify 1 into 1
9.729 * [backup-simplify]: Simplify (/ PI 1) into PI
9.729 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.729 * [taylor]: Taking taylor expansion of -2 in n
9.729 * [backup-simplify]: Simplify -2 into -2
9.729 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.729 * [taylor]: Taking taylor expansion of PI in n
9.729 * [backup-simplify]: Simplify PI into PI
9.729 * [taylor]: Taking taylor expansion of n in n
9.729 * [backup-simplify]: Simplify 0 into 0
9.729 * [backup-simplify]: Simplify 1 into 1
9.730 * [backup-simplify]: Simplify (/ PI 1) into PI
9.730 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.731 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.732 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.732 * [backup-simplify]: Simplify 0 into 0
9.733 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.734 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.734 * [backup-simplify]: Simplify 0 into 0
9.735 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.737 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.737 * [backup-simplify]: Simplify 0 into 0
9.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.739 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.739 * [backup-simplify]: Simplify 0 into 0
9.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.741 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.741 * [backup-simplify]: Simplify 0 into 0
9.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.744 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.744 * [backup-simplify]: Simplify 0 into 0
9.745 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
9.745 * * * * [progress]: [ 3 / 3 ] generating series at (2)
9.746 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
9.746 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (n k) around 0
9.746 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
9.746 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
9.746 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
9.746 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
9.746 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
9.746 * [taylor]: Taking taylor expansion of 1/2 in k
9.746 * [backup-simplify]: Simplify 1/2 into 1/2
9.746 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.746 * [taylor]: Taking taylor expansion of 1 in k
9.746 * [backup-simplify]: Simplify 1 into 1
9.746 * [taylor]: Taking taylor expansion of k in k
9.746 * [backup-simplify]: Simplify 0 into 0
9.746 * [backup-simplify]: Simplify 1 into 1
9.746 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.746 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.746 * [taylor]: Taking taylor expansion of 2 in k
9.746 * [backup-simplify]: Simplify 2 into 2
9.746 * [taylor]: Taking taylor expansion of (* n PI) in k
9.746 * [taylor]: Taking taylor expansion of n in k
9.746 * [backup-simplify]: Simplify n into n
9.746 * [taylor]: Taking taylor expansion of PI in k
9.746 * [backup-simplify]: Simplify PI into PI
9.746 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.746 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.746 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.747 * [backup-simplify]: Simplify (- 0) into 0
9.747 * [backup-simplify]: Simplify (+ 1 0) into 1
9.748 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.748 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.748 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.748 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.748 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.748 * [taylor]: Taking taylor expansion of k in k
9.748 * [backup-simplify]: Simplify 0 into 0
9.748 * [backup-simplify]: Simplify 1 into 1
9.749 * [backup-simplify]: Simplify (/ 1 1) into 1
9.749 * [backup-simplify]: Simplify (sqrt 0) into 0
9.751 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.751 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
9.751 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
9.751 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
9.751 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
9.751 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.751 * [taylor]: Taking taylor expansion of 1/2 in n
9.751 * [backup-simplify]: Simplify 1/2 into 1/2
9.751 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.751 * [taylor]: Taking taylor expansion of 1 in n
9.751 * [backup-simplify]: Simplify 1 into 1
9.751 * [taylor]: Taking taylor expansion of k in n
9.751 * [backup-simplify]: Simplify k into k
9.751 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.751 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.751 * [taylor]: Taking taylor expansion of 2 in n
9.751 * [backup-simplify]: Simplify 2 into 2
9.751 * [taylor]: Taking taylor expansion of (* n PI) in n
9.751 * [taylor]: Taking taylor expansion of n in n
9.751 * [backup-simplify]: Simplify 0 into 0
9.751 * [backup-simplify]: Simplify 1 into 1
9.751 * [taylor]: Taking taylor expansion of PI in n
9.751 * [backup-simplify]: Simplify PI into PI
9.752 * [backup-simplify]: Simplify (* 0 PI) into 0
9.752 * [backup-simplify]: Simplify (* 2 0) into 0
9.753 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.755 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.756 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.756 * [backup-simplify]: Simplify (- k) into (- k)
9.756 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.756 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.758 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.759 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
9.760 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
9.760 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
9.760 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.760 * [taylor]: Taking taylor expansion of k in n
9.760 * [backup-simplify]: Simplify k into k
9.760 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.760 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
9.760 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.760 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
9.760 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
9.760 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
9.760 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
9.760 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
9.760 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
9.760 * [taylor]: Taking taylor expansion of 1/2 in n
9.760 * [backup-simplify]: Simplify 1/2 into 1/2
9.760 * [taylor]: Taking taylor expansion of (- 1 k) in n
9.761 * [taylor]: Taking taylor expansion of 1 in n
9.761 * [backup-simplify]: Simplify 1 into 1
9.761 * [taylor]: Taking taylor expansion of k in n
9.761 * [backup-simplify]: Simplify k into k
9.761 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.761 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.761 * [taylor]: Taking taylor expansion of 2 in n
9.761 * [backup-simplify]: Simplify 2 into 2
9.761 * [taylor]: Taking taylor expansion of (* n PI) in n
9.761 * [taylor]: Taking taylor expansion of n in n
9.761 * [backup-simplify]: Simplify 0 into 0
9.761 * [backup-simplify]: Simplify 1 into 1
9.761 * [taylor]: Taking taylor expansion of PI in n
9.761 * [backup-simplify]: Simplify PI into PI
9.761 * [backup-simplify]: Simplify (* 0 PI) into 0
9.762 * [backup-simplify]: Simplify (* 2 0) into 0
9.763 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.765 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.766 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.766 * [backup-simplify]: Simplify (- k) into (- k)
9.766 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
9.766 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
9.767 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.769 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
9.770 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
9.770 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
9.770 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.770 * [taylor]: Taking taylor expansion of k in n
9.770 * [backup-simplify]: Simplify k into k
9.770 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.770 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
9.770 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.770 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
9.772 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
9.772 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
9.772 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
9.772 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
9.772 * [taylor]: Taking taylor expansion of 1/2 in k
9.772 * [backup-simplify]: Simplify 1/2 into 1/2
9.772 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
9.772 * [taylor]: Taking taylor expansion of (- 1 k) in k
9.772 * [taylor]: Taking taylor expansion of 1 in k
9.772 * [backup-simplify]: Simplify 1 into 1
9.772 * [taylor]: Taking taylor expansion of k in k
9.772 * [backup-simplify]: Simplify 0 into 0
9.772 * [backup-simplify]: Simplify 1 into 1
9.772 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
9.772 * [taylor]: Taking taylor expansion of (log n) in k
9.772 * [taylor]: Taking taylor expansion of n in k
9.772 * [backup-simplify]: Simplify n into n
9.772 * [backup-simplify]: Simplify (log n) into (log n)
9.772 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.772 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.772 * [taylor]: Taking taylor expansion of 2 in k
9.772 * [backup-simplify]: Simplify 2 into 2
9.772 * [taylor]: Taking taylor expansion of PI in k
9.772 * [backup-simplify]: Simplify PI into PI
9.773 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.774 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.774 * [backup-simplify]: Simplify (- 0) into 0
9.775 * [backup-simplify]: Simplify (+ 1 0) into 1
9.776 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.777 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
9.778 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
9.779 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.779 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
9.779 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.779 * [taylor]: Taking taylor expansion of k in k
9.779 * [backup-simplify]: Simplify 0 into 0
9.779 * [backup-simplify]: Simplify 1 into 1
9.779 * [backup-simplify]: Simplify (/ 1 1) into 1
9.780 * [backup-simplify]: Simplify (sqrt 0) into 0
9.781 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.782 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
9.782 * [backup-simplify]: Simplify 0 into 0
9.783 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.784 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.786 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.786 * [backup-simplify]: Simplify (- 0) into 0
9.787 * [backup-simplify]: Simplify (+ 0 0) into 0
9.787 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
9.789 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.790 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
9.792 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.793 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
9.793 * [taylor]: Taking taylor expansion of 0 in k
9.793 * [backup-simplify]: Simplify 0 into 0
9.794 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.795 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.796 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.797 * [backup-simplify]: Simplify (+ 0 0) into 0
9.797 * [backup-simplify]: Simplify (- 1) into -1
9.798 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.799 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
9.801 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
9.804 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.808 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.809 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.809 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.810 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
9.811 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.812 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.816 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.816 * [backup-simplify]: Simplify (- 0) into 0
9.816 * [backup-simplify]: Simplify (+ 0 0) into 0
9.817 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
9.819 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.820 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.823 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.824 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
9.825 * [taylor]: Taking taylor expansion of 0 in k
9.825 * [backup-simplify]: Simplify 0 into 0
9.825 * [backup-simplify]: Simplify 0 into 0
9.826 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
9.828 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.829 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.829 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.831 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.831 * [backup-simplify]: Simplify (+ 0 0) into 0
9.832 * [backup-simplify]: Simplify (- 0) into 0
9.832 * [backup-simplify]: Simplify (+ 0 0) into 0
9.835 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.836 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.838 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.844 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
9.846 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
9.846 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.847 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
9.848 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.849 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
9.852 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.852 * [backup-simplify]: Simplify (- 0) into 0
9.852 * [backup-simplify]: Simplify (+ 0 0) into 0
9.853 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
9.854 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.855 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
9.858 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.860 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
9.860 * [taylor]: Taking taylor expansion of 0 in k
9.860 * [backup-simplify]: Simplify 0 into 0
9.860 * [backup-simplify]: Simplify 0 into 0
9.860 * [backup-simplify]: Simplify 0 into 0
9.861 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.865 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.867 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
9.869 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.874 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.875 * [backup-simplify]: Simplify (+ 0 0) into 0
9.875 * [backup-simplify]: Simplify (- 0) into 0
9.876 * [backup-simplify]: Simplify (+ 0 0) into 0
9.878 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
9.881 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
9.887 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.905 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
9.916 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
9.935 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
9.936 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
9.936 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (n k) around 0
9.936 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
9.936 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
9.936 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.936 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.936 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
9.936 * [taylor]: Taking taylor expansion of 1/2 in k
9.936 * [backup-simplify]: Simplify 1/2 into 1/2
9.936 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.936 * [taylor]: Taking taylor expansion of 1 in k
9.936 * [backup-simplify]: Simplify 1 into 1
9.936 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.936 * [taylor]: Taking taylor expansion of k in k
9.936 * [backup-simplify]: Simplify 0 into 0
9.936 * [backup-simplify]: Simplify 1 into 1
9.937 * [backup-simplify]: Simplify (/ 1 1) into 1
9.937 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.937 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.937 * [taylor]: Taking taylor expansion of 2 in k
9.937 * [backup-simplify]: Simplify 2 into 2
9.937 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.937 * [taylor]: Taking taylor expansion of PI in k
9.937 * [backup-simplify]: Simplify PI into PI
9.937 * [taylor]: Taking taylor expansion of n in k
9.937 * [backup-simplify]: Simplify n into n
9.937 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.937 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.937 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.938 * [backup-simplify]: Simplify (- 1) into -1
9.938 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.939 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
9.939 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.939 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
9.939 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.939 * [taylor]: Taking taylor expansion of k in k
9.939 * [backup-simplify]: Simplify 0 into 0
9.939 * [backup-simplify]: Simplify 1 into 1
9.939 * [backup-simplify]: Simplify (sqrt 0) into 0
9.941 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.941 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
9.941 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
9.941 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.941 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.941 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.941 * [taylor]: Taking taylor expansion of 1/2 in n
9.941 * [backup-simplify]: Simplify 1/2 into 1/2
9.941 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.941 * [taylor]: Taking taylor expansion of 1 in n
9.941 * [backup-simplify]: Simplify 1 into 1
9.941 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.941 * [taylor]: Taking taylor expansion of k in n
9.941 * [backup-simplify]: Simplify k into k
9.942 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.942 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.942 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.942 * [taylor]: Taking taylor expansion of 2 in n
9.942 * [backup-simplify]: Simplify 2 into 2
9.942 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.942 * [taylor]: Taking taylor expansion of PI in n
9.942 * [backup-simplify]: Simplify PI into PI
9.942 * [taylor]: Taking taylor expansion of n in n
9.942 * [backup-simplify]: Simplify 0 into 0
9.942 * [backup-simplify]: Simplify 1 into 1
9.942 * [backup-simplify]: Simplify (/ PI 1) into PI
9.943 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.944 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.944 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.944 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.944 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.945 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.946 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
9.948 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.948 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.948 * [taylor]: Taking taylor expansion of k in n
9.948 * [backup-simplify]: Simplify k into k
9.948 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.948 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.948 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
9.948 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
9.948 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.948 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.948 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
9.948 * [taylor]: Taking taylor expansion of 1/2 in n
9.948 * [backup-simplify]: Simplify 1/2 into 1/2
9.948 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
9.948 * [taylor]: Taking taylor expansion of 1 in n
9.948 * [backup-simplify]: Simplify 1 into 1
9.948 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.948 * [taylor]: Taking taylor expansion of k in n
9.948 * [backup-simplify]: Simplify k into k
9.948 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.948 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.948 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.948 * [taylor]: Taking taylor expansion of 2 in n
9.948 * [backup-simplify]: Simplify 2 into 2
9.949 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.949 * [taylor]: Taking taylor expansion of PI in n
9.949 * [backup-simplify]: Simplify PI into PI
9.949 * [taylor]: Taking taylor expansion of n in n
9.949 * [backup-simplify]: Simplify 0 into 0
9.949 * [backup-simplify]: Simplify 1 into 1
9.949 * [backup-simplify]: Simplify (/ PI 1) into PI
9.950 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.951 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.951 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.951 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
9.951 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
9.952 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.953 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
9.957 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.957 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.957 * [taylor]: Taking taylor expansion of k in n
9.957 * [backup-simplify]: Simplify k into k
9.957 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.957 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.959 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
9.959 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
9.959 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
9.959 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
9.959 * [taylor]: Taking taylor expansion of 1/2 in k
9.959 * [backup-simplify]: Simplify 1/2 into 1/2
9.959 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
9.959 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
9.959 * [taylor]: Taking taylor expansion of 1 in k
9.959 * [backup-simplify]: Simplify 1 into 1
9.959 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.959 * [taylor]: Taking taylor expansion of k in k
9.959 * [backup-simplify]: Simplify 0 into 0
9.959 * [backup-simplify]: Simplify 1 into 1
9.959 * [backup-simplify]: Simplify (/ 1 1) into 1
9.959 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
9.959 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.959 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.959 * [taylor]: Taking taylor expansion of 2 in k
9.959 * [backup-simplify]: Simplify 2 into 2
9.959 * [taylor]: Taking taylor expansion of PI in k
9.959 * [backup-simplify]: Simplify PI into PI
9.960 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.961 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.961 * [taylor]: Taking taylor expansion of (log n) in k
9.961 * [taylor]: Taking taylor expansion of n in k
9.961 * [backup-simplify]: Simplify n into n
9.961 * [backup-simplify]: Simplify (log n) into (log n)
9.961 * [backup-simplify]: Simplify (- 1) into -1
9.962 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.962 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.963 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
9.964 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
9.965 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
9.966 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
9.966 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.966 * [taylor]: Taking taylor expansion of k in k
9.966 * [backup-simplify]: Simplify 0 into 0
9.966 * [backup-simplify]: Simplify 1 into 1
9.966 * [backup-simplify]: Simplify (sqrt 0) into 0
9.968 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.969 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
9.969 * [backup-simplify]: Simplify 0 into 0
9.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.970 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.971 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.972 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.972 * [backup-simplify]: Simplify (- 0) into 0
9.972 * [backup-simplify]: Simplify (+ 0 0) into 0
9.972 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
9.973 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.974 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.975 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.976 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
9.976 * [taylor]: Taking taylor expansion of 0 in k
9.976 * [backup-simplify]: Simplify 0 into 0
9.976 * [backup-simplify]: Simplify 0 into 0
9.977 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.977 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.978 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
9.978 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.979 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.981 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.981 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.981 * [backup-simplify]: Simplify (- 0) into 0
9.982 * [backup-simplify]: Simplify (+ 0 0) into 0
9.982 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
9.983 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.984 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
9.986 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.987 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
9.987 * [taylor]: Taking taylor expansion of 0 in k
9.987 * [backup-simplify]: Simplify 0 into 0
9.987 * [backup-simplify]: Simplify 0 into 0
9.987 * [backup-simplify]: Simplify 0 into 0
9.989 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.990 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.991 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
9.991 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
9.992 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.993 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.996 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.996 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.996 * [backup-simplify]: Simplify (- 0) into 0
9.996 * [backup-simplify]: Simplify (+ 0 0) into 0
9.997 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
9.998 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.000 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
10.003 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
10.005 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
10.005 * [taylor]: Taking taylor expansion of 0 in k
10.005 * [backup-simplify]: Simplify 0 into 0
10.005 * [backup-simplify]: Simplify 0 into 0
10.005 * [backup-simplify]: Simplify 0 into 0
10.005 * [backup-simplify]: Simplify 0 into 0
10.009 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
10.011 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
10.012 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
10.017 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
10.017 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
10.017 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0
10.018 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
10.018 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
10.018 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
10.018 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
10.018 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
10.018 * [taylor]: Taking taylor expansion of 1/2 in k
10.018 * [backup-simplify]: Simplify 1/2 into 1/2
10.018 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
10.018 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.018 * [taylor]: Taking taylor expansion of k in k
10.018 * [backup-simplify]: Simplify 0 into 0
10.018 * [backup-simplify]: Simplify 1 into 1
10.018 * [backup-simplify]: Simplify (/ 1 1) into 1
10.018 * [taylor]: Taking taylor expansion of 1 in k
10.018 * [backup-simplify]: Simplify 1 into 1
10.018 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
10.018 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
10.018 * [taylor]: Taking taylor expansion of -2 in k
10.018 * [backup-simplify]: Simplify -2 into -2
10.018 * [taylor]: Taking taylor expansion of (/ PI n) in k
10.018 * [taylor]: Taking taylor expansion of PI in k
10.019 * [backup-simplify]: Simplify PI into PI
10.019 * [taylor]: Taking taylor expansion of n in k
10.019 * [backup-simplify]: Simplify n into n
10.019 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
10.019 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
10.019 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
10.019 * [backup-simplify]: Simplify (+ 1 0) into 1
10.020 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
10.020 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
10.020 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
10.020 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
10.020 * [taylor]: Taking taylor expansion of (/ -1 k) in k
10.020 * [taylor]: Taking taylor expansion of -1 in k
10.020 * [backup-simplify]: Simplify -1 into -1
10.020 * [taylor]: Taking taylor expansion of k in k
10.020 * [backup-simplify]: Simplify 0 into 0
10.020 * [backup-simplify]: Simplify 1 into 1
10.021 * [backup-simplify]: Simplify (/ -1 1) into -1
10.021 * [backup-simplify]: Simplify (sqrt 0) into 0
10.022 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
10.023 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
10.023 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
10.023 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
10.023 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
10.023 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
10.023 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
10.023 * [taylor]: Taking taylor expansion of 1/2 in n
10.023 * [backup-simplify]: Simplify 1/2 into 1/2
10.023 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
10.023 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.023 * [taylor]: Taking taylor expansion of k in n
10.023 * [backup-simplify]: Simplify k into k
10.023 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.023 * [taylor]: Taking taylor expansion of 1 in n
10.023 * [backup-simplify]: Simplify 1 into 1
10.023 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
10.023 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.023 * [taylor]: Taking taylor expansion of -2 in n
10.023 * [backup-simplify]: Simplify -2 into -2
10.023 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.023 * [taylor]: Taking taylor expansion of PI in n
10.023 * [backup-simplify]: Simplify PI into PI
10.023 * [taylor]: Taking taylor expansion of n in n
10.023 * [backup-simplify]: Simplify 0 into 0
10.023 * [backup-simplify]: Simplify 1 into 1
10.024 * [backup-simplify]: Simplify (/ PI 1) into PI
10.024 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.025 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.026 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
10.026 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
10.027 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.028 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
10.029 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.029 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
10.029 * [taylor]: Taking taylor expansion of (/ -1 k) in n
10.029 * [taylor]: Taking taylor expansion of -1 in n
10.029 * [backup-simplify]: Simplify -1 into -1
10.030 * [taylor]: Taking taylor expansion of k in n
10.030 * [backup-simplify]: Simplify k into k
10.030 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
10.030 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
10.030 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
10.030 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
10.031 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
10.031 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
10.031 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
10.031 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
10.031 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
10.031 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
10.031 * [taylor]: Taking taylor expansion of 1/2 in n
10.031 * [backup-simplify]: Simplify 1/2 into 1/2
10.031 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
10.031 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.031 * [taylor]: Taking taylor expansion of k in n
10.031 * [backup-simplify]: Simplify k into k
10.032 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.032 * [taylor]: Taking taylor expansion of 1 in n
10.032 * [backup-simplify]: Simplify 1 into 1
10.032 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
10.032 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
10.032 * [taylor]: Taking taylor expansion of -2 in n
10.032 * [backup-simplify]: Simplify -2 into -2
10.032 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.032 * [taylor]: Taking taylor expansion of PI in n
10.032 * [backup-simplify]: Simplify PI into PI
10.032 * [taylor]: Taking taylor expansion of n in n
10.032 * [backup-simplify]: Simplify 0 into 0
10.032 * [backup-simplify]: Simplify 1 into 1
10.032 * [backup-simplify]: Simplify (/ PI 1) into PI
10.033 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.034 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.034 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
10.034 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
10.035 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.036 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
10.036 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.036 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
10.036 * [taylor]: Taking taylor expansion of (/ -1 k) in n
10.036 * [taylor]: Taking taylor expansion of -1 in n
10.037 * [backup-simplify]: Simplify -1 into -1
10.037 * [taylor]: Taking taylor expansion of k in n
10.037 * [backup-simplify]: Simplify k into k
10.037 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
10.037 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
10.037 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
10.037 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
10.037 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
10.038 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
10.038 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
10.038 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
10.038 * [taylor]: Taking taylor expansion of 1/2 in k
10.038 * [backup-simplify]: Simplify 1/2 into 1/2
10.038 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
10.038 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
10.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.038 * [taylor]: Taking taylor expansion of k in k
10.038 * [backup-simplify]: Simplify 0 into 0
10.038 * [backup-simplify]: Simplify 1 into 1
10.038 * [backup-simplify]: Simplify (/ 1 1) into 1
10.038 * [taylor]: Taking taylor expansion of 1 in k
10.038 * [backup-simplify]: Simplify 1 into 1
10.038 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
10.038 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
10.038 * [taylor]: Taking taylor expansion of (* -2 PI) in k
10.038 * [taylor]: Taking taylor expansion of -2 in k
10.038 * [backup-simplify]: Simplify -2 into -2
10.038 * [taylor]: Taking taylor expansion of PI in k
10.038 * [backup-simplify]: Simplify PI into PI
10.038 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
10.039 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
10.039 * [taylor]: Taking taylor expansion of (log n) in k
10.039 * [taylor]: Taking taylor expansion of n in k
10.039 * [backup-simplify]: Simplify n into n
10.039 * [backup-simplify]: Simplify (log n) into (log n)
10.039 * [backup-simplify]: Simplify (+ 1 0) into 1
10.039 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
10.040 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
10.041 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
10.041 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
10.042 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
10.042 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
10.042 * [taylor]: Taking taylor expansion of (/ -1 k) in k
10.042 * [taylor]: Taking taylor expansion of -1 in k
10.042 * [backup-simplify]: Simplify -1 into -1
10.042 * [taylor]: Taking taylor expansion of k in k
10.042 * [backup-simplify]: Simplify 0 into 0
10.042 * [backup-simplify]: Simplify 1 into 1
10.043 * [backup-simplify]: Simplify (/ -1 1) into -1
10.043 * [backup-simplify]: Simplify (sqrt 0) into 0
10.044 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
10.044 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
10.045 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
10.046 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
10.046 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
10.047 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
10.047 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
10.047 * [backup-simplify]: Simplify (+ 0 0) into 0
10.048 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
10.049 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.049 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
10.051 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
10.051 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
10.051 * [taylor]: Taking taylor expansion of 0 in k
10.051 * [backup-simplify]: Simplify 0 into 0
10.051 * [backup-simplify]: Simplify 0 into 0
10.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
10.054 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
10.055 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.056 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.057 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.057 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
10.059 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
10.059 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
10.060 * [backup-simplify]: Simplify (+ 0 0) into 0
10.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
10.061 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
10.062 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
10.065 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
10.066 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
10.066 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
10.067 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
10.067 * [taylor]: Taking taylor expansion of 0 in k
10.067 * [backup-simplify]: Simplify 0 into 0
10.068 * [backup-simplify]: Simplify 0 into 0
10.068 * [backup-simplify]: Simplify 0 into 0
10.069 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.073 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
10.076 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.077 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
10.081 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
10.081 * * * [progress]: simplifying candidates
10.081 * * * * [progress]: [ 1 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
10.082 * * * * [progress]: [ 2 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
10.082 * * * * [progress]: [ 3 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 4 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 5 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 6 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 7 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 8 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 9 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 10 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 11 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 12 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 13 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 14 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (sqrt k)))>
10.082 * * * * [progress]: [ 15 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (sqrt k)))>
10.083 * * * * [progress]: [ 16 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 17 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 18 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (sqrt k)))>
10.083 * * * * [progress]: [ 19 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 20 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 21 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
10.083 * * * * [progress]: [ 22 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 23 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 24 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (sqrt k)))>
10.083 * * * * [progress]: [ 25 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 26 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 27 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k)))>
10.083 * * * * [progress]: [ 28 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 29 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
10.083 * * * * [progress]: [ 30 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
10.084 * * * * [progress]: [ 31 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
10.084 * * * * [progress]: [ 32 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1 k)) (/ 1 2)) (sqrt k)))>
10.084 * * * * [progress]: [ 33 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)))>
10.084 * * * * [progress]: [ 34 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
10.084 * * * * [progress]: [ 35 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
10.084 * * * * [progress]: [ 36 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
10.084 * * * * [progress]: [ 37 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
10.084 * * * * [progress]: [ 38 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
10.084 * * * * [progress]: [ 39 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
10.084 * * * * [progress]: [ 40 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))>
10.084 * * * * [progress]: [ 41 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
10.084 * * * * [progress]: [ 42 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
10.084 * * * * [progress]: [ 43 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.084 * * * * [progress]: [ 44 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.084 * * * * [progress]: [ 45 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
10.084 * * * * [progress]: [ 46 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 47 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 48 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 49 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 50 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 51 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 52 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 53 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 54 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 55 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 56 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 57 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 58 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 59 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 60 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 61 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
10.085 * * * * [progress]: [ 62 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
10.086 * * * * [progress]: [ 63 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))>
10.086 * * * * [progress]: [ 64 / 133 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
10.086 * * * * [progress]: [ 65 / 133 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
10.086 * * * * [progress]: [ 66 / 133 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) 1))>
10.086 * * * * [progress]: [ 67 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
10.086 * * * * [progress]: [ 68 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
10.086 * * * * [progress]: [ 69 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
10.086 * * * * [progress]: [ 70 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
10.086 * * * * [progress]: [ 71 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))))>
10.086 * * * * [progress]: [ 72 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
10.086 * * * * [progress]: [ 73 / 133 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
10.086 * * * * [progress]: [ 74 / 133 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
10.086 * * * * [progress]: [ 75 / 133 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
10.086 * * * * [progress]: [ 76 / 133 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
10.086 * * * * [progress]: [ 77 / 133 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
10.086 * * * * [progress]: [ 78 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- (sqrt k))))>
10.087 * * * * [progress]: [ 79 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
10.087 * * * * [progress]: [ 80 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
10.087 * * * * [progress]: [ 81 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
10.087 * * * * [progress]: [ 82 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
10.087 * * * * [progress]: [ 83 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
10.087 * * * * [progress]: [ 84 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
10.087 * * * * [progress]: [ 85 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
10.087 * * * * [progress]: [ 86 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
10.087 * * * * [progress]: [ 87 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
10.087 * * * * [progress]: [ 88 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
10.087 * * * * [progress]: [ 89 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
10.087 * * * * [progress]: [ 90 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
10.087 * * * * [progress]: [ 91 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
10.087 * * * * [progress]: [ 92 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
10.087 * * * * [progress]: [ 93 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
10.088 * * * * [progress]: [ 94 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
10.088 * * * * [progress]: [ 95 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
10.088 * * * * [progress]: [ 96 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
10.088 * * * * [progress]: [ 97 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
10.088 * * * * [progress]: [ 98 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
10.088 * * * * [progress]: [ 99 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
10.088 * * * * [progress]: [ 100 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))>
10.088 * * * * [progress]: [ 101 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
10.088 * * * * [progress]: [ 102 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))>
10.088 * * * * [progress]: [ 103 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))>
10.088 * * * * [progress]: [ 104 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))>
10.088 * * * * [progress]: [ 105 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
10.088 * * * * [progress]: [ 106 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
10.088 * * * * [progress]: [ 107 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
10.088 * * * * [progress]: [ 108 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
10.089 * * * * [progress]: [ 109 / 133 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))>
10.089 * * * * [progress]: [ 110 / 133 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
10.089 * * * * [progress]: [ 111 / 133 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
10.089 * * * * [progress]: [ 112 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
10.089 * * * * [progress]: [ 113 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
10.089 * * * * [progress]: [ 114 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
10.089 * * * * [progress]: [ 115 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt 1)) (sqrt k)))>
10.089 * * * * [progress]: [ 116 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
10.089 * * * * [progress]: [ 117 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
10.089 * * * * [progress]: [ 118 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))))>
10.089 * * * * [progress]: [ 119 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
10.089 * * * * [progress]: [ 120 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
10.089 * * * * [progress]: [ 121 / 133 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
10.089 * * * * [progress]: [ 122 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
10.089 * * * * [progress]: [ 123 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))>
10.089 * * * * [progress]: [ 124 / 133 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
10.089 * * * * [progress]: [ 125 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
10.090 * * * * [progress]: [ 126 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))>
10.090 * * * * [progress]: [ 127 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))>
10.090 * * * * [progress]: [ 128 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
10.090 * * * * [progress]: [ 129 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
10.090 * * * * [progress]: [ 130 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
10.090 * * * * [progress]: [ 131 / 133 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
10.090 * * * * [progress]: [ 132 / 133 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
10.090 * * * * [progress]: [ 133 / 133 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
10.091 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* n (* 2 PI)) (/ 1 2))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (expm1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))
  (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) 1)
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1)
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1)
  (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))
  (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))
  (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
10.094 * * [simplify]: iteration 1: (293 enodes)
10.185 * * [simplify]: iteration 2: (750 enodes)
10.856 * * [simplify]: Extracting #0: cost 104 inf + 0
10.857 * * [simplify]: Extracting #1: cost 390 inf + 1
10.860 * * [simplify]: Extracting #2: cost 619 inf + 13948
10.882 * * [simplify]: Extracting #3: cost 490 inf + 93598
10.928 * * [simplify]: Extracting #4: cost 251 inf + 187121
11.004 * * [simplify]: Extracting #5: cost 129 inf + 248241
11.056 * * [simplify]: Extracting #6: cost 101 inf + 264444
11.111 * * [simplify]: Extracting #7: cost 68 inf + 282859
11.176 * * [simplify]: Extracting #8: cost 38 inf + 304737
11.293 * * [simplify]: Extracting #9: cost 8 inf + 322136
11.415 * * [simplify]: Extracting #10: cost 0 inf + 326645
11.502 * * [simplify]: Extracting #11: cost 0 inf + 326525
11.572 * [simplify]: Simplified to:
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* PI 2) (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (expm1 (* (* PI 2) n))
  (log1p (* (* PI 2) n))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* (* n n) n) (* 8 (* (* PI PI) PI)))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* 2 (* PI (cbrt n)))
  (* 2 (* PI (sqrt n)))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (expm1 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (/ (/ (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3) k) (sqrt k))
  (* (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (* (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow n (/ (- 1 k) 2))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow n (/ (- 1 k) 2))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (* (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (* (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (fabs (cbrt k))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (* (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (* (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 8)) (cbrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 8)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k))
  (real->posit16 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (+ (* -1/2 (* k (+ (* (log n) (sqrt (* (* PI 2) n))) (* (sqrt (* (* PI 2) n)) (log (* PI 2)))))) (fma (* (log (* PI 2)) 1/4) (* (* (sqrt (* (* PI 2) n)) (log n)) (* k k)) (fma (* 1/8 (sqrt (* (* PI 2) n))) (* (* (* k k) (log n)) (log n)) (fma (* (* k k) (* (log (* PI 2)) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))) 1/8 (sqrt (* (* PI 2) n))))))
  (exp (* (* 1/2 (- 1 k)) (log (* (* PI 2) n))))
  (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (- (- (* (* (* (log (* PI 2)) +nan.0) (* (* k k) (log n))) (sqrt (* (* PI 2) n))) (+ (- (* +nan.0 (* (* (* k k) (sqrt (* (* PI 2) n))) (log (* PI 2)))) (* (* (* k (log n)) (* k (log n))) (* (sqrt (* (* PI 2) n)) +nan.0))) (+ (- (* +nan.0 (* k (sqrt (* (* PI 2) n)))) (* (sqrt (* (* PI 2) n)) +nan.0)) (- (* (* (* k k) (* (log (* PI 2)) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))) +nan.0) (+ (- (* (sqrt (* (* PI 2) n)) (* (* (* k k) (log n)) +nan.0)) (* (* (sqrt (* (* PI 2) n)) +nan.0) (* k k))) (- (* (log (* PI 2)) (* +nan.0 (* k (sqrt (* (* PI 2) n))))) (* (* (log n) (sqrt (* (* PI 2) n))) (* k +nan.0)))))))))
  (+ (* +nan.0 (- (/ (exp (* (* 1/2 (- 1 k)) (log (* (* PI 2) n)))) k))) (* +nan.0 (- (/ (exp (* (* 1/2 (- 1 k)) (log (* (* PI 2) n)))) (* k k)) (/ (/ (exp (* (* 1/2 (- 1 k)) (log (* (* PI 2) n)))) k) (* k k)))))
  (+ (- (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (/ k +nan.0))) (* +nan.0 (- (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))))))
11.581 * * * [progress]: adding candidates to table
12.969 * * [progress]: iteration 2 / 4
12.970 * * * [progress]: picking best candidate
13.009 * * * * [pick]: Picked  #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
13.009 * * * [progress]: localizing error
13.043 * * * [progress]: generating rewritten candidates
13.043 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
13.071 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1)
13.094 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
13.104 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
13.132 * * * [progress]: generating series expansions
13.132 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
13.133 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
13.133 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
13.133 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
13.133 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
13.133 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
13.133 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
13.133 * [taylor]: Taking taylor expansion of 1/2 in k
13.133 * [backup-simplify]: Simplify 1/2 into 1/2
13.133 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.133 * [taylor]: Taking taylor expansion of 1 in k
13.133 * [backup-simplify]: Simplify 1 into 1
13.133 * [taylor]: Taking taylor expansion of k in k
13.133 * [backup-simplify]: Simplify 0 into 0
13.134 * [backup-simplify]: Simplify 1 into 1
13.134 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.134 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.134 * [taylor]: Taking taylor expansion of 2 in k
13.134 * [backup-simplify]: Simplify 2 into 2
13.134 * [taylor]: Taking taylor expansion of (* n PI) in k
13.134 * [taylor]: Taking taylor expansion of n in k
13.134 * [backup-simplify]: Simplify n into n
13.134 * [taylor]: Taking taylor expansion of PI in k
13.134 * [backup-simplify]: Simplify PI into PI
13.134 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.134 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.134 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.134 * [backup-simplify]: Simplify (- 0) into 0
13.135 * [backup-simplify]: Simplify (+ 1 0) into 1
13.135 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.135 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
13.135 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
13.135 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
13.135 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
13.135 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
13.135 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
13.135 * [taylor]: Taking taylor expansion of 1/2 in n
13.135 * [backup-simplify]: Simplify 1/2 into 1/2
13.135 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.135 * [taylor]: Taking taylor expansion of 1 in n
13.135 * [backup-simplify]: Simplify 1 into 1
13.135 * [taylor]: Taking taylor expansion of k in n
13.135 * [backup-simplify]: Simplify k into k
13.135 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.135 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.135 * [taylor]: Taking taylor expansion of 2 in n
13.135 * [backup-simplify]: Simplify 2 into 2
13.135 * [taylor]: Taking taylor expansion of (* n PI) in n
13.135 * [taylor]: Taking taylor expansion of n in n
13.135 * [backup-simplify]: Simplify 0 into 0
13.135 * [backup-simplify]: Simplify 1 into 1
13.135 * [taylor]: Taking taylor expansion of PI in n
13.135 * [backup-simplify]: Simplify PI into PI
13.136 * [backup-simplify]: Simplify (* 0 PI) into 0
13.136 * [backup-simplify]: Simplify (* 2 0) into 0
13.137 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.138 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.138 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.138 * [backup-simplify]: Simplify (- k) into (- k)
13.138 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.138 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
13.139 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.140 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.141 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.141 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
13.141 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
13.141 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
13.141 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
13.141 * [taylor]: Taking taylor expansion of 1/2 in n
13.141 * [backup-simplify]: Simplify 1/2 into 1/2
13.141 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.141 * [taylor]: Taking taylor expansion of 1 in n
13.141 * [backup-simplify]: Simplify 1 into 1
13.141 * [taylor]: Taking taylor expansion of k in n
13.141 * [backup-simplify]: Simplify k into k
13.141 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.141 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.141 * [taylor]: Taking taylor expansion of 2 in n
13.141 * [backup-simplify]: Simplify 2 into 2
13.141 * [taylor]: Taking taylor expansion of (* n PI) in n
13.141 * [taylor]: Taking taylor expansion of n in n
13.141 * [backup-simplify]: Simplify 0 into 0
13.141 * [backup-simplify]: Simplify 1 into 1
13.141 * [taylor]: Taking taylor expansion of PI in n
13.141 * [backup-simplify]: Simplify PI into PI
13.141 * [backup-simplify]: Simplify (* 0 PI) into 0
13.141 * [backup-simplify]: Simplify (* 2 0) into 0
13.142 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.143 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.144 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.144 * [backup-simplify]: Simplify (- k) into (- k)
13.144 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.144 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
13.145 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.145 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.146 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.146 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
13.146 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
13.146 * [taylor]: Taking taylor expansion of 1/2 in k
13.146 * [backup-simplify]: Simplify 1/2 into 1/2
13.146 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
13.146 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.146 * [taylor]: Taking taylor expansion of 1 in k
13.146 * [backup-simplify]: Simplify 1 into 1
13.146 * [taylor]: Taking taylor expansion of k in k
13.146 * [backup-simplify]: Simplify 0 into 0
13.146 * [backup-simplify]: Simplify 1 into 1
13.146 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
13.146 * [taylor]: Taking taylor expansion of (log n) in k
13.146 * [taylor]: Taking taylor expansion of n in k
13.146 * [backup-simplify]: Simplify n into n
13.146 * [backup-simplify]: Simplify (log n) into (log n)
13.146 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.146 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.146 * [taylor]: Taking taylor expansion of 2 in k
13.146 * [backup-simplify]: Simplify 2 into 2
13.146 * [taylor]: Taking taylor expansion of PI in k
13.147 * [backup-simplify]: Simplify PI into PI
13.147 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.147 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.148 * [backup-simplify]: Simplify (- 0) into 0
13.148 * [backup-simplify]: Simplify (+ 1 0) into 1
13.148 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.149 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
13.150 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
13.151 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
13.151 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
13.152 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.152 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.153 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.154 * [backup-simplify]: Simplify (- 0) into 0
13.154 * [backup-simplify]: Simplify (+ 0 0) into 0
13.154 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
13.155 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.156 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
13.157 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.157 * [taylor]: Taking taylor expansion of 0 in k
13.157 * [backup-simplify]: Simplify 0 into 0
13.157 * [backup-simplify]: Simplify 0 into 0
13.157 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.158 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.159 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.159 * [backup-simplify]: Simplify (+ 0 0) into 0
13.159 * [backup-simplify]: Simplify (- 1) into -1
13.160 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.161 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
13.166 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
13.170 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
13.173 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
13.174 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.175 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.179 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.179 * [backup-simplify]: Simplify (- 0) into 0
13.179 * [backup-simplify]: Simplify (+ 0 0) into 0
13.180 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
13.182 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.183 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.184 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.184 * [taylor]: Taking taylor expansion of 0 in k
13.184 * [backup-simplify]: Simplify 0 into 0
13.184 * [backup-simplify]: Simplify 0 into 0
13.184 * [backup-simplify]: Simplify 0 into 0
13.185 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.186 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.188 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.188 * [backup-simplify]: Simplify (+ 0 0) into 0
13.188 * [backup-simplify]: Simplify (- 0) into 0
13.188 * [backup-simplify]: Simplify (+ 0 0) into 0
13.189 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.191 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.193 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
13.196 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
13.201 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
13.202 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
13.202 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
13.202 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
13.202 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.202 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.202 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
13.202 * [taylor]: Taking taylor expansion of 1/2 in k
13.202 * [backup-simplify]: Simplify 1/2 into 1/2
13.202 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.202 * [taylor]: Taking taylor expansion of 1 in k
13.202 * [backup-simplify]: Simplify 1 into 1
13.202 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.202 * [taylor]: Taking taylor expansion of k in k
13.202 * [backup-simplify]: Simplify 0 into 0
13.202 * [backup-simplify]: Simplify 1 into 1
13.202 * [backup-simplify]: Simplify (/ 1 1) into 1
13.202 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.202 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.202 * [taylor]: Taking taylor expansion of 2 in k
13.203 * [backup-simplify]: Simplify 2 into 2
13.203 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.203 * [taylor]: Taking taylor expansion of PI in k
13.203 * [backup-simplify]: Simplify PI into PI
13.203 * [taylor]: Taking taylor expansion of n in k
13.203 * [backup-simplify]: Simplify n into n
13.203 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.203 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.203 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.203 * [backup-simplify]: Simplify (- 1) into -1
13.203 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.204 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
13.204 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
13.204 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
13.204 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
13.204 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.204 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.204 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
13.204 * [taylor]: Taking taylor expansion of 1/2 in n
13.204 * [backup-simplify]: Simplify 1/2 into 1/2
13.204 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.204 * [taylor]: Taking taylor expansion of 1 in n
13.204 * [backup-simplify]: Simplify 1 into 1
13.204 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.204 * [taylor]: Taking taylor expansion of k in n
13.204 * [backup-simplify]: Simplify k into k
13.204 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.204 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.204 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.204 * [taylor]: Taking taylor expansion of 2 in n
13.204 * [backup-simplify]: Simplify 2 into 2
13.204 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.204 * [taylor]: Taking taylor expansion of PI in n
13.204 * [backup-simplify]: Simplify PI into PI
13.204 * [taylor]: Taking taylor expansion of n in n
13.204 * [backup-simplify]: Simplify 0 into 0
13.204 * [backup-simplify]: Simplify 1 into 1
13.204 * [backup-simplify]: Simplify (/ PI 1) into PI
13.205 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.205 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.205 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.205 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.205 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
13.206 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.207 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.208 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.208 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
13.208 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.208 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.208 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
13.208 * [taylor]: Taking taylor expansion of 1/2 in n
13.208 * [backup-simplify]: Simplify 1/2 into 1/2
13.208 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.208 * [taylor]: Taking taylor expansion of 1 in n
13.208 * [backup-simplify]: Simplify 1 into 1
13.208 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.208 * [taylor]: Taking taylor expansion of k in n
13.208 * [backup-simplify]: Simplify k into k
13.208 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.208 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.208 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.208 * [taylor]: Taking taylor expansion of 2 in n
13.208 * [backup-simplify]: Simplify 2 into 2
13.208 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.208 * [taylor]: Taking taylor expansion of PI in n
13.208 * [backup-simplify]: Simplify PI into PI
13.208 * [taylor]: Taking taylor expansion of n in n
13.208 * [backup-simplify]: Simplify 0 into 0
13.208 * [backup-simplify]: Simplify 1 into 1
13.208 * [backup-simplify]: Simplify (/ PI 1) into PI
13.209 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.209 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.209 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.209 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.209 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
13.210 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.211 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.212 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.213 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
13.213 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
13.213 * [taylor]: Taking taylor expansion of 1/2 in k
13.213 * [backup-simplify]: Simplify 1/2 into 1/2
13.213 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
13.213 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.213 * [taylor]: Taking taylor expansion of 1 in k
13.213 * [backup-simplify]: Simplify 1 into 1
13.213 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.213 * [taylor]: Taking taylor expansion of k in k
13.213 * [backup-simplify]: Simplify 0 into 0
13.213 * [backup-simplify]: Simplify 1 into 1
13.213 * [backup-simplify]: Simplify (/ 1 1) into 1
13.213 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
13.213 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.213 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.213 * [taylor]: Taking taylor expansion of 2 in k
13.213 * [backup-simplify]: Simplify 2 into 2
13.213 * [taylor]: Taking taylor expansion of PI in k
13.213 * [backup-simplify]: Simplify PI into PI
13.214 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.215 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.215 * [taylor]: Taking taylor expansion of (log n) in k
13.215 * [taylor]: Taking taylor expansion of n in k
13.215 * [backup-simplify]: Simplify n into n
13.215 * [backup-simplify]: Simplify (log n) into (log n)
13.215 * [backup-simplify]: Simplify (- 1) into -1
13.216 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.216 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.217 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
13.218 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
13.219 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
13.220 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.221 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.222 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.223 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.225 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.225 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.225 * [backup-simplify]: Simplify (- 0) into 0
13.226 * [backup-simplify]: Simplify (+ 0 0) into 0
13.226 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
13.228 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.229 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.231 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.231 * [taylor]: Taking taylor expansion of 0 in k
13.231 * [backup-simplify]: Simplify 0 into 0
13.231 * [backup-simplify]: Simplify 0 into 0
13.231 * [backup-simplify]: Simplify 0 into 0
13.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.234 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.237 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.237 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.237 * [backup-simplify]: Simplify (- 0) into 0
13.238 * [backup-simplify]: Simplify (+ 0 0) into 0
13.239 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
13.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.241 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
13.244 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.244 * [taylor]: Taking taylor expansion of 0 in k
13.244 * [backup-simplify]: Simplify 0 into 0
13.244 * [backup-simplify]: Simplify 0 into 0
13.244 * [backup-simplify]: Simplify 0 into 0
13.244 * [backup-simplify]: Simplify 0 into 0
13.245 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.246 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.251 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
13.251 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.252 * [backup-simplify]: Simplify (- 0) into 0
13.252 * [backup-simplify]: Simplify (+ 0 0) into 0
13.253 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
13.254 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.255 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
13.257 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.257 * [taylor]: Taking taylor expansion of 0 in k
13.257 * [backup-simplify]: Simplify 0 into 0
13.257 * [backup-simplify]: Simplify 0 into 0
13.258 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
13.258 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
13.258 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
13.258 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
13.258 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
13.258 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
13.258 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
13.258 * [taylor]: Taking taylor expansion of 1/2 in k
13.258 * [backup-simplify]: Simplify 1/2 into 1/2
13.258 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.258 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.258 * [taylor]: Taking taylor expansion of k in k
13.258 * [backup-simplify]: Simplify 0 into 0
13.258 * [backup-simplify]: Simplify 1 into 1
13.258 * [backup-simplify]: Simplify (/ 1 1) into 1
13.259 * [taylor]: Taking taylor expansion of 1 in k
13.259 * [backup-simplify]: Simplify 1 into 1
13.259 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.259 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.259 * [taylor]: Taking taylor expansion of -2 in k
13.259 * [backup-simplify]: Simplify -2 into -2
13.259 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.259 * [taylor]: Taking taylor expansion of PI in k
13.259 * [backup-simplify]: Simplify PI into PI
13.259 * [taylor]: Taking taylor expansion of n in k
13.259 * [backup-simplify]: Simplify n into n
13.259 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.259 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.259 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.259 * [backup-simplify]: Simplify (+ 1 0) into 1
13.259 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.259 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
13.260 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
13.260 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
13.260 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.260 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.260 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
13.260 * [taylor]: Taking taylor expansion of 1/2 in n
13.260 * [backup-simplify]: Simplify 1/2 into 1/2
13.260 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.260 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.260 * [taylor]: Taking taylor expansion of k in n
13.260 * [backup-simplify]: Simplify k into k
13.260 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.260 * [taylor]: Taking taylor expansion of 1 in n
13.260 * [backup-simplify]: Simplify 1 into 1
13.260 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.260 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.260 * [taylor]: Taking taylor expansion of -2 in n
13.260 * [backup-simplify]: Simplify -2 into -2
13.260 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.260 * [taylor]: Taking taylor expansion of PI in n
13.260 * [backup-simplify]: Simplify PI into PI
13.260 * [taylor]: Taking taylor expansion of n in n
13.260 * [backup-simplify]: Simplify 0 into 0
13.260 * [backup-simplify]: Simplify 1 into 1
13.260 * [backup-simplify]: Simplify (/ PI 1) into PI
13.261 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.261 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.261 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.261 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
13.262 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.263 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.264 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.264 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
13.264 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.264 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.264 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
13.264 * [taylor]: Taking taylor expansion of 1/2 in n
13.264 * [backup-simplify]: Simplify 1/2 into 1/2
13.264 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.264 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.264 * [taylor]: Taking taylor expansion of k in n
13.264 * [backup-simplify]: Simplify k into k
13.264 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.264 * [taylor]: Taking taylor expansion of 1 in n
13.264 * [backup-simplify]: Simplify 1 into 1
13.264 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.264 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.264 * [taylor]: Taking taylor expansion of -2 in n
13.264 * [backup-simplify]: Simplify -2 into -2
13.264 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.264 * [taylor]: Taking taylor expansion of PI in n
13.264 * [backup-simplify]: Simplify PI into PI
13.264 * [taylor]: Taking taylor expansion of n in n
13.264 * [backup-simplify]: Simplify 0 into 0
13.264 * [backup-simplify]: Simplify 1 into 1
13.264 * [backup-simplify]: Simplify (/ PI 1) into PI
13.265 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.265 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.265 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.265 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
13.266 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.267 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.268 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.268 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
13.268 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
13.268 * [taylor]: Taking taylor expansion of 1/2 in k
13.268 * [backup-simplify]: Simplify 1/2 into 1/2
13.268 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
13.268 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.268 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.268 * [taylor]: Taking taylor expansion of k in k
13.268 * [backup-simplify]: Simplify 0 into 0
13.268 * [backup-simplify]: Simplify 1 into 1
13.268 * [backup-simplify]: Simplify (/ 1 1) into 1
13.268 * [taylor]: Taking taylor expansion of 1 in k
13.268 * [backup-simplify]: Simplify 1 into 1
13.268 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
13.268 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
13.268 * [taylor]: Taking taylor expansion of (* -2 PI) in k
13.268 * [taylor]: Taking taylor expansion of -2 in k
13.268 * [backup-simplify]: Simplify -2 into -2
13.268 * [taylor]: Taking taylor expansion of PI in k
13.268 * [backup-simplify]: Simplify PI into PI
13.269 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.269 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.269 * [taylor]: Taking taylor expansion of (log n) in k
13.269 * [taylor]: Taking taylor expansion of n in k
13.269 * [backup-simplify]: Simplify n into n
13.269 * [backup-simplify]: Simplify (log n) into (log n)
13.270 * [backup-simplify]: Simplify (+ 1 0) into 1
13.270 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.270 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
13.271 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
13.271 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
13.272 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.273 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.273 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.275 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.276 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.277 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.277 * [backup-simplify]: Simplify (+ 0 0) into 0
13.277 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
13.278 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.279 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
13.280 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.280 * [taylor]: Taking taylor expansion of 0 in k
13.280 * [backup-simplify]: Simplify 0 into 0
13.280 * [backup-simplify]: Simplify 0 into 0
13.280 * [backup-simplify]: Simplify 0 into 0
13.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.281 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.284 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
13.284 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.284 * [backup-simplify]: Simplify (+ 0 0) into 0
13.285 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
13.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.288 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
13.290 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.291 * [taylor]: Taking taylor expansion of 0 in k
13.291 * [backup-simplify]: Simplify 0 into 0
13.291 * [backup-simplify]: Simplify 0 into 0
13.291 * [backup-simplify]: Simplify 0 into 0
13.291 * [backup-simplify]: Simplify 0 into 0
13.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.293 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.299 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
13.299 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.300 * [backup-simplify]: Simplify (+ 0 0) into 0
13.301 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
13.303 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.305 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
13.308 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.308 * [taylor]: Taking taylor expansion of 0 in k
13.308 * [backup-simplify]: Simplify 0 into 0
13.308 * [backup-simplify]: Simplify 0 into 0
13.309 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
13.309 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1)
13.309 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
13.310 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
13.310 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.310 * [taylor]: Taking taylor expansion of 2 in n
13.310 * [backup-simplify]: Simplify 2 into 2
13.310 * [taylor]: Taking taylor expansion of (* n PI) in n
13.310 * [taylor]: Taking taylor expansion of n in n
13.310 * [backup-simplify]: Simplify 0 into 0
13.310 * [backup-simplify]: Simplify 1 into 1
13.310 * [taylor]: Taking taylor expansion of PI in n
13.310 * [backup-simplify]: Simplify PI into PI
13.310 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.310 * [taylor]: Taking taylor expansion of 2 in n
13.310 * [backup-simplify]: Simplify 2 into 2
13.310 * [taylor]: Taking taylor expansion of (* n PI) in n
13.310 * [taylor]: Taking taylor expansion of n in n
13.310 * [backup-simplify]: Simplify 0 into 0
13.310 * [backup-simplify]: Simplify 1 into 1
13.310 * [taylor]: Taking taylor expansion of PI in n
13.310 * [backup-simplify]: Simplify PI into PI
13.310 * [backup-simplify]: Simplify (* 0 PI) into 0
13.311 * [backup-simplify]: Simplify (* 2 0) into 0
13.311 * [backup-simplify]: Simplify 0 into 0
13.312 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.312 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.313 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.313 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.314 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.314 * [backup-simplify]: Simplify 0 into 0
13.315 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.315 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.315 * [backup-simplify]: Simplify 0 into 0
13.316 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.317 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.317 * [backup-simplify]: Simplify 0 into 0
13.318 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.318 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
13.318 * [backup-simplify]: Simplify 0 into 0
13.319 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.320 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
13.320 * [backup-simplify]: Simplify 0 into 0
13.321 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
13.322 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
13.322 * [backup-simplify]: Simplify 0 into 0
13.323 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
13.323 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
13.323 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
13.323 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.323 * [taylor]: Taking taylor expansion of 2 in n
13.323 * [backup-simplify]: Simplify 2 into 2
13.323 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.323 * [taylor]: Taking taylor expansion of PI in n
13.323 * [backup-simplify]: Simplify PI into PI
13.323 * [taylor]: Taking taylor expansion of n in n
13.323 * [backup-simplify]: Simplify 0 into 0
13.323 * [backup-simplify]: Simplify 1 into 1
13.324 * [backup-simplify]: Simplify (/ PI 1) into PI
13.324 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.324 * [taylor]: Taking taylor expansion of 2 in n
13.324 * [backup-simplify]: Simplify 2 into 2
13.324 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.324 * [taylor]: Taking taylor expansion of PI in n
13.324 * [backup-simplify]: Simplify PI into PI
13.324 * [taylor]: Taking taylor expansion of n in n
13.324 * [backup-simplify]: Simplify 0 into 0
13.324 * [backup-simplify]: Simplify 1 into 1
13.324 * [backup-simplify]: Simplify (/ PI 1) into PI
13.324 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.325 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.325 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.326 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.326 * [backup-simplify]: Simplify 0 into 0
13.326 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.327 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.327 * [backup-simplify]: Simplify 0 into 0
13.327 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.328 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.328 * [backup-simplify]: Simplify 0 into 0
13.329 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.330 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.330 * [backup-simplify]: Simplify 0 into 0
13.330 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.331 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.331 * [backup-simplify]: Simplify 0 into 0
13.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.333 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.333 * [backup-simplify]: Simplify 0 into 0
13.333 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
13.333 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
13.333 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
13.334 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.334 * [taylor]: Taking taylor expansion of -2 in n
13.334 * [backup-simplify]: Simplify -2 into -2
13.334 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.334 * [taylor]: Taking taylor expansion of PI in n
13.334 * [backup-simplify]: Simplify PI into PI
13.334 * [taylor]: Taking taylor expansion of n in n
13.334 * [backup-simplify]: Simplify 0 into 0
13.334 * [backup-simplify]: Simplify 1 into 1
13.334 * [backup-simplify]: Simplify (/ PI 1) into PI
13.334 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.334 * [taylor]: Taking taylor expansion of -2 in n
13.334 * [backup-simplify]: Simplify -2 into -2
13.334 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.334 * [taylor]: Taking taylor expansion of PI in n
13.334 * [backup-simplify]: Simplify PI into PI
13.334 * [taylor]: Taking taylor expansion of n in n
13.334 * [backup-simplify]: Simplify 0 into 0
13.334 * [backup-simplify]: Simplify 1 into 1
13.334 * [backup-simplify]: Simplify (/ PI 1) into PI
13.335 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.335 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.335 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.336 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.336 * [backup-simplify]: Simplify 0 into 0
13.337 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.337 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.337 * [backup-simplify]: Simplify 0 into 0
13.338 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.338 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.338 * [backup-simplify]: Simplify 0 into 0
13.339 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.340 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.340 * [backup-simplify]: Simplify 0 into 0
13.340 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.341 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.341 * [backup-simplify]: Simplify 0 into 0
13.342 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.344 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.344 * [backup-simplify]: Simplify 0 into 0
13.344 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
13.344 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
13.345 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) into (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k))
13.345 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in (k n) around 0
13.345 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in n
13.345 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in n
13.345 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
13.345 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
13.345 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
13.345 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
13.345 * [taylor]: Taking taylor expansion of 1/2 in n
13.345 * [backup-simplify]: Simplify 1/2 into 1/2
13.345 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.345 * [taylor]: Taking taylor expansion of 1 in n
13.345 * [backup-simplify]: Simplify 1 into 1
13.345 * [taylor]: Taking taylor expansion of k in n
13.345 * [backup-simplify]: Simplify k into k
13.345 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.345 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.345 * [taylor]: Taking taylor expansion of 2 in n
13.345 * [backup-simplify]: Simplify 2 into 2
13.345 * [taylor]: Taking taylor expansion of (* n PI) in n
13.345 * [taylor]: Taking taylor expansion of n in n
13.346 * [backup-simplify]: Simplify 0 into 0
13.346 * [backup-simplify]: Simplify 1 into 1
13.346 * [taylor]: Taking taylor expansion of PI in n
13.346 * [backup-simplify]: Simplify PI into PI
13.346 * [backup-simplify]: Simplify (* 0 PI) into 0
13.346 * [backup-simplify]: Simplify (* 2 0) into 0
13.348 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.349 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.350 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.350 * [backup-simplify]: Simplify (- k) into (- k)
13.351 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.351 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
13.352 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.353 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.354 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.355 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) into (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))
13.355 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.355 * [taylor]: Taking taylor expansion of k in n
13.355 * [backup-simplify]: Simplify k into k
13.355 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.355 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.355 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in k
13.356 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in k
13.356 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
13.356 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
13.356 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
13.356 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
13.356 * [taylor]: Taking taylor expansion of 1/2 in k
13.356 * [backup-simplify]: Simplify 1/2 into 1/2
13.356 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.356 * [taylor]: Taking taylor expansion of 1 in k
13.356 * [backup-simplify]: Simplify 1 into 1
13.356 * [taylor]: Taking taylor expansion of k in k
13.356 * [backup-simplify]: Simplify 0 into 0
13.356 * [backup-simplify]: Simplify 1 into 1
13.356 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.356 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.356 * [taylor]: Taking taylor expansion of 2 in k
13.356 * [backup-simplify]: Simplify 2 into 2
13.356 * [taylor]: Taking taylor expansion of (* n PI) in k
13.356 * [taylor]: Taking taylor expansion of n in k
13.356 * [backup-simplify]: Simplify n into n
13.356 * [taylor]: Taking taylor expansion of PI in k
13.356 * [backup-simplify]: Simplify PI into PI
13.356 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.356 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.356 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.357 * [backup-simplify]: Simplify (- 0) into 0
13.357 * [backup-simplify]: Simplify (+ 1 0) into 1
13.358 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.358 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
13.358 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
13.358 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2))))
13.358 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.358 * [taylor]: Taking taylor expansion of k in k
13.358 * [backup-simplify]: Simplify 0 into 0
13.358 * [backup-simplify]: Simplify 1 into 1
13.358 * [backup-simplify]: Simplify (sqrt 0) into 0
13.360 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.360 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in k
13.360 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in k
13.360 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
13.360 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
13.360 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
13.360 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
13.360 * [taylor]: Taking taylor expansion of 1/2 in k
13.360 * [backup-simplify]: Simplify 1/2 into 1/2
13.360 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.360 * [taylor]: Taking taylor expansion of 1 in k
13.360 * [backup-simplify]: Simplify 1 into 1
13.360 * [taylor]: Taking taylor expansion of k in k
13.360 * [backup-simplify]: Simplify 0 into 0
13.360 * [backup-simplify]: Simplify 1 into 1
13.360 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.360 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.360 * [taylor]: Taking taylor expansion of 2 in k
13.360 * [backup-simplify]: Simplify 2 into 2
13.360 * [taylor]: Taking taylor expansion of (* n PI) in k
13.360 * [taylor]: Taking taylor expansion of n in k
13.360 * [backup-simplify]: Simplify n into n
13.360 * [taylor]: Taking taylor expansion of PI in k
13.360 * [backup-simplify]: Simplify PI into PI
13.361 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.361 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.361 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.361 * [backup-simplify]: Simplify (- 0) into 0
13.362 * [backup-simplify]: Simplify (+ 1 0) into 1
13.362 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.362 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
13.363 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
13.363 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2))))
13.363 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.363 * [taylor]: Taking taylor expansion of k in k
13.363 * [backup-simplify]: Simplify 0 into 0
13.363 * [backup-simplify]: Simplify 1 into 1
13.363 * [backup-simplify]: Simplify (sqrt 0) into 0
13.365 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.365 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0
13.365 * [taylor]: Taking taylor expansion of 0 in n
13.365 * [backup-simplify]: Simplify 0 into 0
13.365 * [backup-simplify]: Simplify 0 into 0
13.366 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
13.366 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
13.367 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
13.367 * [backup-simplify]: Simplify (- 1) into -1
13.368 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.368 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
13.369 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
13.369 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
13.370 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))
13.372 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))
13.372 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n
13.372 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
13.372 * [taylor]: Taking taylor expansion of +nan.0 in n
13.372 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.372 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
13.372 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
13.372 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
13.372 * [taylor]: Taking taylor expansion of (* n PI) in n
13.372 * [taylor]: Taking taylor expansion of n in n
13.372 * [backup-simplify]: Simplify 0 into 0
13.372 * [backup-simplify]: Simplify 1 into 1
13.372 * [taylor]: Taking taylor expansion of PI in n
13.372 * [backup-simplify]: Simplify PI into PI
13.373 * [backup-simplify]: Simplify (* 0 PI) into 0
13.374 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.375 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
13.375 * [backup-simplify]: Simplify (sqrt 0) into 0
13.377 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
13.377 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
13.377 * [taylor]: Taking taylor expansion of 1/2 in n
13.377 * [backup-simplify]: Simplify 1/2 into 1/2
13.378 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
13.378 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
13.381 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
13.382 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0
13.387 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
13.391 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
13.396 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
13.396 * [backup-simplify]: Simplify 0 into 0
13.399 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.400 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
13.401 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
13.403 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
13.403 * [backup-simplify]: Simplify (- 0) into 0
13.403 * [backup-simplify]: Simplify (+ 0 0) into 0
13.404 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
13.405 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
13.407 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
13.410 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))))
13.416 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))))
13.416 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n
13.416 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n
13.416 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n
13.416 * [taylor]: Taking taylor expansion of +nan.0 in n
13.416 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.416 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n
13.416 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n
13.416 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.416 * [taylor]: Taking taylor expansion of 2 in n
13.416 * [backup-simplify]: Simplify 2 into 2
13.417 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.417 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.417 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n
13.418 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.418 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.418 * [taylor]: Taking taylor expansion of 2 in n
13.418 * [backup-simplify]: Simplify 2 into 2
13.418 * [taylor]: Taking taylor expansion of (* n PI) in n
13.418 * [taylor]: Taking taylor expansion of n in n
13.418 * [backup-simplify]: Simplify 0 into 0
13.418 * [backup-simplify]: Simplify 1 into 1
13.418 * [taylor]: Taking taylor expansion of PI in n
13.418 * [backup-simplify]: Simplify PI into PI
13.418 * [backup-simplify]: Simplify (* 0 PI) into 0
13.419 * [backup-simplify]: Simplify (* 2 0) into 0
13.420 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.421 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.422 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.422 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n
13.423 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
13.423 * [taylor]: Taking taylor expansion of 1/2 in n
13.423 * [backup-simplify]: Simplify 1/2 into 1/2
13.423 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
13.424 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
13.424 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
13.424 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
13.424 * [taylor]: Taking taylor expansion of (* n PI) in n
13.424 * [taylor]: Taking taylor expansion of n in n
13.424 * [backup-simplify]: Simplify 0 into 0
13.424 * [backup-simplify]: Simplify 1 into 1
13.424 * [taylor]: Taking taylor expansion of PI in n
13.424 * [backup-simplify]: Simplify PI into PI
13.424 * [backup-simplify]: Simplify (* 0 PI) into 0
13.426 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.426 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
13.427 * [backup-simplify]: Simplify (sqrt 0) into 0
13.429 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
13.429 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n
13.429 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
13.429 * [taylor]: Taking taylor expansion of +nan.0 in n
13.429 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.429 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
13.429 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
13.429 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
13.429 * [taylor]: Taking taylor expansion of (* n PI) in n
13.429 * [taylor]: Taking taylor expansion of n in n
13.429 * [backup-simplify]: Simplify 0 into 0
13.429 * [backup-simplify]: Simplify 1 into 1
13.429 * [taylor]: Taking taylor expansion of PI in n
13.429 * [backup-simplify]: Simplify PI into PI
13.430 * [backup-simplify]: Simplify (* 0 PI) into 0
13.431 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.432 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
13.432 * [backup-simplify]: Simplify (sqrt 0) into 0
13.434 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
13.434 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
13.434 * [taylor]: Taking taylor expansion of 1/2 in n
13.434 * [backup-simplify]: Simplify 1/2 into 1/2
13.434 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
13.435 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
13.436 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.438 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2)
13.439 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))
13.441 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))
13.441 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.442 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0
13.443 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.443 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.444 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.445 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0
13.447 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0
13.449 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
13.450 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0
13.457 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
13.459 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
13.460 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0
13.463 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
13.465 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
13.478 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
13.497 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
13.519 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
13.520 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0
13.521 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.522 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0
13.526 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2))
13.530 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
13.536 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
13.538 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
13.541 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
13.556 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))
13.556 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2))) into (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k)))
13.556 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0
13.556 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in n
13.556 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in n
13.556 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
13.556 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.556 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.556 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
13.556 * [taylor]: Taking taylor expansion of 1/2 in n
13.556 * [backup-simplify]: Simplify 1/2 into 1/2
13.556 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.556 * [taylor]: Taking taylor expansion of 1 in n
13.556 * [backup-simplify]: Simplify 1 into 1
13.557 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.557 * [taylor]: Taking taylor expansion of k in n
13.557 * [backup-simplify]: Simplify k into k
13.557 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.557 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.557 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.557 * [taylor]: Taking taylor expansion of 2 in n
13.557 * [backup-simplify]: Simplify 2 into 2
13.557 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.557 * [taylor]: Taking taylor expansion of PI in n
13.557 * [backup-simplify]: Simplify PI into PI
13.557 * [taylor]: Taking taylor expansion of n in n
13.557 * [backup-simplify]: Simplify 0 into 0
13.557 * [backup-simplify]: Simplify 1 into 1
13.557 * [backup-simplify]: Simplify (/ PI 1) into PI
13.557 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.558 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.558 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.558 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.558 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
13.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.560 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.560 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.561 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.561 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.561 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.561 * [taylor]: Taking taylor expansion of k in n
13.561 * [backup-simplify]: Simplify k into k
13.561 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.561 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.561 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.561 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.561 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in k
13.562 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in k
13.562 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
13.562 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.562 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.562 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
13.562 * [taylor]: Taking taylor expansion of 1/2 in k
13.562 * [backup-simplify]: Simplify 1/2 into 1/2
13.562 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.562 * [taylor]: Taking taylor expansion of 1 in k
13.562 * [backup-simplify]: Simplify 1 into 1
13.562 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.562 * [taylor]: Taking taylor expansion of k in k
13.562 * [backup-simplify]: Simplify 0 into 0
13.562 * [backup-simplify]: Simplify 1 into 1
13.562 * [backup-simplify]: Simplify (/ 1 1) into 1
13.562 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.562 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.562 * [taylor]: Taking taylor expansion of 2 in k
13.562 * [backup-simplify]: Simplify 2 into 2
13.562 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.562 * [taylor]: Taking taylor expansion of PI in k
13.562 * [backup-simplify]: Simplify PI into PI
13.562 * [taylor]: Taking taylor expansion of n in k
13.562 * [backup-simplify]: Simplify n into n
13.562 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.562 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.562 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.562 * [backup-simplify]: Simplify (- 1) into -1
13.563 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.563 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
13.563 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
13.563 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
13.563 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
13.563 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.563 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.563 * [taylor]: Taking taylor expansion of k in k
13.563 * [backup-simplify]: Simplify 0 into 0
13.563 * [backup-simplify]: Simplify 1 into 1
13.564 * [backup-simplify]: Simplify (/ 1 1) into 1
13.564 * [backup-simplify]: Simplify (sqrt 0) into 0
13.565 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.565 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in k
13.565 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in k
13.565 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
13.565 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.565 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.565 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
13.565 * [taylor]: Taking taylor expansion of 1/2 in k
13.565 * [backup-simplify]: Simplify 1/2 into 1/2
13.565 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.565 * [taylor]: Taking taylor expansion of 1 in k
13.565 * [backup-simplify]: Simplify 1 into 1
13.565 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.565 * [taylor]: Taking taylor expansion of k in k
13.565 * [backup-simplify]: Simplify 0 into 0
13.565 * [backup-simplify]: Simplify 1 into 1
13.565 * [backup-simplify]: Simplify (/ 1 1) into 1
13.565 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.565 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.565 * [taylor]: Taking taylor expansion of 2 in k
13.565 * [backup-simplify]: Simplify 2 into 2
13.565 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.565 * [taylor]: Taking taylor expansion of PI in k
13.565 * [backup-simplify]: Simplify PI into PI
13.565 * [taylor]: Taking taylor expansion of n in k
13.565 * [backup-simplify]: Simplify n into n
13.566 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.566 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.566 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.566 * [backup-simplify]: Simplify (- 1) into -1
13.566 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.567 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
13.567 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
13.567 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
13.567 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
13.567 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.567 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.567 * [taylor]: Taking taylor expansion of k in k
13.567 * [backup-simplify]: Simplify 0 into 0
13.567 * [backup-simplify]: Simplify 1 into 1
13.568 * [backup-simplify]: Simplify (/ 1 1) into 1
13.568 * [backup-simplify]: Simplify (sqrt 0) into 0
13.569 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.570 * [backup-simplify]: Simplify (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) 0) into 0
13.570 * [taylor]: Taking taylor expansion of 0 in n
13.570 * [backup-simplify]: Simplify 0 into 0
13.570 * [backup-simplify]: Simplify 0 into 0
13.570 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into 0
13.571 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
13.571 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) in n
13.571 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
13.571 * [taylor]: Taking taylor expansion of +nan.0 in n
13.571 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.571 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
13.571 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
13.571 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
13.571 * [taylor]: Taking taylor expansion of 1/2 in n
13.571 * [backup-simplify]: Simplify 1/2 into 1/2
13.571 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
13.571 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.571 * [taylor]: Taking taylor expansion of 1 in n
13.571 * [backup-simplify]: Simplify 1 into 1
13.571 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.571 * [taylor]: Taking taylor expansion of k in n
13.571 * [backup-simplify]: Simplify k into k
13.571 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.571 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.571 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.571 * [taylor]: Taking taylor expansion of 2 in n
13.571 * [backup-simplify]: Simplify 2 into 2
13.571 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.571 * [taylor]: Taking taylor expansion of PI in n
13.571 * [backup-simplify]: Simplify PI into PI
13.571 * [taylor]: Taking taylor expansion of n in n
13.571 * [backup-simplify]: Simplify 0 into 0
13.572 * [backup-simplify]: Simplify 1 into 1
13.572 * [backup-simplify]: Simplify (/ PI 1) into PI
13.572 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.573 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.573 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.574 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.575 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.576 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
13.577 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.578 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.579 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.581 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.582 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
13.583 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
13.583 * [backup-simplify]: Simplify 0 into 0
13.584 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
13.587 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.588 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into 0
13.589 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
13.589 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) in n
13.589 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
13.589 * [taylor]: Taking taylor expansion of +nan.0 in n
13.589 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.589 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
13.589 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
13.589 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
13.589 * [taylor]: Taking taylor expansion of 1/2 in n
13.589 * [backup-simplify]: Simplify 1/2 into 1/2
13.589 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
13.589 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.589 * [taylor]: Taking taylor expansion of 1 in n
13.589 * [backup-simplify]: Simplify 1 into 1
13.589 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.589 * [taylor]: Taking taylor expansion of k in n
13.589 * [backup-simplify]: Simplify k into k
13.589 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.589 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.589 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.589 * [taylor]: Taking taylor expansion of 2 in n
13.589 * [backup-simplify]: Simplify 2 into 2
13.589 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.589 * [taylor]: Taking taylor expansion of PI in n
13.589 * [backup-simplify]: Simplify PI into PI
13.589 * [taylor]: Taking taylor expansion of n in n
13.589 * [backup-simplify]: Simplify 0 into 0
13.589 * [backup-simplify]: Simplify 1 into 1
13.590 * [backup-simplify]: Simplify (/ PI 1) into PI
13.590 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.591 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.591 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.592 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.593 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.594 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
13.595 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.596 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.597 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.598 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.599 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
13.601 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
13.602 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.602 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.604 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.604 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.605 * [backup-simplify]: Simplify (- 0) into 0
13.605 * [backup-simplify]: Simplify (+ 0 0) into 0
13.606 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.608 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.609 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
13.611 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.613 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
13.615 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0
13.615 * [backup-simplify]: Simplify (- 0) into 0
13.615 * [backup-simplify]: Simplify 0 into 0
13.615 * [backup-simplify]: Simplify 0 into 0
13.616 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.620 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.621 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into 0
13.622 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
13.622 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) in n
13.622 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
13.622 * [taylor]: Taking taylor expansion of +nan.0 in n
13.622 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.622 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
13.622 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
13.622 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
13.622 * [taylor]: Taking taylor expansion of 1/2 in n
13.622 * [backup-simplify]: Simplify 1/2 into 1/2
13.622 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
13.622 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.622 * [taylor]: Taking taylor expansion of 1 in n
13.622 * [backup-simplify]: Simplify 1 into 1
13.622 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.622 * [taylor]: Taking taylor expansion of k in n
13.622 * [backup-simplify]: Simplify k into k
13.622 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.622 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.622 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.622 * [taylor]: Taking taylor expansion of 2 in n
13.622 * [backup-simplify]: Simplify 2 into 2
13.622 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.622 * [taylor]: Taking taylor expansion of PI in n
13.622 * [backup-simplify]: Simplify PI into PI
13.622 * [taylor]: Taking taylor expansion of n in n
13.622 * [backup-simplify]: Simplify 0 into 0
13.622 * [backup-simplify]: Simplify 1 into 1
13.623 * [backup-simplify]: Simplify (/ PI 1) into PI
13.623 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.624 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.625 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.625 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.629 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.630 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
13.631 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.632 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.634 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.635 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.636 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
13.637 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
13.641 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))))) into (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))
13.642 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))))
13.642 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in (k n) around 0
13.642 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in n
13.642 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.642 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.642 * [taylor]: Taking taylor expansion of -1 in n
13.642 * [backup-simplify]: Simplify -1 into -1
13.642 * [taylor]: Taking taylor expansion of k in n
13.642 * [backup-simplify]: Simplify k into k
13.642 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.642 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.642 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.643 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.643 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
13.643 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.643 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.643 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
13.643 * [taylor]: Taking taylor expansion of 1/2 in n
13.643 * [backup-simplify]: Simplify 1/2 into 1/2
13.643 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.643 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.643 * [taylor]: Taking taylor expansion of k in n
13.643 * [backup-simplify]: Simplify k into k
13.643 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.643 * [taylor]: Taking taylor expansion of 1 in n
13.643 * [backup-simplify]: Simplify 1 into 1
13.643 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.643 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.643 * [taylor]: Taking taylor expansion of -2 in n
13.643 * [backup-simplify]: Simplify -2 into -2
13.643 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.643 * [taylor]: Taking taylor expansion of PI in n
13.643 * [backup-simplify]: Simplify PI into PI
13.643 * [taylor]: Taking taylor expansion of n in n
13.643 * [backup-simplify]: Simplify 0 into 0
13.643 * [backup-simplify]: Simplify 1 into 1
13.644 * [backup-simplify]: Simplify (/ PI 1) into PI
13.644 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.645 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.645 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.645 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
13.647 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.648 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.649 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.651 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
13.651 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k
13.651 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.651 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.651 * [taylor]: Taking taylor expansion of -1 in k
13.651 * [backup-simplify]: Simplify -1 into -1
13.651 * [taylor]: Taking taylor expansion of k in k
13.651 * [backup-simplify]: Simplify 0 into 0
13.651 * [backup-simplify]: Simplify 1 into 1
13.651 * [backup-simplify]: Simplify (/ -1 1) into -1
13.652 * [backup-simplify]: Simplify (sqrt 0) into 0
13.653 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.653 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
13.653 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
13.653 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
13.653 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
13.653 * [taylor]: Taking taylor expansion of 1/2 in k
13.653 * [backup-simplify]: Simplify 1/2 into 1/2
13.653 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.653 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.653 * [taylor]: Taking taylor expansion of k in k
13.653 * [backup-simplify]: Simplify 0 into 0
13.653 * [backup-simplify]: Simplify 1 into 1
13.654 * [backup-simplify]: Simplify (/ 1 1) into 1
13.654 * [taylor]: Taking taylor expansion of 1 in k
13.654 * [backup-simplify]: Simplify 1 into 1
13.654 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.654 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.654 * [taylor]: Taking taylor expansion of -2 in k
13.654 * [backup-simplify]: Simplify -2 into -2
13.654 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.654 * [taylor]: Taking taylor expansion of PI in k
13.654 * [backup-simplify]: Simplify PI into PI
13.654 * [taylor]: Taking taylor expansion of n in k
13.654 * [backup-simplify]: Simplify n into n
13.654 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.654 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.654 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.655 * [backup-simplify]: Simplify (+ 1 0) into 1
13.655 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.655 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
13.655 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
13.656 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
13.656 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k
13.656 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.656 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.656 * [taylor]: Taking taylor expansion of -1 in k
13.656 * [backup-simplify]: Simplify -1 into -1
13.656 * [taylor]: Taking taylor expansion of k in k
13.656 * [backup-simplify]: Simplify 0 into 0
13.656 * [backup-simplify]: Simplify 1 into 1
13.656 * [backup-simplify]: Simplify (/ -1 1) into -1
13.657 * [backup-simplify]: Simplify (sqrt 0) into 0
13.658 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.658 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
13.658 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
13.658 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
13.658 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
13.658 * [taylor]: Taking taylor expansion of 1/2 in k
13.658 * [backup-simplify]: Simplify 1/2 into 1/2
13.658 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
13.658 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.658 * [taylor]: Taking taylor expansion of k in k
13.658 * [backup-simplify]: Simplify 0 into 0
13.658 * [backup-simplify]: Simplify 1 into 1
13.659 * [backup-simplify]: Simplify (/ 1 1) into 1
13.659 * [taylor]: Taking taylor expansion of 1 in k
13.659 * [backup-simplify]: Simplify 1 into 1
13.659 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.659 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.659 * [taylor]: Taking taylor expansion of -2 in k
13.659 * [backup-simplify]: Simplify -2 into -2
13.659 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.659 * [taylor]: Taking taylor expansion of PI in k
13.659 * [backup-simplify]: Simplify PI into PI
13.659 * [taylor]: Taking taylor expansion of n in k
13.659 * [backup-simplify]: Simplify n into n
13.659 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.659 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.659 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.660 * [backup-simplify]: Simplify (+ 1 0) into 1
13.660 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.660 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
13.660 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
13.660 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
13.661 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
13.661 * [taylor]: Taking taylor expansion of +nan.0 in n
13.661 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.661 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
13.661 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
13.661 * [taylor]: Taking taylor expansion of 1/2 in n
13.661 * [backup-simplify]: Simplify 1/2 into 1/2
13.661 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
13.661 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.661 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.661 * [taylor]: Taking taylor expansion of -2 in n
13.661 * [backup-simplify]: Simplify -2 into -2
13.661 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.661 * [taylor]: Taking taylor expansion of PI in n
13.661 * [backup-simplify]: Simplify PI into PI
13.661 * [taylor]: Taking taylor expansion of n in n
13.661 * [backup-simplify]: Simplify 0 into 0
13.661 * [backup-simplify]: Simplify 1 into 1
13.661 * [backup-simplify]: Simplify (/ PI 1) into PI
13.662 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.663 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.663 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.663 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.663 * [taylor]: Taking taylor expansion of k in n
13.663 * [backup-simplify]: Simplify k into k
13.663 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.663 * [taylor]: Taking taylor expansion of 1 in n
13.663 * [backup-simplify]: Simplify 1 into 1
13.664 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.665 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.666 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
13.667 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.668 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.669 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
13.670 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
13.671 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
13.674 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.674 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))
13.675 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) in n
13.675 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
13.675 * [taylor]: Taking taylor expansion of +nan.0 in n
13.675 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.675 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
13.675 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
13.675 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
13.675 * [taylor]: Taking taylor expansion of 1/2 in n
13.675 * [backup-simplify]: Simplify 1/2 into 1/2
13.675 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
13.675 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.675 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.675 * [taylor]: Taking taylor expansion of -2 in n
13.675 * [backup-simplify]: Simplify -2 into -2
13.675 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.675 * [taylor]: Taking taylor expansion of PI in n
13.675 * [backup-simplify]: Simplify PI into PI
13.675 * [taylor]: Taking taylor expansion of n in n
13.675 * [backup-simplify]: Simplify 0 into 0
13.675 * [backup-simplify]: Simplify 1 into 1
13.676 * [backup-simplify]: Simplify (/ PI 1) into PI
13.676 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.677 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.677 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.677 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.677 * [taylor]: Taking taylor expansion of k in n
13.677 * [backup-simplify]: Simplify k into k
13.677 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.677 * [taylor]: Taking taylor expansion of 1 in n
13.677 * [backup-simplify]: Simplify 1 into 1
13.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.679 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.680 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
13.681 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.682 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.683 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
13.684 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
13.685 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
13.687 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
13.688 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.688 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.689 * [backup-simplify]: Simplify (+ 0 0) into 0
13.689 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.690 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.692 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.693 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
13.695 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
13.697 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.700 * [backup-simplify]: Simplify (- (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))) into 0
13.700 * [backup-simplify]: Simplify 0 into 0
13.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.705 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.706 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))
13.706 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) in n
13.706 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
13.706 * [taylor]: Taking taylor expansion of +nan.0 in n
13.706 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.706 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
13.706 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
13.706 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
13.706 * [taylor]: Taking taylor expansion of 1/2 in n
13.706 * [backup-simplify]: Simplify 1/2 into 1/2
13.706 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
13.706 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.706 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.706 * [taylor]: Taking taylor expansion of -2 in n
13.706 * [backup-simplify]: Simplify -2 into -2
13.706 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.706 * [taylor]: Taking taylor expansion of PI in n
13.706 * [backup-simplify]: Simplify PI into PI
13.706 * [taylor]: Taking taylor expansion of n in n
13.707 * [backup-simplify]: Simplify 0 into 0
13.707 * [backup-simplify]: Simplify 1 into 1
13.707 * [backup-simplify]: Simplify (/ PI 1) into PI
13.707 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.708 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.708 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.708 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.708 * [taylor]: Taking taylor expansion of k in n
13.709 * [backup-simplify]: Simplify k into k
13.709 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.709 * [taylor]: Taking taylor expansion of 1 in n
13.709 * [backup-simplify]: Simplify 1 into 1
13.710 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.710 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.711 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
13.712 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
13.713 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
13.715 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
13.716 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
13.717 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
13.718 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
13.720 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))
13.721 * * * * [progress]: [ 4 / 4 ] generating series at (2)
13.721 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
13.721 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
13.721 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
13.721 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
13.721 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
13.721 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
13.721 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
13.721 * [taylor]: Taking taylor expansion of 1/2 in n
13.721 * [backup-simplify]: Simplify 1/2 into 1/2
13.721 * [taylor]: Taking taylor expansion of (- 1 k) in n
13.721 * [taylor]: Taking taylor expansion of 1 in n
13.721 * [backup-simplify]: Simplify 1 into 1
13.721 * [taylor]: Taking taylor expansion of k in n
13.721 * [backup-simplify]: Simplify k into k
13.721 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.721 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.721 * [taylor]: Taking taylor expansion of 2 in n
13.721 * [backup-simplify]: Simplify 2 into 2
13.721 * [taylor]: Taking taylor expansion of (* n PI) in n
13.721 * [taylor]: Taking taylor expansion of n in n
13.721 * [backup-simplify]: Simplify 0 into 0
13.721 * [backup-simplify]: Simplify 1 into 1
13.721 * [taylor]: Taking taylor expansion of PI in n
13.721 * [backup-simplify]: Simplify PI into PI
13.722 * [backup-simplify]: Simplify (* 0 PI) into 0
13.722 * [backup-simplify]: Simplify (* 2 0) into 0
13.723 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.724 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.725 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.725 * [backup-simplify]: Simplify (- k) into (- k)
13.725 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
13.725 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
13.726 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.726 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
13.727 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
13.727 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.727 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.727 * [taylor]: Taking taylor expansion of k in n
13.727 * [backup-simplify]: Simplify k into k
13.727 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.727 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.727 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.727 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.727 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
13.727 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
13.727 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
13.727 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
13.727 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
13.727 * [taylor]: Taking taylor expansion of 1/2 in k
13.727 * [backup-simplify]: Simplify 1/2 into 1/2
13.727 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.727 * [taylor]: Taking taylor expansion of 1 in k
13.727 * [backup-simplify]: Simplify 1 into 1
13.727 * [taylor]: Taking taylor expansion of k in k
13.727 * [backup-simplify]: Simplify 0 into 0
13.727 * [backup-simplify]: Simplify 1 into 1
13.727 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.727 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.727 * [taylor]: Taking taylor expansion of 2 in k
13.727 * [backup-simplify]: Simplify 2 into 2
13.727 * [taylor]: Taking taylor expansion of (* n PI) in k
13.727 * [taylor]: Taking taylor expansion of n in k
13.727 * [backup-simplify]: Simplify n into n
13.727 * [taylor]: Taking taylor expansion of PI in k
13.727 * [backup-simplify]: Simplify PI into PI
13.727 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.728 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.728 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.728 * [backup-simplify]: Simplify (- 0) into 0
13.728 * [backup-simplify]: Simplify (+ 1 0) into 1
13.728 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.728 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
13.728 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
13.728 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.728 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.729 * [taylor]: Taking taylor expansion of k in k
13.729 * [backup-simplify]: Simplify 0 into 0
13.729 * [backup-simplify]: Simplify 1 into 1
13.729 * [backup-simplify]: Simplify (/ 1 1) into 1
13.729 * [backup-simplify]: Simplify (sqrt 0) into 0
13.730 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.730 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
13.730 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
13.730 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
13.730 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
13.730 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
13.730 * [taylor]: Taking taylor expansion of 1/2 in k
13.730 * [backup-simplify]: Simplify 1/2 into 1/2
13.730 * [taylor]: Taking taylor expansion of (- 1 k) in k
13.730 * [taylor]: Taking taylor expansion of 1 in k
13.730 * [backup-simplify]: Simplify 1 into 1
13.730 * [taylor]: Taking taylor expansion of k in k
13.730 * [backup-simplify]: Simplify 0 into 0
13.730 * [backup-simplify]: Simplify 1 into 1
13.730 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.730 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.730 * [taylor]: Taking taylor expansion of 2 in k
13.730 * [backup-simplify]: Simplify 2 into 2
13.730 * [taylor]: Taking taylor expansion of (* n PI) in k
13.730 * [taylor]: Taking taylor expansion of n in k
13.730 * [backup-simplify]: Simplify n into n
13.730 * [taylor]: Taking taylor expansion of PI in k
13.730 * [backup-simplify]: Simplify PI into PI
13.730 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.730 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.730 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.731 * [backup-simplify]: Simplify (- 0) into 0
13.731 * [backup-simplify]: Simplify (+ 1 0) into 1
13.731 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.731 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
13.731 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
13.731 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.731 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.731 * [taylor]: Taking taylor expansion of k in k
13.731 * [backup-simplify]: Simplify 0 into 0
13.731 * [backup-simplify]: Simplify 1 into 1
13.732 * [backup-simplify]: Simplify (/ 1 1) into 1
13.732 * [backup-simplify]: Simplify (sqrt 0) into 0
13.733 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.733 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
13.733 * [taylor]: Taking taylor expansion of 0 in n
13.733 * [backup-simplify]: Simplify 0 into 0
13.733 * [backup-simplify]: Simplify 0 into 0
13.733 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
13.733 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
13.734 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
13.734 * [backup-simplify]: Simplify (- 1) into -1
13.734 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.735 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
13.735 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
13.735 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
13.736 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
13.736 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
13.736 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
13.736 * [taylor]: Taking taylor expansion of +nan.0 in n
13.736 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.736 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
13.736 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.736 * [taylor]: Taking taylor expansion of 2 in n
13.736 * [backup-simplify]: Simplify 2 into 2
13.736 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.736 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.736 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.736 * [taylor]: Taking taylor expansion of (* n PI) in n
13.736 * [taylor]: Taking taylor expansion of n in n
13.736 * [backup-simplify]: Simplify 0 into 0
13.736 * [backup-simplify]: Simplify 1 into 1
13.737 * [taylor]: Taking taylor expansion of PI in n
13.737 * [backup-simplify]: Simplify PI into PI
13.737 * [backup-simplify]: Simplify (* 0 PI) into 0
13.738 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.738 * [backup-simplify]: Simplify (sqrt 0) into 0
13.739 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.739 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
13.739 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.740 * [backup-simplify]: Simplify (- 0) into 0
13.740 * [backup-simplify]: Simplify 0 into 0
13.740 * [backup-simplify]: Simplify 0 into 0
13.740 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
13.742 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.742 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
13.743 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
13.744 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
13.744 * [backup-simplify]: Simplify (- 0) into 0
13.745 * [backup-simplify]: Simplify (+ 0 0) into 0
13.745 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
13.746 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
13.746 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
13.747 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))
13.747 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
13.747 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
13.747 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
13.747 * [taylor]: Taking taylor expansion of +nan.0 in n
13.747 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.747 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
13.747 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
13.747 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.747 * [taylor]: Taking taylor expansion of 2 in n
13.747 * [backup-simplify]: Simplify 2 into 2
13.747 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.748 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.748 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.748 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.748 * [taylor]: Taking taylor expansion of 2 in n
13.748 * [backup-simplify]: Simplify 2 into 2
13.748 * [taylor]: Taking taylor expansion of (* n PI) in n
13.748 * [taylor]: Taking taylor expansion of n in n
13.748 * [backup-simplify]: Simplify 0 into 0
13.748 * [backup-simplify]: Simplify 1 into 1
13.748 * [taylor]: Taking taylor expansion of PI in n
13.748 * [backup-simplify]: Simplify PI into PI
13.748 * [backup-simplify]: Simplify (* 0 PI) into 0
13.750 * [backup-simplify]: Simplify (* 2 0) into 0
13.751 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.752 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.753 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.753 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.753 * [taylor]: Taking taylor expansion of (* n PI) in n
13.753 * [taylor]: Taking taylor expansion of n in n
13.753 * [backup-simplify]: Simplify 0 into 0
13.753 * [backup-simplify]: Simplify 1 into 1
13.753 * [taylor]: Taking taylor expansion of PI in n
13.753 * [backup-simplify]: Simplify PI into PI
13.753 * [backup-simplify]: Simplify (* 0 PI) into 0
13.754 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.754 * [backup-simplify]: Simplify (sqrt 0) into 0
13.756 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.756 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
13.756 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
13.756 * [taylor]: Taking taylor expansion of +nan.0 in n
13.756 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.756 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
13.756 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.756 * [taylor]: Taking taylor expansion of 2 in n
13.756 * [backup-simplify]: Simplify 2 into 2
13.757 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.757 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.757 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.757 * [taylor]: Taking taylor expansion of (* n PI) in n
13.757 * [taylor]: Taking taylor expansion of n in n
13.757 * [backup-simplify]: Simplify 0 into 0
13.757 * [backup-simplify]: Simplify 1 into 1
13.757 * [taylor]: Taking taylor expansion of PI in n
13.757 * [backup-simplify]: Simplify PI into PI
13.758 * [backup-simplify]: Simplify (* 0 PI) into 0
13.759 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.760 * [backup-simplify]: Simplify (sqrt 0) into 0
13.761 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.763 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.764 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
13.766 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
13.766 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.767 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
13.767 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.767 * [backup-simplify]: Simplify (- 0) into 0
13.768 * [backup-simplify]: Simplify (+ 0 0) into 0
13.768 * [backup-simplify]: Simplify (- 0) into 0
13.768 * [backup-simplify]: Simplify 0 into 0
13.771 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
13.777 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
13.780 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
13.783 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
13.783 * [backup-simplify]: Simplify 0 into 0
13.784 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.788 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.789 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.790 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
13.793 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0
13.794 * [backup-simplify]: Simplify (- 0) into 0
13.794 * [backup-simplify]: Simplify (+ 0 0) into 0
13.796 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
13.797 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
13.799 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))
13.800 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))))
13.800 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n
13.801 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n
13.801 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
13.801 * [taylor]: Taking taylor expansion of +nan.0 in n
13.801 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.801 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
13.801 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
13.801 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.801 * [taylor]: Taking taylor expansion of 2 in n
13.801 * [backup-simplify]: Simplify 2 into 2
13.801 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.802 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.802 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.802 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.802 * [taylor]: Taking taylor expansion of 2 in n
13.802 * [backup-simplify]: Simplify 2 into 2
13.802 * [taylor]: Taking taylor expansion of (* n PI) in n
13.802 * [taylor]: Taking taylor expansion of n in n
13.802 * [backup-simplify]: Simplify 0 into 0
13.802 * [backup-simplify]: Simplify 1 into 1
13.802 * [taylor]: Taking taylor expansion of PI in n
13.802 * [backup-simplify]: Simplify PI into PI
13.803 * [backup-simplify]: Simplify (* 0 PI) into 0
13.803 * [backup-simplify]: Simplify (* 2 0) into 0
13.805 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.806 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.807 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.807 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.807 * [taylor]: Taking taylor expansion of (* n PI) in n
13.807 * [taylor]: Taking taylor expansion of n in n
13.807 * [backup-simplify]: Simplify 0 into 0
13.807 * [backup-simplify]: Simplify 1 into 1
13.807 * [taylor]: Taking taylor expansion of PI in n
13.808 * [backup-simplify]: Simplify PI into PI
13.808 * [backup-simplify]: Simplify (* 0 PI) into 0
13.810 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.810 * [backup-simplify]: Simplify (sqrt 0) into 0
13.812 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.812 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n
13.812 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n
13.812 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
13.812 * [taylor]: Taking taylor expansion of +nan.0 in n
13.812 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.812 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
13.812 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.812 * [taylor]: Taking taylor expansion of 2 in n
13.812 * [backup-simplify]: Simplify 2 into 2
13.813 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.813 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.813 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.813 * [taylor]: Taking taylor expansion of (* n PI) in n
13.813 * [taylor]: Taking taylor expansion of n in n
13.813 * [backup-simplify]: Simplify 0 into 0
13.813 * [backup-simplify]: Simplify 1 into 1
13.813 * [taylor]: Taking taylor expansion of PI in n
13.813 * [backup-simplify]: Simplify PI into PI
13.814 * [backup-simplify]: Simplify (* 0 PI) into 0
13.815 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.816 * [backup-simplify]: Simplify (sqrt 0) into 0
13.817 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.817 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
13.817 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
13.817 * [taylor]: Taking taylor expansion of +nan.0 in n
13.817 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.817 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
13.817 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
13.817 * [taylor]: Taking taylor expansion of (sqrt 2) in n
13.817 * [taylor]: Taking taylor expansion of 2 in n
13.817 * [backup-simplify]: Simplify 2 into 2
13.818 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
13.819 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
13.819 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
13.819 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.819 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.819 * [taylor]: Taking taylor expansion of 2 in n
13.819 * [backup-simplify]: Simplify 2 into 2
13.819 * [taylor]: Taking taylor expansion of (* n PI) in n
13.819 * [taylor]: Taking taylor expansion of n in n
13.819 * [backup-simplify]: Simplify 0 into 0
13.819 * [backup-simplify]: Simplify 1 into 1
13.819 * [taylor]: Taking taylor expansion of PI in n
13.819 * [backup-simplify]: Simplify PI into PI
13.819 * [backup-simplify]: Simplify (* 0 PI) into 0
13.820 * [backup-simplify]: Simplify (* 2 0) into 0
13.821 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.823 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.824 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.825 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.825 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
13.825 * [taylor]: Taking taylor expansion of (* n PI) in n
13.825 * [taylor]: Taking taylor expansion of n in n
13.825 * [backup-simplify]: Simplify 0 into 0
13.825 * [backup-simplify]: Simplify 1 into 1
13.826 * [taylor]: Taking taylor expansion of PI in n
13.826 * [backup-simplify]: Simplify PI into PI
13.826 * [backup-simplify]: Simplify (* 0 PI) into 0
13.827 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.827 * [backup-simplify]: Simplify (sqrt 0) into 0
13.828 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
13.829 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.830 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
13.831 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
13.831 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.831 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
13.832 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.832 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.833 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.835 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
13.836 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
13.836 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
13.837 * [backup-simplify]: Simplify (* +nan.0 0) into 0
13.837 * [backup-simplify]: Simplify (- 0) into 0
13.837 * [backup-simplify]: Simplify (+ 0 0) into 0
13.838 * [backup-simplify]: Simplify (- 0) into 0
13.838 * [backup-simplify]: Simplify (+ 0 0) into 0
13.838 * [backup-simplify]: Simplify (- 0) into 0
13.838 * [backup-simplify]: Simplify 0 into 0
13.839 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.840 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.841 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.842 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.842 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
13.844 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
13.848 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
13.849 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
13.852 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
13.855 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
13.860 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))
13.867 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
13.875 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
13.876 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.880 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
13.881 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
13.886 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
13.895 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
13.900 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
13.903 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
13.918 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
13.919 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
13.919 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
13.919 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
13.919 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
13.919 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.919 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.919 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
13.919 * [taylor]: Taking taylor expansion of 1/2 in n
13.919 * [backup-simplify]: Simplify 1/2 into 1/2
13.919 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.919 * [taylor]: Taking taylor expansion of 1 in n
13.919 * [backup-simplify]: Simplify 1 into 1
13.919 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.919 * [taylor]: Taking taylor expansion of k in n
13.919 * [backup-simplify]: Simplify k into k
13.919 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.919 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.919 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.919 * [taylor]: Taking taylor expansion of 2 in n
13.919 * [backup-simplify]: Simplify 2 into 2
13.919 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.919 * [taylor]: Taking taylor expansion of PI in n
13.919 * [backup-simplify]: Simplify PI into PI
13.919 * [taylor]: Taking taylor expansion of n in n
13.919 * [backup-simplify]: Simplify 0 into 0
13.919 * [backup-simplify]: Simplify 1 into 1
13.920 * [backup-simplify]: Simplify (/ PI 1) into PI
13.920 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.921 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.921 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.921 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.922 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
13.923 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.924 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.925 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.925 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.925 * [taylor]: Taking taylor expansion of k in n
13.925 * [backup-simplify]: Simplify k into k
13.925 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.925 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.925 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
13.925 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
13.925 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.925 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.925 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
13.925 * [taylor]: Taking taylor expansion of 1/2 in k
13.925 * [backup-simplify]: Simplify 1/2 into 1/2
13.926 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.926 * [taylor]: Taking taylor expansion of 1 in k
13.926 * [backup-simplify]: Simplify 1 into 1
13.926 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.926 * [taylor]: Taking taylor expansion of k in k
13.926 * [backup-simplify]: Simplify 0 into 0
13.926 * [backup-simplify]: Simplify 1 into 1
13.926 * [backup-simplify]: Simplify (/ 1 1) into 1
13.926 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.926 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.926 * [taylor]: Taking taylor expansion of 2 in k
13.926 * [backup-simplify]: Simplify 2 into 2
13.926 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.926 * [taylor]: Taking taylor expansion of PI in k
13.926 * [backup-simplify]: Simplify PI into PI
13.926 * [taylor]: Taking taylor expansion of n in k
13.926 * [backup-simplify]: Simplify n into n
13.926 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.926 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.926 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.927 * [backup-simplify]: Simplify (- 1) into -1
13.927 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.928 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
13.928 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
13.928 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
13.928 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.928 * [taylor]: Taking taylor expansion of k in k
13.928 * [backup-simplify]: Simplify 0 into 0
13.928 * [backup-simplify]: Simplify 1 into 1
13.929 * [backup-simplify]: Simplify (sqrt 0) into 0
13.930 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.930 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
13.930 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
13.930 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.930 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.930 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
13.930 * [taylor]: Taking taylor expansion of 1/2 in k
13.930 * [backup-simplify]: Simplify 1/2 into 1/2
13.930 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
13.930 * [taylor]: Taking taylor expansion of 1 in k
13.930 * [backup-simplify]: Simplify 1 into 1
13.930 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.930 * [taylor]: Taking taylor expansion of k in k
13.930 * [backup-simplify]: Simplify 0 into 0
13.931 * [backup-simplify]: Simplify 1 into 1
13.931 * [backup-simplify]: Simplify (/ 1 1) into 1
13.931 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.931 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.931 * [taylor]: Taking taylor expansion of 2 in k
13.931 * [backup-simplify]: Simplify 2 into 2
13.931 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.931 * [taylor]: Taking taylor expansion of PI in k
13.931 * [backup-simplify]: Simplify PI into PI
13.931 * [taylor]: Taking taylor expansion of n in k
13.931 * [backup-simplify]: Simplify n into n
13.931 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.931 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.931 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.932 * [backup-simplify]: Simplify (- 1) into -1
13.932 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.933 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
13.933 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
13.933 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
13.933 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.933 * [taylor]: Taking taylor expansion of k in k
13.933 * [backup-simplify]: Simplify 0 into 0
13.933 * [backup-simplify]: Simplify 1 into 1
13.933 * [backup-simplify]: Simplify (sqrt 0) into 0
13.935 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.935 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
13.935 * [taylor]: Taking taylor expansion of 0 in n
13.935 * [backup-simplify]: Simplify 0 into 0
13.935 * [backup-simplify]: Simplify 0 into 0
13.936 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
13.936 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
13.936 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
13.936 * [taylor]: Taking taylor expansion of +nan.0 in n
13.936 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.936 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
13.936 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
13.936 * [taylor]: Taking taylor expansion of 1/2 in n
13.936 * [backup-simplify]: Simplify 1/2 into 1/2
13.936 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
13.936 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.936 * [taylor]: Taking taylor expansion of 1 in n
13.936 * [backup-simplify]: Simplify 1 into 1
13.936 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.936 * [taylor]: Taking taylor expansion of k in n
13.936 * [backup-simplify]: Simplify k into k
13.936 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.936 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.936 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.936 * [taylor]: Taking taylor expansion of 2 in n
13.936 * [backup-simplify]: Simplify 2 into 2
13.936 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.936 * [taylor]: Taking taylor expansion of PI in n
13.936 * [backup-simplify]: Simplify PI into PI
13.936 * [taylor]: Taking taylor expansion of n in n
13.936 * [backup-simplify]: Simplify 0 into 0
13.936 * [backup-simplify]: Simplify 1 into 1
13.937 * [backup-simplify]: Simplify (/ PI 1) into PI
13.937 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.938 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.938 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.938 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.940 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.941 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
13.942 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.943 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.944 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.945 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
13.946 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
13.946 * [backup-simplify]: Simplify 0 into 0
13.949 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.950 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
13.950 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
13.950 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
13.950 * [taylor]: Taking taylor expansion of +nan.0 in n
13.950 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.950 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
13.950 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
13.951 * [taylor]: Taking taylor expansion of 1/2 in n
13.951 * [backup-simplify]: Simplify 1/2 into 1/2
13.951 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
13.951 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.951 * [taylor]: Taking taylor expansion of 1 in n
13.951 * [backup-simplify]: Simplify 1 into 1
13.951 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.951 * [taylor]: Taking taylor expansion of k in n
13.951 * [backup-simplify]: Simplify k into k
13.951 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.951 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.951 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.951 * [taylor]: Taking taylor expansion of 2 in n
13.951 * [backup-simplify]: Simplify 2 into 2
13.951 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.951 * [taylor]: Taking taylor expansion of PI in n
13.951 * [backup-simplify]: Simplify PI into PI
13.951 * [taylor]: Taking taylor expansion of n in n
13.951 * [backup-simplify]: Simplify 0 into 0
13.951 * [backup-simplify]: Simplify 1 into 1
13.951 * [backup-simplify]: Simplify (/ PI 1) into PI
13.952 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.953 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.953 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.953 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.955 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.956 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
13.957 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.958 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.959 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.960 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
13.961 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
13.962 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.963 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.965 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.965 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.966 * [backup-simplify]: Simplify (- 0) into 0
13.966 * [backup-simplify]: Simplify (+ 0 0) into 0
13.967 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.968 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.970 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
13.972 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.973 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
13.974 * [backup-simplify]: Simplify (- 0) into 0
13.974 * [backup-simplify]: Simplify 0 into 0
13.974 * [backup-simplify]: Simplify 0 into 0
13.978 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.979 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
13.979 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
13.979 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
13.979 * [taylor]: Taking taylor expansion of +nan.0 in n
13.979 * [backup-simplify]: Simplify +nan.0 into +nan.0
13.979 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
13.979 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
13.979 * [taylor]: Taking taylor expansion of 1/2 in n
13.979 * [backup-simplify]: Simplify 1/2 into 1/2
13.979 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
13.979 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
13.979 * [taylor]: Taking taylor expansion of 1 in n
13.979 * [backup-simplify]: Simplify 1 into 1
13.979 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.979 * [taylor]: Taking taylor expansion of k in n
13.979 * [backup-simplify]: Simplify k into k
13.980 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.980 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.980 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.980 * [taylor]: Taking taylor expansion of 2 in n
13.980 * [backup-simplify]: Simplify 2 into 2
13.980 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.980 * [taylor]: Taking taylor expansion of PI in n
13.980 * [backup-simplify]: Simplify PI into PI
13.980 * [taylor]: Taking taylor expansion of n in n
13.980 * [backup-simplify]: Simplify 0 into 0
13.980 * [backup-simplify]: Simplify 1 into 1
13.980 * [backup-simplify]: Simplify (/ PI 1) into PI
13.981 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.982 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.982 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.982 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
13.983 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.984 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
13.985 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
13.987 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
13.988 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
13.989 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
13.990 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
13.994 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
13.995 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
13.995 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
13.995 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
13.995 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
13.995 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
13.995 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
13.995 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
13.995 * [taylor]: Taking taylor expansion of 1/2 in n
13.995 * [backup-simplify]: Simplify 1/2 into 1/2
13.995 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
13.995 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.995 * [taylor]: Taking taylor expansion of k in n
13.995 * [backup-simplify]: Simplify k into k
13.995 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.995 * [taylor]: Taking taylor expansion of 1 in n
13.995 * [backup-simplify]: Simplify 1 into 1
13.996 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.996 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.996 * [taylor]: Taking taylor expansion of -2 in n
13.996 * [backup-simplify]: Simplify -2 into -2
13.996 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.996 * [taylor]: Taking taylor expansion of PI in n
13.996 * [backup-simplify]: Simplify PI into PI
13.996 * [taylor]: Taking taylor expansion of n in n
13.996 * [backup-simplify]: Simplify 0 into 0
13.996 * [backup-simplify]: Simplify 1 into 1
13.996 * [backup-simplify]: Simplify (/ PI 1) into PI
13.997 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.998 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.998 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
13.998 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
13.999 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
14.000 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
14.001 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
14.001 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
14.001 * [taylor]: Taking taylor expansion of (/ -1 k) in n
14.001 * [taylor]: Taking taylor expansion of -1 in n
14.001 * [backup-simplify]: Simplify -1 into -1
14.001 * [taylor]: Taking taylor expansion of k in n
14.002 * [backup-simplify]: Simplify k into k
14.002 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
14.002 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
14.002 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
14.002 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
14.003 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
14.003 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
14.003 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
14.003 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
14.003 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
14.003 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
14.003 * [taylor]: Taking taylor expansion of 1/2 in k
14.003 * [backup-simplify]: Simplify 1/2 into 1/2
14.003 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
14.003 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.003 * [taylor]: Taking taylor expansion of k in k
14.003 * [backup-simplify]: Simplify 0 into 0
14.003 * [backup-simplify]: Simplify 1 into 1
14.006 * [backup-simplify]: Simplify (/ 1 1) into 1
14.006 * [taylor]: Taking taylor expansion of 1 in k
14.006 * [backup-simplify]: Simplify 1 into 1
14.006 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
14.006 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
14.006 * [taylor]: Taking taylor expansion of -2 in k
14.007 * [backup-simplify]: Simplify -2 into -2
14.007 * [taylor]: Taking taylor expansion of (/ PI n) in k
14.007 * [taylor]: Taking taylor expansion of PI in k
14.007 * [backup-simplify]: Simplify PI into PI
14.007 * [taylor]: Taking taylor expansion of n in k
14.007 * [backup-simplify]: Simplify n into n
14.007 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
14.007 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
14.007 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
14.007 * [backup-simplify]: Simplify (+ 1 0) into 1
14.008 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
14.008 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
14.008 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
14.008 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.008 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.008 * [taylor]: Taking taylor expansion of -1 in k
14.008 * [backup-simplify]: Simplify -1 into -1
14.008 * [taylor]: Taking taylor expansion of k in k
14.008 * [backup-simplify]: Simplify 0 into 0
14.008 * [backup-simplify]: Simplify 1 into 1
14.009 * [backup-simplify]: Simplify (/ -1 1) into -1
14.009 * [backup-simplify]: Simplify (sqrt 0) into 0
14.011 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.011 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
14.011 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
14.011 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
14.011 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
14.011 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
14.011 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
14.011 * [taylor]: Taking taylor expansion of 1/2 in k
14.011 * [backup-simplify]: Simplify 1/2 into 1/2
14.011 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
14.011 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.011 * [taylor]: Taking taylor expansion of k in k
14.011 * [backup-simplify]: Simplify 0 into 0
14.011 * [backup-simplify]: Simplify 1 into 1
14.012 * [backup-simplify]: Simplify (/ 1 1) into 1
14.012 * [taylor]: Taking taylor expansion of 1 in k
14.012 * [backup-simplify]: Simplify 1 into 1
14.012 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
14.012 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
14.012 * [taylor]: Taking taylor expansion of -2 in k
14.012 * [backup-simplify]: Simplify -2 into -2
14.012 * [taylor]: Taking taylor expansion of (/ PI n) in k
14.012 * [taylor]: Taking taylor expansion of PI in k
14.012 * [backup-simplify]: Simplify PI into PI
14.012 * [taylor]: Taking taylor expansion of n in k
14.012 * [backup-simplify]: Simplify n into n
14.012 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
14.012 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
14.012 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
14.013 * [backup-simplify]: Simplify (+ 1 0) into 1
14.013 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
14.013 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
14.013 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
14.013 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.013 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.014 * [taylor]: Taking taylor expansion of -1 in k
14.014 * [backup-simplify]: Simplify -1 into -1
14.014 * [taylor]: Taking taylor expansion of k in k
14.014 * [backup-simplify]: Simplify 0 into 0
14.014 * [backup-simplify]: Simplify 1 into 1
14.014 * [backup-simplify]: Simplify (/ -1 1) into -1
14.014 * [backup-simplify]: Simplify (sqrt 0) into 0
14.016 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.016 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
14.016 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
14.016 * [taylor]: Taking taylor expansion of +nan.0 in n
14.016 * [backup-simplify]: Simplify +nan.0 into +nan.0
14.016 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
14.016 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
14.016 * [taylor]: Taking taylor expansion of 1/2 in n
14.016 * [backup-simplify]: Simplify 1/2 into 1/2
14.016 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
14.016 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
14.017 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
14.017 * [taylor]: Taking taylor expansion of -2 in n
14.017 * [backup-simplify]: Simplify -2 into -2
14.017 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.017 * [taylor]: Taking taylor expansion of PI in n
14.017 * [backup-simplify]: Simplify PI into PI
14.017 * [taylor]: Taking taylor expansion of n in n
14.017 * [backup-simplify]: Simplify 0 into 0
14.017 * [backup-simplify]: Simplify 1 into 1
14.017 * [backup-simplify]: Simplify (/ PI 1) into PI
14.018 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
14.019 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
14.019 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
14.019 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.019 * [taylor]: Taking taylor expansion of k in n
14.019 * [backup-simplify]: Simplify k into k
14.019 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.019 * [taylor]: Taking taylor expansion of 1 in n
14.019 * [backup-simplify]: Simplify 1 into 1
14.020 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
14.020 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
14.021 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
14.022 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
14.024 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
14.025 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
14.026 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
14.027 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
14.030 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.031 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
14.031 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
14.031 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
14.031 * [taylor]: Taking taylor expansion of +nan.0 in n
14.031 * [backup-simplify]: Simplify +nan.0 into +nan.0
14.031 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
14.031 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
14.031 * [taylor]: Taking taylor expansion of 1/2 in n
14.031 * [backup-simplify]: Simplify 1/2 into 1/2
14.031 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
14.031 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
14.031 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
14.032 * [taylor]: Taking taylor expansion of -2 in n
14.032 * [backup-simplify]: Simplify -2 into -2
14.032 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.032 * [taylor]: Taking taylor expansion of PI in n
14.032 * [backup-simplify]: Simplify PI into PI
14.032 * [taylor]: Taking taylor expansion of n in n
14.032 * [backup-simplify]: Simplify 0 into 0
14.032 * [backup-simplify]: Simplify 1 into 1
14.032 * [backup-simplify]: Simplify (/ PI 1) into PI
14.033 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
14.034 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
14.034 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
14.034 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.034 * [taylor]: Taking taylor expansion of k in n
14.034 * [backup-simplify]: Simplify k into k
14.034 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.034 * [taylor]: Taking taylor expansion of 1 in n
14.034 * [backup-simplify]: Simplify 1 into 1
14.035 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
14.035 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
14.036 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
14.037 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
14.039 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
14.040 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
14.041 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
14.042 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
14.043 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
14.044 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.044 * [backup-simplify]: Simplify (+ 0 0) into 0
14.045 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.046 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
14.047 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
14.048 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
14.050 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
14.052 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.053 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
14.053 * [backup-simplify]: Simplify 0 into 0
14.054 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.058 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.060 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
14.060 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
14.060 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
14.060 * [taylor]: Taking taylor expansion of +nan.0 in n
14.060 * [backup-simplify]: Simplify +nan.0 into +nan.0
14.060 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
14.060 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
14.060 * [taylor]: Taking taylor expansion of 1/2 in n
14.060 * [backup-simplify]: Simplify 1/2 into 1/2
14.060 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
14.060 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
14.061 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
14.061 * [taylor]: Taking taylor expansion of -2 in n
14.061 * [backup-simplify]: Simplify -2 into -2
14.061 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.061 * [taylor]: Taking taylor expansion of PI in n
14.061 * [backup-simplify]: Simplify PI into PI
14.061 * [taylor]: Taking taylor expansion of n in n
14.061 * [backup-simplify]: Simplify 0 into 0
14.061 * [backup-simplify]: Simplify 1 into 1
14.061 * [backup-simplify]: Simplify (/ PI 1) into PI
14.062 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
14.063 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
14.063 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
14.063 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.063 * [taylor]: Taking taylor expansion of k in n
14.063 * [backup-simplify]: Simplify k into k
14.063 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.063 * [taylor]: Taking taylor expansion of 1 in n
14.063 * [backup-simplify]: Simplify 1 into 1
14.064 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
14.064 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
14.065 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
14.066 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
14.068 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
14.069 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
14.070 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
14.071 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
14.075 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
14.075 * * * [progress]: simplifying candidates
14.075 * * * * [progress]: [ 1 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.075 * * * * [progress]: [ 2 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.075 * * * * [progress]: [ 3 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
14.076 * * * * [progress]: [ 4 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
14.076 * * * * [progress]: [ 5 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.076 * * * * [progress]: [ 6 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.076 * * * * [progress]: [ 7 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))))))>
14.076 * * * * [progress]: [ 8 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))))))>
14.076 * * * * [progress]: [ 9 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))))))>
14.076 * * * * [progress]: [ 10 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))))))>
14.076 * * * * [progress]: [ 11 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))))>
14.076 * * * * [progress]: [ 12 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))))>
14.076 * * * * [progress]: [ 13 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))))))>
14.076 * * * * [progress]: [ 14 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))))))>
14.076 * * * * [progress]: [ 15 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)))))>
14.076 * * * * [progress]: [ 16 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))))))>
14.076 * * * * [progress]: [ 17 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))))))>
14.077 * * * * [progress]: [ 18 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)))))>
14.077 * * * * [progress]: [ 19 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))))))>
14.077 * * * * [progress]: [ 20 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))))))>
14.077 * * * * [progress]: [ 21 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)))))>
14.077 * * * * [progress]: [ 22 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))))))>
14.077 * * * * [progress]: [ 23 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))))))>
14.077 * * * * [progress]: [ 24 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)))))>
14.077 * * * * [progress]: [ 25 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))))))>
14.077 * * * * [progress]: [ 26 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))))))>
14.077 * * * * [progress]: [ 27 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))))>
14.077 * * * * [progress]: [ 28 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))))))>
14.077 * * * * [progress]: [ 29 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))))))>
14.077 * * * * [progress]: [ 30 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)))))>
14.077 * * * * [progress]: [ 31 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)))))>
14.078 * * * * [progress]: [ 32 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1 k)) (/ 1 2)))))>
14.078 * * * * [progress]: [ 33 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.078 * * * * [progress]: [ 34 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1))))>
14.078 * * * * [progress]: [ 35 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.078 * * * * [progress]: [ 36 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (log (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.078 * * * * [progress]: [ 37 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.078 * * * * [progress]: [ 38 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.078 * * * * [progress]: [ 39 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.078 * * * * [progress]: [ 40 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.078 * * * * [progress]: [ 41 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.078 * * * * [progress]: [ 42 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.078 * * * * [progress]: [ 43 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
14.078 * * * * [progress]: [ 44 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
14.078 * * * * [progress]: [ 45 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)))))>
14.078 * * * * [progress]: [ 46 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)))))>
14.078 * * * * [progress]: [ 47 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 48 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 49 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 50 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (log (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 51 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (log (exp (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 52 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 53 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 54 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 55 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 56 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 57 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 58 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 59 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 60 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 61 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)))))>
14.079 * * * * [progress]: [ 62 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
14.080 * * * * [progress]: [ 63 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
14.080 * * * * [progress]: [ 64 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (log1p (expm1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.080 * * * * [progress]: [ 65 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (expm1 (log1p (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.080 * * * * [progress]: [ 66 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (pow (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)))>
14.080 * * * * [progress]: [ 67 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
14.080 * * * * [progress]: [ 68 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
14.080 * * * * [progress]: [ 69 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.080 * * * * [progress]: [ 70 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.080 * * * * [progress]: [ 71 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.080 * * * * [progress]: [ 72 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.080 * * * * [progress]: [ 73 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (log (exp (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.080 * * * * [progress]: [ 74 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.080 * * * * [progress]: [ 75 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.080 * * * * [progress]: [ 76 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.080 * * * * [progress]: [ 77 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.080 * * * * [progress]: [ 78 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (- (sqrt k)) (- (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.081 * * * * [progress]: [ 79 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.081 * * * * [progress]: [ 80 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.081 * * * * [progress]: [ 81 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.081 * * * * [progress]: [ 82 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.081 * * * * [progress]: [ 83 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.081 * * * * [progress]: [ 84 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2))) (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.081 * * * * [progress]: [ 85 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.081 * * * * [progress]: [ 86 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.081 * * * * [progress]: [ 87 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.081 * * * * [progress]: [ 88 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.081 * * * * [progress]: [ 89 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.081 * * * * [progress]: [ 90 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.081 * * * * [progress]: [ 91 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.081 * * * * [progress]: [ 92 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.081 * * * * [progress]: [ 93 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.082 * * * * [progress]: [ 94 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.082 * * * * [progress]: [ 95 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.082 * * * * [progress]: [ 96 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.082 * * * * [progress]: [ 97 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.082 * * * * [progress]: [ 98 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.082 * * * * [progress]: [ 99 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.082 * * * * [progress]: [ 100 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.082 * * * * [progress]: [ 101 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.082 * * * * [progress]: [ 102 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.082 * * * * [progress]: [ 103 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.082 * * * * [progress]: [ 104 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.082 * * * * [progress]: [ 105 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.082 * * * * [progress]: [ 106 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.082 * * * * [progress]: [ 107 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.082 * * * * [progress]: [ 108 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.082 * * * * [progress]: [ 109 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.083 * * * * [progress]: [ 110 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.083 * * * * [progress]: [ 111 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
14.083 * * * * [progress]: [ 112 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow n (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2)))))>
14.083 * * * * [progress]: [ 113 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.083 * * * * [progress]: [ 114 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.083 * * * * [progress]: [ 115 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
14.083 * * * * [progress]: [ 116 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
14.083 * * * * [progress]: [ 117 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
14.083 * * * * [progress]: [ 118 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))))))>
14.083 * * * * [progress]: [ 119 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
14.083 * * * * [progress]: [ 120 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
14.083 * * * * [progress]: [ 121 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
14.083 * * * * [progress]: [ 122 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
14.083 * * * * [progress]: [ 123 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2))) (pow (* n (* 2 PI)) (/ k 2)))))>
14.083 * * * * [progress]: [ 124 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (posit16->real (real->posit16 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.083 * * * * [progress]: [ 125 / 315 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.084 * * * * [progress]: [ 126 / 315 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.084 * * * * [progress]: [ 127 / 315 ] simplifiying candidate #<alt (λ (k n) (pow (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) -1))>
14.084 * * * * [progress]: [ 128 / 315 ] simplifiying candidate #<alt (λ (k n) (pow (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- 1)))>
14.084 * * * * [progress]: [ 129 / 315 ] simplifiying candidate #<alt (λ (k n) (pow (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1))>
14.084 * * * * [progress]: [ 130 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
14.084 * * * * [progress]: [ 131 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
14.084 * * * * [progress]: [ 132 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.084 * * * * [progress]: [ 133 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.084 * * * * [progress]: [ 134 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.084 * * * * [progress]: [ 135 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.084 * * * * [progress]: [ 136 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
14.084 * * * * [progress]: [ 137 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
14.084 * * * * [progress]: [ 138 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.084 * * * * [progress]: [ 139 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.084 * * * * [progress]: [ 140 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.084 * * * * [progress]: [ 141 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.085 * * * * [progress]: [ 142 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
14.085 * * * * [progress]: [ 143 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
14.085 * * * * [progress]: [ 144 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.085 * * * * [progress]: [ 145 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
14.085 * * * * [progress]: [ 146 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.085 * * * * [progress]: [ 147 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.085 * * * * [progress]: [ 148 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.085 * * * * [progress]: [ 149 / 315 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.085 * * * * [progress]: [ 150 / 315 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* 1 1) 1) (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.085 * * * * [progress]: [ 151 / 315 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* 1 1) 1) (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.085 * * * * [progress]: [ 152 / 315 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.086 * * * * [progress]: [ 153 / 315 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.086 * * * * [progress]: [ 154 / 315 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (sqrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.086 * * * * [progress]: [ 155 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (- 1) (- (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.086 * * * * [progress]: [ 156 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.086 * * * * [progress]: [ 157 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.086 * * * * [progress]: [ 158 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.086 * * * * [progress]: [ 159 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.086 * * * * [progress]: [ 160 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.086 * * * * [progress]: [ 161 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.086 * * * * [progress]: [ 162 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.086 * * * * [progress]: [ 163 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.086 * * * * [progress]: [ 164 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.087 * * * * [progress]: [ 165 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.087 * * * * [progress]: [ 166 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.087 * * * * [progress]: [ 167 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.087 * * * * [progress]: [ 168 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.087 * * * * [progress]: [ 169 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.087 * * * * [progress]: [ 170 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.087 * * * * [progress]: [ 171 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) 1)) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.087 * * * * [progress]: [ 172 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.087 * * * * [progress]: [ 173 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.087 * * * * [progress]: [ 174 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.087 * * * * [progress]: [ 175 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.087 * * * * [progress]: [ 176 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) 1)) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.087 * * * * [progress]: [ 177 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.088 * * * * [progress]: [ 178 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.088 * * * * [progress]: [ 179 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.088 * * * * [progress]: [ 180 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.088 * * * * [progress]: [ 181 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) 1)) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.088 * * * * [progress]: [ 182 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.088 * * * * [progress]: [ 183 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.088 * * * * [progress]: [ 184 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.088 * * * * [progress]: [ 185 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.088 * * * * [progress]: [ 186 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 1)) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.088 * * * * [progress]: [ 187 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.088 * * * * [progress]: [ 188 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.088 * * * * [progress]: [ 189 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt k)) (/ (cbrt 1) (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.088 * * * * [progress]: [ 190 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2)))) (/ (cbrt 1) (pow (* n (* 2 PI)) (/ k 2)))))>
14.088 * * * * [progress]: [ 191 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.089 * * * * [progress]: [ 192 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.089 * * * * [progress]: [ 193 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.089 * * * * [progress]: [ 194 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.089 * * * * [progress]: [ 195 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.089 * * * * [progress]: [ 196 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.089 * * * * [progress]: [ 197 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.089 * * * * [progress]: [ 198 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.089 * * * * [progress]: [ 199 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.089 * * * * [progress]: [ 200 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.089 * * * * [progress]: [ 201 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.089 * * * * [progress]: [ 202 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.089 * * * * [progress]: [ 203 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.089 * * * * [progress]: [ 204 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.089 * * * * [progress]: [ 205 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.090 * * * * [progress]: [ 206 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) 1)) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.090 * * * * [progress]: [ 207 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.090 * * * * [progress]: [ 208 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.090 * * * * [progress]: [ 209 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.090 * * * * [progress]: [ 210 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.090 * * * * [progress]: [ 211 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) 1)) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.090 * * * * [progress]: [ 212 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.090 * * * * [progress]: [ 213 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.090 * * * * [progress]: [ 214 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.090 * * * * [progress]: [ 215 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.090 * * * * [progress]: [ 216 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) 1)) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.090 * * * * [progress]: [ 217 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.090 * * * * [progress]: [ 218 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.090 * * * * [progress]: [ 219 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.090 * * * * [progress]: [ 220 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.090 * * * * [progress]: [ 221 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 1)) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.090 * * * * [progress]: [ 222 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.091 * * * * [progress]: [ 223 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 224 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt k)) (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 225 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2)))) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ k 2)))))>
14.091 * * * * [progress]: [ 226 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 227 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 228 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 229 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 230 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 231 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 232 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.091 * * * * [progress]: [ 233 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 234 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 235 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 236 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 237 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.091 * * * * [progress]: [ 238 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 239 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 240 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 241 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 242 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.091 * * * * [progress]: [ 243 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 244 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 245 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.091 * * * * [progress]: [ 246 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) 1)) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.091 * * * * [progress]: [ 247 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.092 * * * * [progress]: [ 248 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 249 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.092 * * * * [progress]: [ 250 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.092 * * * * [progress]: [ 251 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 252 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.092 * * * * [progress]: [ 253 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 254 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.092 * * * * [progress]: [ 255 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.092 * * * * [progress]: [ 256 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 1)) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 257 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
14.092 * * * * [progress]: [ 258 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 259 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 260 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2)))) (/ 1 (pow (* n (* 2 PI)) (/ k 2)))))>
14.092 * * * * [progress]: [ 261 / 315 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 262 / 315 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 263 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)))>
14.092 * * * * [progress]: [ 264 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 265 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 266 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))))>
14.092 * * * * [progress]: [ 267 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 268 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.092 * * * * [progress]: [ 269 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
14.092 * * * * [progress]: [ 270 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
14.092 * * * * [progress]: [ 271 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))) (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))))>
14.092 * * * * [progress]: [ 272 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 273 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 274 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
14.093 * * * * [progress]: [ 275 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
14.093 * * * * [progress]: [ 276 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))))>
14.093 * * * * [progress]: [ 277 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 278 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 279 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
14.093 * * * * [progress]: [ 280 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
14.093 * * * * [progress]: [ 281 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow n (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))))>
14.093 * * * * [progress]: [ 282 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 283 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 284 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
14.093 * * * * [progress]: [ 285 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
14.093 * * * * [progress]: [ 286 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))))>
14.093 * * * * [progress]: [ 287 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 288 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 289 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
14.093 * * * * [progress]: [ 290 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
14.093 * * * * [progress]: [ 291 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow n (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))))>
14.093 * * * * [progress]: [ 292 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 293 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
14.093 * * * * [progress]: [ 294 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
14.093 * * * * [progress]: [ 295 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
14.093 * * * * [progress]: [ 296 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
14.094 * * * * [progress]: [ 297 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
14.094 * * * * [progress]: [ 298 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2)))) (pow (* n (* 2 PI)) (/ k 2))))>
14.094 * * * * [progress]: [ 299 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt 1) (cbrt 1)) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt 1))))>
14.094 * * * * [progress]: [ 300 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt 1) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))))>
14.094 * * * * [progress]: [ 301 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)))>
14.094 * * * * [progress]: [ 302 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
14.094 * * * * [progress]: [ 303 / 315 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
14.094 * * * * [progress]: [ 304 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))))))>
14.094 * * * * [progress]: [ 305 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))))>
14.094 * * * * [progress]: [ 306 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))>
14.094 * * * * [progress]: [ 307 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
14.094 * * * * [progress]: [ 308 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
14.094 * * * * [progress]: [ 309 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
14.094 * * * * [progress]: [ 310 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))))>
14.094 * * * * [progress]: [ 311 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))))>
14.094 * * * * [progress]: [ 312 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))))>
14.094 * * * * [progress]: [ 313 / 315 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))>
14.094 * * * * [progress]: [ 314 / 315 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
14.094 * * * * [progress]: [ 315 / 315 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
14.098 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* n (* 2 PI)) (/ 1 2))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (expm1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (log1p (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)))
  (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)))
  (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2)))
  (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2)))
  (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (exp (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (- (sqrt k))
  (- (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))
  (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))
  (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
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  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt 1) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt 1) 1))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ 1 1))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 1)
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (sqrt k))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2))))
  (/ 1 (pow (* n (* 2 PI)) (/ k 2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt 1) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt 1) 1))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
  (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ 1 1))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2))))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt 1))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)
  (/ 1 (sqrt k))
  (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))
  (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))
  (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
14.105 * * [simplify]: iteration 1: (535 enodes)
14.367 * * [simplify]: iteration 2: (1448 enodes)
15.608 * * [simplify]: Extracting #0: cost 161 inf + 0
15.610 * * [simplify]: Extracting #1: cost 723 inf + 2
15.615 * * [simplify]: Extracting #2: cost 1017 inf + 17585
15.635 * * [simplify]: Extracting #3: cost 748 inf + 155440
15.710 * * [simplify]: Extracting #4: cost 465 inf + 290888
15.792 * * [simplify]: Extracting #5: cost 232 inf + 373127
15.879 * * [simplify]: Extracting #6: cost 61 inf + 431796
16.007 * * [simplify]: Extracting #7: cost 6 inf + 462637
16.119 * * [simplify]: Extracting #8: cost 0 inf + 466629
16.236 * * [simplify]: Extracting #9: cost 0 inf + 466264
16.347 * * [simplify]: Extracting #10: cost 0 inf + 466174
16.469 * [simplify]: Simplified to:
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (/ (+ 1 (sqrt k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* PI 2) n) (+ 1 (sqrt k)))
  (pow (* (* PI 2) n) (/ (/ (+ 1 (sqrt k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* PI 2) n) (+ 1 (sqrt k)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* PI 2) (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (expm1 (* (* PI 2) n))
  (log1p (* (* PI 2) n))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* 8 (* (* n n) n)) (* (* PI PI) PI))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* 2 (* PI (cbrt n)))
  (* (* 2 (sqrt n)) PI)
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (expm1 (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (log1p (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n))))
  (exp (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (pow (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))) 3)
  (* (cbrt (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
  (cbrt (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (pow (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))) 3)
  (sqrt (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (sqrt (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (- (sqrt k))
  (- (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (cbrt (sqrt k)) (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt k))))
  (/ (cbrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
  (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (* (cbrt (sqrt k)) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (cbrt (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (fabs (cbrt k)) (pow n (/ (- 1 k) 2)))
  (/ (sqrt (cbrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (fabs (cbrt k)) (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (fabs (cbrt k)) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (fabs (cbrt k))
  (/ (sqrt (cbrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (fabs (cbrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (sqrt (cbrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ 1 (pow n (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (/ 1 (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ 1 (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  1
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ 1 (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (sqrt (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ 1 (pow n (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (/ 1 (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ 1 (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  1
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ 1 (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ 1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (sqrt k) (pow n (/ (- 1 k) 2)))
  (/ (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (sqrt k)
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (sqrt k) (sqrt (* (* PI 2) n)))
  (real->posit16 (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (expm1 (/ (* 1 (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k)))
  (log1p (/ (* 1 (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k)))
  -1
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n)))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n)))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n)))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n)))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n)))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n)))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n)))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n)))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* (* PI 2) n)))))
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  (- (+ (- (/ +nan.0 (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k))))) (/ (/ +nan.0 (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k))))) (* k k))) (/ +nan.0 (* k (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k))))))))
  (- (- (* (/ +nan.0 k) (exp (* (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)) -1/2))) (* +nan.0 (- (/ (exp (* (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)) -1/2)) (* k k)) (exp (* (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)) -1/2))))))
  (- (- (* (sqrt 2) (* (* (* n PI) k) +nan.0)) (- (* (* (* +nan.0 (sqrt 2)) n) PI) (- (* (* (sqrt 2) (* (* (* n PI) k) +nan.0)) (log (* PI 2))) (* (* +nan.0 (sqrt 2)) (- (* (* n PI) (* (log n) k)) (* (* PI n) (* PI n))))))))
  (+ (* (- +nan.0) (/ (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k)))) k)) (* +nan.0 (- (/ (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k)))) (* k k)) (/ (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k)))) (* k (* k k))))))
  (- (+ (- (/ (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) +nan.0) k) (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (/ (* k k) +nan.0))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) +nan.0)))
16.503 * * * [progress]: adding candidates to table
20.196 * * [progress]: iteration 3 / 4
20.196 * * * [progress]: picking best candidate
20.223 * * * * [pick]: Picked  #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
20.223 * * * [progress]: localizing error
20.249 * * * [progress]: generating rewritten candidates
20.249 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1)
20.268 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1 1)
20.300 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2)
20.323 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2)
20.351 * * * [progress]: generating series expansions
20.351 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1)
20.352 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
20.352 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
20.353 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
20.353 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
20.353 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
20.353 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
20.353 * [taylor]: Taking taylor expansion of 1/2 in k
20.353 * [backup-simplify]: Simplify 1/2 into 1/2
20.353 * [taylor]: Taking taylor expansion of (- 1 k) in k
20.353 * [taylor]: Taking taylor expansion of 1 in k
20.353 * [backup-simplify]: Simplify 1 into 1
20.353 * [taylor]: Taking taylor expansion of k in k
20.353 * [backup-simplify]: Simplify 0 into 0
20.353 * [backup-simplify]: Simplify 1 into 1
20.353 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
20.353 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
20.353 * [taylor]: Taking taylor expansion of 2 in k
20.353 * [backup-simplify]: Simplify 2 into 2
20.353 * [taylor]: Taking taylor expansion of (* n PI) in k
20.353 * [taylor]: Taking taylor expansion of n in k
20.353 * [backup-simplify]: Simplify n into n
20.353 * [taylor]: Taking taylor expansion of PI in k
20.353 * [backup-simplify]: Simplify PI into PI
20.353 * [backup-simplify]: Simplify (* n PI) into (* n PI)
20.353 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
20.353 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
20.354 * [backup-simplify]: Simplify (- 0) into 0
20.354 * [backup-simplify]: Simplify (+ 1 0) into 1
20.355 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
20.355 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
20.355 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
20.355 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
20.355 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
20.355 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
20.355 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
20.355 * [taylor]: Taking taylor expansion of 1/2 in n
20.355 * [backup-simplify]: Simplify 1/2 into 1/2
20.355 * [taylor]: Taking taylor expansion of (- 1 k) in n
20.355 * [taylor]: Taking taylor expansion of 1 in n
20.355 * [backup-simplify]: Simplify 1 into 1
20.355 * [taylor]: Taking taylor expansion of k in n
20.355 * [backup-simplify]: Simplify k into k
20.355 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
20.355 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.355 * [taylor]: Taking taylor expansion of 2 in n
20.355 * [backup-simplify]: Simplify 2 into 2
20.355 * [taylor]: Taking taylor expansion of (* n PI) in n
20.355 * [taylor]: Taking taylor expansion of n in n
20.355 * [backup-simplify]: Simplify 0 into 0
20.355 * [backup-simplify]: Simplify 1 into 1
20.355 * [taylor]: Taking taylor expansion of PI in n
20.355 * [backup-simplify]: Simplify PI into PI
20.356 * [backup-simplify]: Simplify (* 0 PI) into 0
20.356 * [backup-simplify]: Simplify (* 2 0) into 0
20.358 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.359 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
20.360 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.360 * [backup-simplify]: Simplify (- k) into (- k)
20.361 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
20.361 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
20.362 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.363 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
20.364 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
20.364 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
20.364 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
20.364 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
20.364 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
20.364 * [taylor]: Taking taylor expansion of 1/2 in n
20.364 * [backup-simplify]: Simplify 1/2 into 1/2
20.364 * [taylor]: Taking taylor expansion of (- 1 k) in n
20.364 * [taylor]: Taking taylor expansion of 1 in n
20.364 * [backup-simplify]: Simplify 1 into 1
20.364 * [taylor]: Taking taylor expansion of k in n
20.364 * [backup-simplify]: Simplify k into k
20.364 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
20.365 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.365 * [taylor]: Taking taylor expansion of 2 in n
20.365 * [backup-simplify]: Simplify 2 into 2
20.365 * [taylor]: Taking taylor expansion of (* n PI) in n
20.365 * [taylor]: Taking taylor expansion of n in n
20.365 * [backup-simplify]: Simplify 0 into 0
20.365 * [backup-simplify]: Simplify 1 into 1
20.365 * [taylor]: Taking taylor expansion of PI in n
20.365 * [backup-simplify]: Simplify PI into PI
20.365 * [backup-simplify]: Simplify (* 0 PI) into 0
20.366 * [backup-simplify]: Simplify (* 2 0) into 0
20.367 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.369 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
20.370 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.370 * [backup-simplify]: Simplify (- k) into (- k)
20.370 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
20.370 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
20.371 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.372 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
20.373 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
20.373 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
20.373 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
20.373 * [taylor]: Taking taylor expansion of 1/2 in k
20.373 * [backup-simplify]: Simplify 1/2 into 1/2
20.373 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
20.374 * [taylor]: Taking taylor expansion of (- 1 k) in k
20.374 * [taylor]: Taking taylor expansion of 1 in k
20.374 * [backup-simplify]: Simplify 1 into 1
20.374 * [taylor]: Taking taylor expansion of k in k
20.374 * [backup-simplify]: Simplify 0 into 0
20.374 * [backup-simplify]: Simplify 1 into 1
20.374 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
20.374 * [taylor]: Taking taylor expansion of (log n) in k
20.374 * [taylor]: Taking taylor expansion of n in k
20.374 * [backup-simplify]: Simplify n into n
20.374 * [backup-simplify]: Simplify (log n) into (log n)
20.374 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
20.374 * [taylor]: Taking taylor expansion of (* 2 PI) in k
20.374 * [taylor]: Taking taylor expansion of 2 in k
20.374 * [backup-simplify]: Simplify 2 into 2
20.374 * [taylor]: Taking taylor expansion of PI in k
20.374 * [backup-simplify]: Simplify PI into PI
20.374 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.375 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.376 * [backup-simplify]: Simplify (- 0) into 0
20.376 * [backup-simplify]: Simplify (+ 1 0) into 1
20.377 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.378 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
20.379 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
20.380 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
20.381 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
20.383 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
20.384 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
20.386 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
20.386 * [backup-simplify]: Simplify (- 0) into 0
20.386 * [backup-simplify]: Simplify (+ 0 0) into 0
20.387 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
20.388 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.389 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
20.391 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.391 * [taylor]: Taking taylor expansion of 0 in k
20.391 * [backup-simplify]: Simplify 0 into 0
20.391 * [backup-simplify]: Simplify 0 into 0
20.392 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
20.393 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
20.395 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
20.395 * [backup-simplify]: Simplify (+ 0 0) into 0
20.396 * [backup-simplify]: Simplify (- 1) into -1
20.396 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.397 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
20.399 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
20.402 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
20.405 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
20.407 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
20.408 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
20.411 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
20.412 * [backup-simplify]: Simplify (- 0) into 0
20.412 * [backup-simplify]: Simplify (+ 0 0) into 0
20.413 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
20.414 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.416 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
20.418 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.418 * [taylor]: Taking taylor expansion of 0 in k
20.418 * [backup-simplify]: Simplify 0 into 0
20.418 * [backup-simplify]: Simplify 0 into 0
20.419 * [backup-simplify]: Simplify 0 into 0
20.420 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
20.421 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
20.434 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
20.436 * [backup-simplify]: Simplify (+ 0 0) into 0
20.436 * [backup-simplify]: Simplify (- 0) into 0
20.437 * [backup-simplify]: Simplify (+ 0 0) into 0
20.438 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
20.441 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
20.445 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
20.450 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
20.459 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
20.460 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
20.460 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
20.460 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
20.460 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
20.460 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
20.460 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
20.460 * [taylor]: Taking taylor expansion of 1/2 in k
20.460 * [backup-simplify]: Simplify 1/2 into 1/2
20.461 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
20.461 * [taylor]: Taking taylor expansion of 1 in k
20.461 * [backup-simplify]: Simplify 1 into 1
20.461 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.461 * [taylor]: Taking taylor expansion of k in k
20.461 * [backup-simplify]: Simplify 0 into 0
20.461 * [backup-simplify]: Simplify 1 into 1
20.461 * [backup-simplify]: Simplify (/ 1 1) into 1
20.461 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
20.461 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
20.461 * [taylor]: Taking taylor expansion of 2 in k
20.461 * [backup-simplify]: Simplify 2 into 2
20.461 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.461 * [taylor]: Taking taylor expansion of PI in k
20.461 * [backup-simplify]: Simplify PI into PI
20.461 * [taylor]: Taking taylor expansion of n in k
20.461 * [backup-simplify]: Simplify n into n
20.461 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.461 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
20.462 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
20.462 * [backup-simplify]: Simplify (- 1) into -1
20.462 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.463 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
20.463 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
20.463 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
20.463 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
20.463 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
20.463 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
20.463 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
20.463 * [taylor]: Taking taylor expansion of 1/2 in n
20.463 * [backup-simplify]: Simplify 1/2 into 1/2
20.463 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
20.463 * [taylor]: Taking taylor expansion of 1 in n
20.463 * [backup-simplify]: Simplify 1 into 1
20.463 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.463 * [taylor]: Taking taylor expansion of k in n
20.463 * [backup-simplify]: Simplify k into k
20.464 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.464 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
20.464 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.464 * [taylor]: Taking taylor expansion of 2 in n
20.464 * [backup-simplify]: Simplify 2 into 2
20.464 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.464 * [taylor]: Taking taylor expansion of PI in n
20.464 * [backup-simplify]: Simplify PI into PI
20.464 * [taylor]: Taking taylor expansion of n in n
20.464 * [backup-simplify]: Simplify 0 into 0
20.464 * [backup-simplify]: Simplify 1 into 1
20.464 * [backup-simplify]: Simplify (/ PI 1) into PI
20.465 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.466 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.466 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.466 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
20.466 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
20.468 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.469 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
20.470 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
20.470 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
20.470 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
20.470 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
20.470 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
20.470 * [taylor]: Taking taylor expansion of 1/2 in n
20.470 * [backup-simplify]: Simplify 1/2 into 1/2
20.470 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
20.470 * [taylor]: Taking taylor expansion of 1 in n
20.470 * [backup-simplify]: Simplify 1 into 1
20.470 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.470 * [taylor]: Taking taylor expansion of k in n
20.470 * [backup-simplify]: Simplify k into k
20.470 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.470 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
20.470 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.470 * [taylor]: Taking taylor expansion of 2 in n
20.470 * [backup-simplify]: Simplify 2 into 2
20.471 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.471 * [taylor]: Taking taylor expansion of PI in n
20.471 * [backup-simplify]: Simplify PI into PI
20.471 * [taylor]: Taking taylor expansion of n in n
20.471 * [backup-simplify]: Simplify 0 into 0
20.471 * [backup-simplify]: Simplify 1 into 1
20.471 * [backup-simplify]: Simplify (/ PI 1) into PI
20.472 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.473 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.473 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.473 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
20.473 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
20.474 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.475 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
20.477 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
20.477 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
20.477 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
20.477 * [taylor]: Taking taylor expansion of 1/2 in k
20.477 * [backup-simplify]: Simplify 1/2 into 1/2
20.477 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
20.477 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
20.477 * [taylor]: Taking taylor expansion of 1 in k
20.477 * [backup-simplify]: Simplify 1 into 1
20.477 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.477 * [taylor]: Taking taylor expansion of k in k
20.477 * [backup-simplify]: Simplify 0 into 0
20.477 * [backup-simplify]: Simplify 1 into 1
20.478 * [backup-simplify]: Simplify (/ 1 1) into 1
20.478 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
20.478 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
20.478 * [taylor]: Taking taylor expansion of (* 2 PI) in k
20.478 * [taylor]: Taking taylor expansion of 2 in k
20.478 * [backup-simplify]: Simplify 2 into 2
20.478 * [taylor]: Taking taylor expansion of PI in k
20.478 * [backup-simplify]: Simplify PI into PI
20.479 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.480 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.480 * [taylor]: Taking taylor expansion of (log n) in k
20.480 * [taylor]: Taking taylor expansion of n in k
20.480 * [backup-simplify]: Simplify n into n
20.480 * [backup-simplify]: Simplify (log n) into (log n)
20.481 * [backup-simplify]: Simplify (- 1) into -1
20.481 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.481 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.482 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
20.483 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
20.484 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
20.486 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
20.487 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
20.488 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.488 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
20.490 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
20.490 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.491 * [backup-simplify]: Simplify (- 0) into 0
20.491 * [backup-simplify]: Simplify (+ 0 0) into 0
20.492 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
20.493 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.495 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
20.497 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.497 * [taylor]: Taking taylor expansion of 0 in k
20.497 * [backup-simplify]: Simplify 0 into 0
20.497 * [backup-simplify]: Simplify 0 into 0
20.497 * [backup-simplify]: Simplify 0 into 0
20.498 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.499 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
20.502 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
20.503 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.503 * [backup-simplify]: Simplify (- 0) into 0
20.504 * [backup-simplify]: Simplify (+ 0 0) into 0
20.505 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
20.506 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.508 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
20.510 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.510 * [taylor]: Taking taylor expansion of 0 in k
20.510 * [backup-simplify]: Simplify 0 into 0
20.510 * [backup-simplify]: Simplify 0 into 0
20.510 * [backup-simplify]: Simplify 0 into 0
20.510 * [backup-simplify]: Simplify 0 into 0
20.512 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.513 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.519 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
20.520 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.520 * [backup-simplify]: Simplify (- 0) into 0
20.521 * [backup-simplify]: Simplify (+ 0 0) into 0
20.522 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
20.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.525 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
20.528 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.528 * [taylor]: Taking taylor expansion of 0 in k
20.528 * [backup-simplify]: Simplify 0 into 0
20.529 * [backup-simplify]: Simplify 0 into 0
20.530 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
20.530 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
20.531 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
20.531 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
20.531 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
20.531 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
20.531 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
20.531 * [taylor]: Taking taylor expansion of 1/2 in k
20.531 * [backup-simplify]: Simplify 1/2 into 1/2
20.531 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
20.531 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.531 * [taylor]: Taking taylor expansion of k in k
20.531 * [backup-simplify]: Simplify 0 into 0
20.531 * [backup-simplify]: Simplify 1 into 1
20.531 * [backup-simplify]: Simplify (/ 1 1) into 1
20.531 * [taylor]: Taking taylor expansion of 1 in k
20.531 * [backup-simplify]: Simplify 1 into 1
20.531 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
20.531 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
20.531 * [taylor]: Taking taylor expansion of -2 in k
20.531 * [backup-simplify]: Simplify -2 into -2
20.531 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.531 * [taylor]: Taking taylor expansion of PI in k
20.532 * [backup-simplify]: Simplify PI into PI
20.532 * [taylor]: Taking taylor expansion of n in k
20.532 * [backup-simplify]: Simplify n into n
20.532 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.532 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
20.532 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
20.532 * [backup-simplify]: Simplify (+ 1 0) into 1
20.533 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
20.533 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
20.533 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
20.533 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
20.533 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
20.533 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
20.533 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
20.533 * [taylor]: Taking taylor expansion of 1/2 in n
20.533 * [backup-simplify]: Simplify 1/2 into 1/2
20.533 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
20.533 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.533 * [taylor]: Taking taylor expansion of k in n
20.533 * [backup-simplify]: Simplify k into k
20.533 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.533 * [taylor]: Taking taylor expansion of 1 in n
20.534 * [backup-simplify]: Simplify 1 into 1
20.534 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
20.534 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.534 * [taylor]: Taking taylor expansion of -2 in n
20.534 * [backup-simplify]: Simplify -2 into -2
20.534 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.534 * [taylor]: Taking taylor expansion of PI in n
20.534 * [backup-simplify]: Simplify PI into PI
20.534 * [taylor]: Taking taylor expansion of n in n
20.534 * [backup-simplify]: Simplify 0 into 0
20.534 * [backup-simplify]: Simplify 1 into 1
20.534 * [backup-simplify]: Simplify (/ PI 1) into PI
20.535 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.536 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
20.536 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
20.536 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
20.537 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.539 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
20.540 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
20.540 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
20.540 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
20.540 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
20.540 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
20.540 * [taylor]: Taking taylor expansion of 1/2 in n
20.540 * [backup-simplify]: Simplify 1/2 into 1/2
20.540 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
20.540 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.540 * [taylor]: Taking taylor expansion of k in n
20.540 * [backup-simplify]: Simplify k into k
20.540 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.540 * [taylor]: Taking taylor expansion of 1 in n
20.540 * [backup-simplify]: Simplify 1 into 1
20.540 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
20.540 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.540 * [taylor]: Taking taylor expansion of -2 in n
20.540 * [backup-simplify]: Simplify -2 into -2
20.541 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.541 * [taylor]: Taking taylor expansion of PI in n
20.541 * [backup-simplify]: Simplify PI into PI
20.541 * [taylor]: Taking taylor expansion of n in n
20.541 * [backup-simplify]: Simplify 0 into 0
20.541 * [backup-simplify]: Simplify 1 into 1
20.541 * [backup-simplify]: Simplify (/ PI 1) into PI
20.542 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.543 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
20.543 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
20.543 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
20.544 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.545 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
20.547 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
20.547 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
20.547 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
20.547 * [taylor]: Taking taylor expansion of 1/2 in k
20.547 * [backup-simplify]: Simplify 1/2 into 1/2
20.547 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
20.547 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
20.547 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.547 * [taylor]: Taking taylor expansion of k in k
20.547 * [backup-simplify]: Simplify 0 into 0
20.548 * [backup-simplify]: Simplify 1 into 1
20.548 * [backup-simplify]: Simplify (/ 1 1) into 1
20.548 * [taylor]: Taking taylor expansion of 1 in k
20.548 * [backup-simplify]: Simplify 1 into 1
20.548 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
20.548 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
20.548 * [taylor]: Taking taylor expansion of (* -2 PI) in k
20.548 * [taylor]: Taking taylor expansion of -2 in k
20.548 * [backup-simplify]: Simplify -2 into -2
20.548 * [taylor]: Taking taylor expansion of PI in k
20.548 * [backup-simplify]: Simplify PI into PI
20.549 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.550 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
20.550 * [taylor]: Taking taylor expansion of (log n) in k
20.550 * [taylor]: Taking taylor expansion of n in k
20.550 * [backup-simplify]: Simplify n into n
20.550 * [backup-simplify]: Simplify (log n) into (log n)
20.550 * [backup-simplify]: Simplify (+ 1 0) into 1
20.550 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.551 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
20.552 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
20.554 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
20.555 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
20.556 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
20.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.558 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
20.560 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
20.560 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.560 * [backup-simplify]: Simplify (+ 0 0) into 0
20.561 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
20.562 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.563 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
20.565 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.566 * [taylor]: Taking taylor expansion of 0 in k
20.566 * [backup-simplify]: Simplify 0 into 0
20.566 * [backup-simplify]: Simplify 0 into 0
20.566 * [backup-simplify]: Simplify 0 into 0
20.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.568 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
20.572 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
20.572 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.573 * [backup-simplify]: Simplify (+ 0 0) into 0
20.574 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
20.576 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.577 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
20.580 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.580 * [taylor]: Taking taylor expansion of 0 in k
20.580 * [backup-simplify]: Simplify 0 into 0
20.580 * [backup-simplify]: Simplify 0 into 0
20.580 * [backup-simplify]: Simplify 0 into 0
20.580 * [backup-simplify]: Simplify 0 into 0
20.582 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.584 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.596 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
20.596 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.597 * [backup-simplify]: Simplify (+ 0 0) into 0
20.598 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
20.599 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.600 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
20.602 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.602 * [taylor]: Taking taylor expansion of 0 in k
20.602 * [backup-simplify]: Simplify 0 into 0
20.602 * [backup-simplify]: Simplify 0 into 0
20.603 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
20.603 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1 1)
20.603 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
20.604 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
20.604 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.604 * [taylor]: Taking taylor expansion of 2 in n
20.604 * [backup-simplify]: Simplify 2 into 2
20.604 * [taylor]: Taking taylor expansion of (* n PI) in n
20.604 * [taylor]: Taking taylor expansion of n in n
20.604 * [backup-simplify]: Simplify 0 into 0
20.604 * [backup-simplify]: Simplify 1 into 1
20.604 * [taylor]: Taking taylor expansion of PI in n
20.604 * [backup-simplify]: Simplify PI into PI
20.604 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.604 * [taylor]: Taking taylor expansion of 2 in n
20.604 * [backup-simplify]: Simplify 2 into 2
20.604 * [taylor]: Taking taylor expansion of (* n PI) in n
20.604 * [taylor]: Taking taylor expansion of n in n
20.604 * [backup-simplify]: Simplify 0 into 0
20.604 * [backup-simplify]: Simplify 1 into 1
20.604 * [taylor]: Taking taylor expansion of PI in n
20.604 * [backup-simplify]: Simplify PI into PI
20.604 * [backup-simplify]: Simplify (* 0 PI) into 0
20.604 * [backup-simplify]: Simplify (* 2 0) into 0
20.604 * [backup-simplify]: Simplify 0 into 0
20.605 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.606 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
20.607 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.607 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
20.608 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
20.608 * [backup-simplify]: Simplify 0 into 0
20.609 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
20.610 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
20.610 * [backup-simplify]: Simplify 0 into 0
20.610 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.611 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
20.611 * [backup-simplify]: Simplify 0 into 0
20.612 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.613 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
20.613 * [backup-simplify]: Simplify 0 into 0
20.614 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.615 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
20.615 * [backup-simplify]: Simplify 0 into 0
20.616 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
20.617 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
20.617 * [backup-simplify]: Simplify 0 into 0
20.618 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
20.618 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
20.618 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
20.618 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.618 * [taylor]: Taking taylor expansion of 2 in n
20.618 * [backup-simplify]: Simplify 2 into 2
20.618 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.618 * [taylor]: Taking taylor expansion of PI in n
20.618 * [backup-simplify]: Simplify PI into PI
20.618 * [taylor]: Taking taylor expansion of n in n
20.618 * [backup-simplify]: Simplify 0 into 0
20.618 * [backup-simplify]: Simplify 1 into 1
20.619 * [backup-simplify]: Simplify (/ PI 1) into PI
20.619 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.619 * [taylor]: Taking taylor expansion of 2 in n
20.619 * [backup-simplify]: Simplify 2 into 2
20.619 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.619 * [taylor]: Taking taylor expansion of PI in n
20.619 * [backup-simplify]: Simplify PI into PI
20.619 * [taylor]: Taking taylor expansion of n in n
20.619 * [backup-simplify]: Simplify 0 into 0
20.619 * [backup-simplify]: Simplify 1 into 1
20.619 * [backup-simplify]: Simplify (/ PI 1) into PI
20.619 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.620 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.621 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.621 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
20.621 * [backup-simplify]: Simplify 0 into 0
20.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.623 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
20.623 * [backup-simplify]: Simplify 0 into 0
20.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.624 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.624 * [backup-simplify]: Simplify 0 into 0
20.625 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.626 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.626 * [backup-simplify]: Simplify 0 into 0
20.627 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.627 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.627 * [backup-simplify]: Simplify 0 into 0
20.628 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.629 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.629 * [backup-simplify]: Simplify 0 into 0
20.629 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
20.630 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
20.630 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
20.630 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.630 * [taylor]: Taking taylor expansion of -2 in n
20.630 * [backup-simplify]: Simplify -2 into -2
20.630 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.630 * [taylor]: Taking taylor expansion of PI in n
20.630 * [backup-simplify]: Simplify PI into PI
20.630 * [taylor]: Taking taylor expansion of n in n
20.630 * [backup-simplify]: Simplify 0 into 0
20.630 * [backup-simplify]: Simplify 1 into 1
20.630 * [backup-simplify]: Simplify (/ PI 1) into PI
20.630 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.630 * [taylor]: Taking taylor expansion of -2 in n
20.630 * [backup-simplify]: Simplify -2 into -2
20.630 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.630 * [taylor]: Taking taylor expansion of PI in n
20.630 * [backup-simplify]: Simplify PI into PI
20.630 * [taylor]: Taking taylor expansion of n in n
20.630 * [backup-simplify]: Simplify 0 into 0
20.630 * [backup-simplify]: Simplify 1 into 1
20.631 * [backup-simplify]: Simplify (/ PI 1) into PI
20.631 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.631 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.632 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
20.632 * [backup-simplify]: Simplify 0 into 0
20.633 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.633 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
20.634 * [backup-simplify]: Simplify 0 into 0
20.634 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.635 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.635 * [backup-simplify]: Simplify 0 into 0
20.636 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.636 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.636 * [backup-simplify]: Simplify 0 into 0
20.637 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.638 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.638 * [backup-simplify]: Simplify 0 into 0
20.638 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.639 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.639 * [backup-simplify]: Simplify 0 into 0
20.640 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
20.640 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2)
20.640 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
20.640 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (n k) around 0
20.640 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
20.640 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
20.640 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
20.640 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
20.640 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
20.640 * [taylor]: Taking taylor expansion of 1/2 in k
20.640 * [backup-simplify]: Simplify 1/2 into 1/2
20.640 * [taylor]: Taking taylor expansion of (- 1 k) in k
20.640 * [taylor]: Taking taylor expansion of 1 in k
20.641 * [backup-simplify]: Simplify 1 into 1
20.641 * [taylor]: Taking taylor expansion of k in k
20.641 * [backup-simplify]: Simplify 0 into 0
20.641 * [backup-simplify]: Simplify 1 into 1
20.641 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
20.641 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
20.641 * [taylor]: Taking taylor expansion of 2 in k
20.641 * [backup-simplify]: Simplify 2 into 2
20.641 * [taylor]: Taking taylor expansion of (* n PI) in k
20.641 * [taylor]: Taking taylor expansion of n in k
20.641 * [backup-simplify]: Simplify n into n
20.641 * [taylor]: Taking taylor expansion of PI in k
20.641 * [backup-simplify]: Simplify PI into PI
20.641 * [backup-simplify]: Simplify (* n PI) into (* n PI)
20.641 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
20.641 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
20.641 * [backup-simplify]: Simplify (- 0) into 0
20.641 * [backup-simplify]: Simplify (+ 1 0) into 1
20.642 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
20.642 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
20.642 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
20.642 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.642 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.642 * [taylor]: Taking taylor expansion of k in k
20.642 * [backup-simplify]: Simplify 0 into 0
20.642 * [backup-simplify]: Simplify 1 into 1
20.642 * [backup-simplify]: Simplify (/ 1 1) into 1
20.642 * [backup-simplify]: Simplify (sqrt 0) into 0
20.643 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.643 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
20.643 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
20.643 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
20.643 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
20.643 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
20.643 * [taylor]: Taking taylor expansion of 1/2 in n
20.643 * [backup-simplify]: Simplify 1/2 into 1/2
20.643 * [taylor]: Taking taylor expansion of (- 1 k) in n
20.643 * [taylor]: Taking taylor expansion of 1 in n
20.643 * [backup-simplify]: Simplify 1 into 1
20.643 * [taylor]: Taking taylor expansion of k in n
20.643 * [backup-simplify]: Simplify k into k
20.644 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
20.644 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.644 * [taylor]: Taking taylor expansion of 2 in n
20.644 * [backup-simplify]: Simplify 2 into 2
20.644 * [taylor]: Taking taylor expansion of (* n PI) in n
20.644 * [taylor]: Taking taylor expansion of n in n
20.644 * [backup-simplify]: Simplify 0 into 0
20.644 * [backup-simplify]: Simplify 1 into 1
20.644 * [taylor]: Taking taylor expansion of PI in n
20.644 * [backup-simplify]: Simplify PI into PI
20.644 * [backup-simplify]: Simplify (* 0 PI) into 0
20.644 * [backup-simplify]: Simplify (* 2 0) into 0
20.645 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.646 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
20.647 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.647 * [backup-simplify]: Simplify (- k) into (- k)
20.647 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
20.647 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
20.648 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.648 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
20.649 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
20.649 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
20.649 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.649 * [taylor]: Taking taylor expansion of k in n
20.649 * [backup-simplify]: Simplify k into k
20.649 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.649 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
20.649 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.649 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
20.649 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
20.649 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
20.649 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
20.649 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
20.649 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
20.649 * [taylor]: Taking taylor expansion of 1/2 in n
20.649 * [backup-simplify]: Simplify 1/2 into 1/2
20.649 * [taylor]: Taking taylor expansion of (- 1 k) in n
20.649 * [taylor]: Taking taylor expansion of 1 in n
20.649 * [backup-simplify]: Simplify 1 into 1
20.649 * [taylor]: Taking taylor expansion of k in n
20.649 * [backup-simplify]: Simplify k into k
20.649 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
20.649 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.649 * [taylor]: Taking taylor expansion of 2 in n
20.649 * [backup-simplify]: Simplify 2 into 2
20.649 * [taylor]: Taking taylor expansion of (* n PI) in n
20.649 * [taylor]: Taking taylor expansion of n in n
20.649 * [backup-simplify]: Simplify 0 into 0
20.649 * [backup-simplify]: Simplify 1 into 1
20.649 * [taylor]: Taking taylor expansion of PI in n
20.650 * [backup-simplify]: Simplify PI into PI
20.650 * [backup-simplify]: Simplify (* 0 PI) into 0
20.650 * [backup-simplify]: Simplify (* 2 0) into 0
20.651 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.652 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
20.653 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.653 * [backup-simplify]: Simplify (- k) into (- k)
20.653 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
20.653 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
20.654 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.654 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
20.655 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
20.655 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
20.655 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.655 * [taylor]: Taking taylor expansion of k in n
20.655 * [backup-simplify]: Simplify k into k
20.655 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.655 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
20.655 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.655 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
20.656 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
20.656 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
20.656 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
20.656 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
20.656 * [taylor]: Taking taylor expansion of 1/2 in k
20.656 * [backup-simplify]: Simplify 1/2 into 1/2
20.656 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
20.656 * [taylor]: Taking taylor expansion of (- 1 k) in k
20.656 * [taylor]: Taking taylor expansion of 1 in k
20.656 * [backup-simplify]: Simplify 1 into 1
20.656 * [taylor]: Taking taylor expansion of k in k
20.656 * [backup-simplify]: Simplify 0 into 0
20.656 * [backup-simplify]: Simplify 1 into 1
20.656 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
20.656 * [taylor]: Taking taylor expansion of (log n) in k
20.656 * [taylor]: Taking taylor expansion of n in k
20.656 * [backup-simplify]: Simplify n into n
20.657 * [backup-simplify]: Simplify (log n) into (log n)
20.657 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
20.657 * [taylor]: Taking taylor expansion of (* 2 PI) in k
20.657 * [taylor]: Taking taylor expansion of 2 in k
20.657 * [backup-simplify]: Simplify 2 into 2
20.657 * [taylor]: Taking taylor expansion of PI in k
20.657 * [backup-simplify]: Simplify PI into PI
20.657 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.658 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.658 * [backup-simplify]: Simplify (- 0) into 0
20.658 * [backup-simplify]: Simplify (+ 1 0) into 1
20.659 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.660 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
20.660 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
20.661 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
20.661 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.661 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.661 * [taylor]: Taking taylor expansion of k in k
20.661 * [backup-simplify]: Simplify 0 into 0
20.661 * [backup-simplify]: Simplify 1 into 1
20.661 * [backup-simplify]: Simplify (/ 1 1) into 1
20.661 * [backup-simplify]: Simplify (sqrt 0) into 0
20.663 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.664 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
20.664 * [backup-simplify]: Simplify 0 into 0
20.665 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
20.666 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
20.668 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
20.669 * [backup-simplify]: Simplify (- 0) into 0
20.669 * [backup-simplify]: Simplify (+ 0 0) into 0
20.670 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
20.671 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.672 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
20.675 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.676 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
20.676 * [taylor]: Taking taylor expansion of 0 in k
20.676 * [backup-simplify]: Simplify 0 into 0
20.677 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
20.678 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
20.680 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
20.680 * [backup-simplify]: Simplify (+ 0 0) into 0
20.681 * [backup-simplify]: Simplify (- 1) into -1
20.681 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.683 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
20.686 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
20.689 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
20.693 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
20.694 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
20.695 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.695 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
20.697 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
20.698 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
20.701 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
20.702 * [backup-simplify]: Simplify (- 0) into 0
20.702 * [backup-simplify]: Simplify (+ 0 0) into 0
20.709 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
20.710 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.711 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
20.712 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.713 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
20.713 * [taylor]: Taking taylor expansion of 0 in k
20.713 * [backup-simplify]: Simplify 0 into 0
20.714 * [backup-simplify]: Simplify 0 into 0
20.714 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
20.716 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.717 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
20.718 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
20.719 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
20.720 * [backup-simplify]: Simplify (+ 0 0) into 0
20.720 * [backup-simplify]: Simplify (- 0) into 0
20.720 * [backup-simplify]: Simplify (+ 0 0) into 0
20.721 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
20.723 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
20.725 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
20.731 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
20.733 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
20.734 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.734 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
20.735 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.736 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
20.739 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
20.739 * [backup-simplify]: Simplify (- 0) into 0
20.740 * [backup-simplify]: Simplify (+ 0 0) into 0
20.740 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
20.741 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.742 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
20.745 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.746 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
20.746 * [taylor]: Taking taylor expansion of 0 in k
20.746 * [backup-simplify]: Simplify 0 into 0
20.746 * [backup-simplify]: Simplify 0 into 0
20.746 * [backup-simplify]: Simplify 0 into 0
20.747 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.751 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.754 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
20.756 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.762 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
20.763 * [backup-simplify]: Simplify (+ 0 0) into 0
20.763 * [backup-simplify]: Simplify (- 0) into 0
20.763 * [backup-simplify]: Simplify (+ 0 0) into 0
20.766 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
20.769 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
20.776 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
20.792 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
20.804 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
20.824 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
20.824 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
20.824 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (n k) around 0
20.824 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
20.824 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
20.824 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
20.825 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
20.825 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
20.825 * [taylor]: Taking taylor expansion of 1/2 in k
20.825 * [backup-simplify]: Simplify 1/2 into 1/2
20.825 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
20.825 * [taylor]: Taking taylor expansion of 1 in k
20.825 * [backup-simplify]: Simplify 1 into 1
20.825 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.825 * [taylor]: Taking taylor expansion of k in k
20.825 * [backup-simplify]: Simplify 0 into 0
20.825 * [backup-simplify]: Simplify 1 into 1
20.825 * [backup-simplify]: Simplify (/ 1 1) into 1
20.825 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
20.825 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
20.825 * [taylor]: Taking taylor expansion of 2 in k
20.825 * [backup-simplify]: Simplify 2 into 2
20.825 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.825 * [taylor]: Taking taylor expansion of PI in k
20.825 * [backup-simplify]: Simplify PI into PI
20.825 * [taylor]: Taking taylor expansion of n in k
20.825 * [backup-simplify]: Simplify n into n
20.825 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.825 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
20.825 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
20.825 * [backup-simplify]: Simplify (- 1) into -1
20.826 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.826 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
20.826 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
20.826 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
20.826 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.826 * [taylor]: Taking taylor expansion of k in k
20.826 * [backup-simplify]: Simplify 0 into 0
20.826 * [backup-simplify]: Simplify 1 into 1
20.827 * [backup-simplify]: Simplify (sqrt 0) into 0
20.828 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.828 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
20.828 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
20.828 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
20.828 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
20.828 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
20.828 * [taylor]: Taking taylor expansion of 1/2 in n
20.828 * [backup-simplify]: Simplify 1/2 into 1/2
20.828 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
20.828 * [taylor]: Taking taylor expansion of 1 in n
20.828 * [backup-simplify]: Simplify 1 into 1
20.828 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.828 * [taylor]: Taking taylor expansion of k in n
20.828 * [backup-simplify]: Simplify k into k
20.828 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.828 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
20.828 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.828 * [taylor]: Taking taylor expansion of 2 in n
20.828 * [backup-simplify]: Simplify 2 into 2
20.828 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.828 * [taylor]: Taking taylor expansion of PI in n
20.828 * [backup-simplify]: Simplify PI into PI
20.828 * [taylor]: Taking taylor expansion of n in n
20.828 * [backup-simplify]: Simplify 0 into 0
20.828 * [backup-simplify]: Simplify 1 into 1
20.828 * [backup-simplify]: Simplify (/ PI 1) into PI
20.829 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.829 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.829 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.829 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
20.829 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
20.830 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.831 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
20.832 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
20.832 * [taylor]: Taking taylor expansion of (sqrt k) in n
20.832 * [taylor]: Taking taylor expansion of k in n
20.832 * [backup-simplify]: Simplify k into k
20.832 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
20.832 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
20.832 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
20.832 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
20.832 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
20.832 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
20.832 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
20.832 * [taylor]: Taking taylor expansion of 1/2 in n
20.832 * [backup-simplify]: Simplify 1/2 into 1/2
20.832 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
20.832 * [taylor]: Taking taylor expansion of 1 in n
20.832 * [backup-simplify]: Simplify 1 into 1
20.832 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.832 * [taylor]: Taking taylor expansion of k in n
20.832 * [backup-simplify]: Simplify k into k
20.832 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.832 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
20.832 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
20.832 * [taylor]: Taking taylor expansion of 2 in n
20.832 * [backup-simplify]: Simplify 2 into 2
20.832 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.832 * [taylor]: Taking taylor expansion of PI in n
20.832 * [backup-simplify]: Simplify PI into PI
20.832 * [taylor]: Taking taylor expansion of n in n
20.832 * [backup-simplify]: Simplify 0 into 0
20.832 * [backup-simplify]: Simplify 1 into 1
20.833 * [backup-simplify]: Simplify (/ PI 1) into PI
20.833 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.833 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.834 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.834 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
20.834 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
20.835 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.835 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
20.836 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
20.836 * [taylor]: Taking taylor expansion of (sqrt k) in n
20.836 * [taylor]: Taking taylor expansion of k in n
20.836 * [backup-simplify]: Simplify k into k
20.836 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
20.836 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
20.837 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
20.837 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
20.837 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
20.837 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
20.837 * [taylor]: Taking taylor expansion of 1/2 in k
20.837 * [backup-simplify]: Simplify 1/2 into 1/2
20.837 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
20.837 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
20.837 * [taylor]: Taking taylor expansion of 1 in k
20.837 * [backup-simplify]: Simplify 1 into 1
20.837 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.837 * [taylor]: Taking taylor expansion of k in k
20.837 * [backup-simplify]: Simplify 0 into 0
20.837 * [backup-simplify]: Simplify 1 into 1
20.837 * [backup-simplify]: Simplify (/ 1 1) into 1
20.837 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
20.837 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
20.837 * [taylor]: Taking taylor expansion of (* 2 PI) in k
20.837 * [taylor]: Taking taylor expansion of 2 in k
20.837 * [backup-simplify]: Simplify 2 into 2
20.837 * [taylor]: Taking taylor expansion of PI in k
20.837 * [backup-simplify]: Simplify PI into PI
20.838 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.838 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.838 * [taylor]: Taking taylor expansion of (log n) in k
20.838 * [taylor]: Taking taylor expansion of n in k
20.838 * [backup-simplify]: Simplify n into n
20.838 * [backup-simplify]: Simplify (log n) into (log n)
20.839 * [backup-simplify]: Simplify (- 1) into -1
20.839 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.839 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.840 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
20.840 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
20.841 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
20.842 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
20.842 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.842 * [taylor]: Taking taylor expansion of k in k
20.842 * [backup-simplify]: Simplify 0 into 0
20.842 * [backup-simplify]: Simplify 1 into 1
20.842 * [backup-simplify]: Simplify (sqrt 0) into 0
20.843 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.844 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
20.845 * [backup-simplify]: Simplify 0 into 0
20.846 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.846 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
20.848 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
20.849 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.849 * [backup-simplify]: Simplify (- 0) into 0
20.850 * [backup-simplify]: Simplify (+ 0 0) into 0
20.850 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
20.852 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.853 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
20.855 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.857 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
20.857 * [taylor]: Taking taylor expansion of 0 in k
20.857 * [backup-simplify]: Simplify 0 into 0
20.857 * [backup-simplify]: Simplify 0 into 0
20.858 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
20.860 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
20.860 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
20.861 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.862 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
20.866 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
20.866 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.866 * [backup-simplify]: Simplify (- 0) into 0
20.867 * [backup-simplify]: Simplify (+ 0 0) into 0
20.868 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
20.869 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.871 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
20.872 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.873 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
20.873 * [taylor]: Taking taylor expansion of 0 in k
20.873 * [backup-simplify]: Simplify 0 into 0
20.873 * [backup-simplify]: Simplify 0 into 0
20.873 * [backup-simplify]: Simplify 0 into 0
20.875 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.876 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
20.877 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
20.877 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
20.878 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.878 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.882 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
20.882 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.882 * [backup-simplify]: Simplify (- 0) into 0
20.882 * [backup-simplify]: Simplify (+ 0 0) into 0
20.883 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
20.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
20.885 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
20.887 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
20.888 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
20.888 * [taylor]: Taking taylor expansion of 0 in k
20.888 * [backup-simplify]: Simplify 0 into 0
20.888 * [backup-simplify]: Simplify 0 into 0
20.888 * [backup-simplify]: Simplify 0 into 0
20.888 * [backup-simplify]: Simplify 0 into 0
20.890 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.891 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
20.892 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
20.895 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
20.895 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
20.895 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0
20.895 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
20.895 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
20.895 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
20.895 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
20.895 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
20.895 * [taylor]: Taking taylor expansion of 1/2 in k
20.895 * [backup-simplify]: Simplify 1/2 into 1/2
20.895 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
20.895 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.895 * [taylor]: Taking taylor expansion of k in k
20.896 * [backup-simplify]: Simplify 0 into 0
20.896 * [backup-simplify]: Simplify 1 into 1
20.896 * [backup-simplify]: Simplify (/ 1 1) into 1
20.896 * [taylor]: Taking taylor expansion of 1 in k
20.896 * [backup-simplify]: Simplify 1 into 1
20.896 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
20.896 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
20.896 * [taylor]: Taking taylor expansion of -2 in k
20.896 * [backup-simplify]: Simplify -2 into -2
20.896 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.896 * [taylor]: Taking taylor expansion of PI in k
20.896 * [backup-simplify]: Simplify PI into PI
20.896 * [taylor]: Taking taylor expansion of n in k
20.896 * [backup-simplify]: Simplify n into n
20.896 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.896 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
20.896 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
20.896 * [backup-simplify]: Simplify (+ 1 0) into 1
20.897 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
20.897 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
20.897 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
20.897 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
20.897 * [taylor]: Taking taylor expansion of (/ -1 k) in k
20.897 * [taylor]: Taking taylor expansion of -1 in k
20.897 * [backup-simplify]: Simplify -1 into -1
20.897 * [taylor]: Taking taylor expansion of k in k
20.897 * [backup-simplify]: Simplify 0 into 0
20.897 * [backup-simplify]: Simplify 1 into 1
20.897 * [backup-simplify]: Simplify (/ -1 1) into -1
20.897 * [backup-simplify]: Simplify (sqrt 0) into 0
20.898 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
20.898 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
20.898 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
20.898 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
20.898 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
20.898 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
20.898 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
20.898 * [taylor]: Taking taylor expansion of 1/2 in n
20.899 * [backup-simplify]: Simplify 1/2 into 1/2
20.899 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
20.899 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.899 * [taylor]: Taking taylor expansion of k in n
20.899 * [backup-simplify]: Simplify k into k
20.899 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.899 * [taylor]: Taking taylor expansion of 1 in n
20.899 * [backup-simplify]: Simplify 1 into 1
20.899 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
20.899 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.899 * [taylor]: Taking taylor expansion of -2 in n
20.899 * [backup-simplify]: Simplify -2 into -2
20.899 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.899 * [taylor]: Taking taylor expansion of PI in n
20.899 * [backup-simplify]: Simplify PI into PI
20.899 * [taylor]: Taking taylor expansion of n in n
20.899 * [backup-simplify]: Simplify 0 into 0
20.899 * [backup-simplify]: Simplify 1 into 1
20.899 * [backup-simplify]: Simplify (/ PI 1) into PI
20.899 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.900 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
20.900 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
20.900 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
20.901 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.902 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
20.902 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
20.902 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
20.902 * [taylor]: Taking taylor expansion of (/ -1 k) in n
20.902 * [taylor]: Taking taylor expansion of -1 in n
20.902 * [backup-simplify]: Simplify -1 into -1
20.902 * [taylor]: Taking taylor expansion of k in n
20.903 * [backup-simplify]: Simplify k into k
20.903 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
20.903 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
20.903 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
20.903 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
20.904 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
20.904 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
20.904 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
20.904 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
20.904 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
20.904 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
20.904 * [taylor]: Taking taylor expansion of 1/2 in n
20.904 * [backup-simplify]: Simplify 1/2 into 1/2
20.904 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
20.904 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.904 * [taylor]: Taking taylor expansion of k in n
20.905 * [backup-simplify]: Simplify k into k
20.905 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.905 * [taylor]: Taking taylor expansion of 1 in n
20.905 * [backup-simplify]: Simplify 1 into 1
20.905 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
20.905 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
20.905 * [taylor]: Taking taylor expansion of -2 in n
20.905 * [backup-simplify]: Simplify -2 into -2
20.905 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.905 * [taylor]: Taking taylor expansion of PI in n
20.905 * [backup-simplify]: Simplify PI into PI
20.905 * [taylor]: Taking taylor expansion of n in n
20.905 * [backup-simplify]: Simplify 0 into 0
20.905 * [backup-simplify]: Simplify 1 into 1
20.905 * [backup-simplify]: Simplify (/ PI 1) into PI
20.906 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.907 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
20.907 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
20.907 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
20.908 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.910 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
20.911 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
20.911 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
20.911 * [taylor]: Taking taylor expansion of (/ -1 k) in n
20.911 * [taylor]: Taking taylor expansion of -1 in n
20.911 * [backup-simplify]: Simplify -1 into -1
20.911 * [taylor]: Taking taylor expansion of k in n
20.911 * [backup-simplify]: Simplify k into k
20.911 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
20.911 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
20.911 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
20.911 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
20.912 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
20.912 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
20.912 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
20.912 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
20.912 * [taylor]: Taking taylor expansion of 1/2 in k
20.912 * [backup-simplify]: Simplify 1/2 into 1/2
20.912 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
20.912 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
20.912 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.912 * [taylor]: Taking taylor expansion of k in k
20.912 * [backup-simplify]: Simplify 0 into 0
20.912 * [backup-simplify]: Simplify 1 into 1
20.913 * [backup-simplify]: Simplify (/ 1 1) into 1
20.913 * [taylor]: Taking taylor expansion of 1 in k
20.913 * [backup-simplify]: Simplify 1 into 1
20.913 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
20.913 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
20.913 * [taylor]: Taking taylor expansion of (* -2 PI) in k
20.913 * [taylor]: Taking taylor expansion of -2 in k
20.913 * [backup-simplify]: Simplify -2 into -2
20.913 * [taylor]: Taking taylor expansion of PI in k
20.913 * [backup-simplify]: Simplify PI into PI
20.913 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
20.914 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
20.914 * [taylor]: Taking taylor expansion of (log n) in k
20.914 * [taylor]: Taking taylor expansion of n in k
20.914 * [backup-simplify]: Simplify n into n
20.914 * [backup-simplify]: Simplify (log n) into (log n)
20.915 * [backup-simplify]: Simplify (+ 1 0) into 1
20.915 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.916 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
20.917 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
20.918 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
20.919 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
20.919 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
20.919 * [taylor]: Taking taylor expansion of (/ -1 k) in k
20.919 * [taylor]: Taking taylor expansion of -1 in k
20.919 * [backup-simplify]: Simplify -1 into -1
20.919 * [taylor]: Taking taylor expansion of k in k
20.919 * [backup-simplify]: Simplify 0 into 0
20.919 * [backup-simplify]: Simplify 1 into 1
20.919 * [backup-simplify]: Simplify (/ -1 1) into -1
20.920 * [backup-simplify]: Simplify (sqrt 0) into 0
20.921 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
20.922 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
20.925 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
20.926 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.926 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
20.928 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
20.929 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.929 * [backup-simplify]: Simplify (+ 0 0) into 0
20.929 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
20.931 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.936 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
20.937 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.938 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
20.938 * [taylor]: Taking taylor expansion of 0 in k
20.938 * [backup-simplify]: Simplify 0 into 0
20.938 * [backup-simplify]: Simplify 0 into 0
20.939 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
20.941 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.942 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
20.943 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
20.944 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.944 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
20.946 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
20.946 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.946 * [backup-simplify]: Simplify (+ 0 0) into 0
20.947 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
20.948 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
20.949 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
20.950 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
20.950 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.951 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
20.952 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
20.952 * [taylor]: Taking taylor expansion of 0 in k
20.952 * [backup-simplify]: Simplify 0 into 0
20.952 * [backup-simplify]: Simplify 0 into 0
20.952 * [backup-simplify]: Simplify 0 into 0
20.952 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.955 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.957 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
20.957 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
20.960 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
20.960 * * * * [progress]: [ 4 / 4 ] generating series at (2 2)
20.960 * [backup-simplify]: Simplify (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) into (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k))
20.960 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in (n k) around 0
20.960 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in k
20.960 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in k
20.960 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
20.960 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
20.960 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
20.960 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
20.961 * [taylor]: Taking taylor expansion of 1/2 in k
20.961 * [backup-simplify]: Simplify 1/2 into 1/2
20.961 * [taylor]: Taking taylor expansion of (- 1 k) in k
20.961 * [taylor]: Taking taylor expansion of 1 in k
20.961 * [backup-simplify]: Simplify 1 into 1
20.961 * [taylor]: Taking taylor expansion of k in k
20.961 * [backup-simplify]: Simplify 0 into 0
20.961 * [backup-simplify]: Simplify 1 into 1
20.961 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
20.961 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
20.961 * [taylor]: Taking taylor expansion of 2 in k
20.961 * [backup-simplify]: Simplify 2 into 2
20.961 * [taylor]: Taking taylor expansion of (* n PI) in k
20.961 * [taylor]: Taking taylor expansion of n in k
20.961 * [backup-simplify]: Simplify n into n
20.961 * [taylor]: Taking taylor expansion of PI in k
20.961 * [backup-simplify]: Simplify PI into PI
20.961 * [backup-simplify]: Simplify (* n PI) into (* n PI)
20.961 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
20.961 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
20.961 * [backup-simplify]: Simplify (- 0) into 0
20.961 * [backup-simplify]: Simplify (+ 1 0) into 1
20.962 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
20.962 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
20.962 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
20.962 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2))))
20.962 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.962 * [taylor]: Taking taylor expansion of k in k
20.962 * [backup-simplify]: Simplify 0 into 0
20.962 * [backup-simplify]: Simplify 1 into 1
20.962 * [backup-simplify]: Simplify (sqrt 0) into 0
20.963 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.963 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in n
20.963 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in n
20.963 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
20.963 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
20.963 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
20.963 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
20.963 * [taylor]: Taking taylor expansion of 1/2 in n
20.963 * [backup-simplify]: Simplify 1/2 into 1/2
20.963 * [taylor]: Taking taylor expansion of (- 1 k) in n
20.963 * [taylor]: Taking taylor expansion of 1 in n
20.963 * [backup-simplify]: Simplify 1 into 1
20.963 * [taylor]: Taking taylor expansion of k in n
20.963 * [backup-simplify]: Simplify k into k
20.963 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
20.963 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.963 * [taylor]: Taking taylor expansion of 2 in n
20.963 * [backup-simplify]: Simplify 2 into 2
20.963 * [taylor]: Taking taylor expansion of (* n PI) in n
20.963 * [taylor]: Taking taylor expansion of n in n
20.963 * [backup-simplify]: Simplify 0 into 0
20.963 * [backup-simplify]: Simplify 1 into 1
20.963 * [taylor]: Taking taylor expansion of PI in n
20.963 * [backup-simplify]: Simplify PI into PI
20.964 * [backup-simplify]: Simplify (* 0 PI) into 0
20.964 * [backup-simplify]: Simplify (* 2 0) into 0
20.965 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.966 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
20.966 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.967 * [backup-simplify]: Simplify (- k) into (- k)
20.967 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
20.967 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
20.967 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.968 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
20.969 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
20.969 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) into (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))
20.969 * [taylor]: Taking taylor expansion of (sqrt k) in n
20.970 * [taylor]: Taking taylor expansion of k in n
20.970 * [backup-simplify]: Simplify k into k
20.970 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
20.970 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
20.970 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in n
20.970 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in n
20.970 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
20.970 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
20.970 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
20.970 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
20.970 * [taylor]: Taking taylor expansion of 1/2 in n
20.970 * [backup-simplify]: Simplify 1/2 into 1/2
20.970 * [taylor]: Taking taylor expansion of (- 1 k) in n
20.970 * [taylor]: Taking taylor expansion of 1 in n
20.970 * [backup-simplify]: Simplify 1 into 1
20.970 * [taylor]: Taking taylor expansion of k in n
20.970 * [backup-simplify]: Simplify k into k
20.970 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
20.970 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
20.970 * [taylor]: Taking taylor expansion of 2 in n
20.970 * [backup-simplify]: Simplify 2 into 2
20.970 * [taylor]: Taking taylor expansion of (* n PI) in n
20.970 * [taylor]: Taking taylor expansion of n in n
20.970 * [backup-simplify]: Simplify 0 into 0
20.970 * [backup-simplify]: Simplify 1 into 1
20.970 * [taylor]: Taking taylor expansion of PI in n
20.970 * [backup-simplify]: Simplify PI into PI
20.970 * [backup-simplify]: Simplify (* 0 PI) into 0
20.971 * [backup-simplify]: Simplify (* 2 0) into 0
20.971 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.972 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
20.973 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.973 * [backup-simplify]: Simplify (- k) into (- k)
20.973 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
20.973 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
20.974 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.975 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
20.975 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
20.976 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) into (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))
20.976 * [taylor]: Taking taylor expansion of (sqrt k) in n
20.976 * [taylor]: Taking taylor expansion of k in n
20.976 * [backup-simplify]: Simplify k into k
20.976 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
20.976 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
20.977 * [backup-simplify]: Simplify (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) (sqrt k)) into (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) (sqrt k))
20.977 * [taylor]: Taking taylor expansion of (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) (sqrt k)) in k
20.977 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) in k
20.977 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
20.977 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
20.977 * [taylor]: Taking taylor expansion of 1/2 in k
20.977 * [backup-simplify]: Simplify 1/2 into 1/2
20.977 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
20.977 * [taylor]: Taking taylor expansion of (- 1 k) in k
20.977 * [taylor]: Taking taylor expansion of 1 in k
20.977 * [backup-simplify]: Simplify 1 into 1
20.977 * [taylor]: Taking taylor expansion of k in k
20.977 * [backup-simplify]: Simplify 0 into 0
20.977 * [backup-simplify]: Simplify 1 into 1
20.977 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
20.977 * [taylor]: Taking taylor expansion of (log n) in k
20.977 * [taylor]: Taking taylor expansion of n in k
20.977 * [backup-simplify]: Simplify n into n
20.977 * [backup-simplify]: Simplify (log n) into (log n)
20.977 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
20.977 * [taylor]: Taking taylor expansion of (* 2 PI) in k
20.977 * [taylor]: Taking taylor expansion of 2 in k
20.977 * [backup-simplify]: Simplify 2 into 2
20.977 * [taylor]: Taking taylor expansion of PI in k
20.977 * [backup-simplify]: Simplify PI into PI
20.977 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
20.978 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
20.979 * [backup-simplify]: Simplify (- 0) into 0
20.979 * [backup-simplify]: Simplify (+ 1 0) into 1
20.979 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.980 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
20.981 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
20.981 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
20.982 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))
20.982 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.982 * [taylor]: Taking taylor expansion of k in k
20.982 * [backup-simplify]: Simplify 0 into 0
20.982 * [backup-simplify]: Simplify 1 into 1
20.982 * [backup-simplify]: Simplify (sqrt 0) into 0
20.983 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.984 * [backup-simplify]: Simplify (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 0) into 0
20.984 * [backup-simplify]: Simplify 0 into 0
20.985 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
20.985 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
20.986 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
20.987 * [backup-simplify]: Simplify (- 0) into 0
20.987 * [backup-simplify]: Simplify (+ 0 0) into 0
20.988 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
20.989 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
20.990 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
20.992 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.994 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) (/ 0 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))))) into 0
20.996 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) 0) (* 0 (sqrt k))) into 0
20.996 * [taylor]: Taking taylor expansion of 0 in k
20.996 * [backup-simplify]: Simplify 0 into 0
20.996 * [backup-simplify]: Simplify 0 into 0
20.997 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
20.997 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
20.999 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
21.000 * [backup-simplify]: Simplify (+ 0 0) into 0
21.000 * [backup-simplify]: Simplify (- 1) into -1
21.000 * [backup-simplify]: Simplify (+ 0 -1) into -1
21.002 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
21.004 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
21.007 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
21.012 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))
21.016 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) +nan.0) (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) 0)) into (- (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))
21.017 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))
21.018 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
21.020 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
21.021 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
21.024 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
21.024 * [backup-simplify]: Simplify (- 0) into 0
21.025 * [backup-simplify]: Simplify (+ 0 0) into 0
21.026 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
21.027 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
21.029 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
21.031 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
21.035 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) (/ 0 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))))) into 0
21.037 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
21.037 * [taylor]: Taking taylor expansion of 0 in k
21.037 * [backup-simplify]: Simplify 0 into 0
21.037 * [backup-simplify]: Simplify 0 into 0
21.037 * [backup-simplify]: Simplify 0 into 0
21.040 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.042 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
21.049 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
21.053 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
21.054 * [backup-simplify]: Simplify (+ 0 0) into 0
21.054 * [backup-simplify]: Simplify (- 0) into 0
21.054 * [backup-simplify]: Simplify (+ 0 0) into 0
21.056 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
21.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
21.064 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
21.080 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))
21.091 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) +nan.0) (+ (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) +nan.0) (* (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) 0))) into (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))
21.096 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) into (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))
21.097 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
21.098 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
21.100 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
21.106 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
21.107 * [backup-simplify]: Simplify (- 0) into 0
21.107 * [backup-simplify]: Simplify (+ 0 0) into 0
21.108 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
21.110 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
21.112 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
21.114 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
21.119 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) (/ 0 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))))) into 0
21.121 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
21.121 * [taylor]: Taking taylor expansion of 0 in k
21.121 * [backup-simplify]: Simplify 0 into 0
21.121 * [backup-simplify]: Simplify 0 into 0
21.121 * [backup-simplify]: Simplify 0 into 0
21.121 * [backup-simplify]: Simplify 0 into 0
21.126 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.129 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
21.130 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
21.136 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
21.136 * [backup-simplify]: Simplify (+ 0 0) into 0
21.137 * [backup-simplify]: Simplify (- 0) into 0
21.137 * [backup-simplify]: Simplify (+ 0 0) into 0
21.140 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
21.143 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
21.149 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
21.177 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (/ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/48 (/ (pow (log (* 2 PI)) 3) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/16 (/ (* (pow (log n) 2) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/16 (/ (* (log n) (pow (log (* 2 PI)) 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/48 (/ (pow (log n) 3) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))
21.194 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) +nan.0) (+ (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) +nan.0) (+ (* (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) +nan.0) (* (+ (* 1/48 (/ (pow (log (* 2 PI)) 3) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/16 (/ (* (pow (log n) 2) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/16 (/ (* (log n) (pow (log (* 2 PI)) 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/48 (/ (pow (log n) 3) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))) 0)))) into (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))))))))
21.202 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))))))))) into (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))))))))
21.214 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))))))))) (pow (* k 1) 3)) (+ (* (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) (pow (* k 1) 2)) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* k 1)))) into (- (+ (* +nan.0 (/ k (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (pow (log n) 2) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log (* 2 PI)) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow k 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (pow k 2) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (pow (log (* 2 PI)) 2) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log n) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log (* 2 PI)) (* (log n) (pow k 3))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (pow k 3) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))))))))))))))))
21.214 * [backup-simplify]: Simplify (/ 1 (/ (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) into (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k)))
21.214 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in (n k) around 0
21.214 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in k
21.214 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in k
21.214 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
21.214 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
21.214 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
21.214 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
21.214 * [taylor]: Taking taylor expansion of 1/2 in k
21.214 * [backup-simplify]: Simplify 1/2 into 1/2
21.215 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
21.215 * [taylor]: Taking taylor expansion of 1 in k
21.215 * [backup-simplify]: Simplify 1 into 1
21.215 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.215 * [taylor]: Taking taylor expansion of k in k
21.215 * [backup-simplify]: Simplify 0 into 0
21.215 * [backup-simplify]: Simplify 1 into 1
21.215 * [backup-simplify]: Simplify (/ 1 1) into 1
21.215 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
21.215 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
21.215 * [taylor]: Taking taylor expansion of 2 in k
21.215 * [backup-simplify]: Simplify 2 into 2
21.215 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.215 * [taylor]: Taking taylor expansion of PI in k
21.215 * [backup-simplify]: Simplify PI into PI
21.215 * [taylor]: Taking taylor expansion of n in k
21.215 * [backup-simplify]: Simplify n into n
21.215 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.215 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
21.215 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
21.215 * [backup-simplify]: Simplify (- 1) into -1
21.216 * [backup-simplify]: Simplify (+ 0 -1) into -1
21.216 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
21.216 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
21.216 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
21.216 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
21.216 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
21.216 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.216 * [taylor]: Taking taylor expansion of k in k
21.216 * [backup-simplify]: Simplify 0 into 0
21.216 * [backup-simplify]: Simplify 1 into 1
21.217 * [backup-simplify]: Simplify (/ 1 1) into 1
21.217 * [backup-simplify]: Simplify (sqrt 0) into 0
21.218 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.218 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in n
21.218 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in n
21.218 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
21.218 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
21.218 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
21.218 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
21.218 * [taylor]: Taking taylor expansion of 1/2 in n
21.218 * [backup-simplify]: Simplify 1/2 into 1/2
21.218 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
21.218 * [taylor]: Taking taylor expansion of 1 in n
21.218 * [backup-simplify]: Simplify 1 into 1
21.218 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.218 * [taylor]: Taking taylor expansion of k in n
21.218 * [backup-simplify]: Simplify k into k
21.218 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.218 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
21.218 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
21.218 * [taylor]: Taking taylor expansion of 2 in n
21.218 * [backup-simplify]: Simplify 2 into 2
21.218 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.218 * [taylor]: Taking taylor expansion of PI in n
21.218 * [backup-simplify]: Simplify PI into PI
21.218 * [taylor]: Taking taylor expansion of n in n
21.218 * [backup-simplify]: Simplify 0 into 0
21.218 * [backup-simplify]: Simplify 1 into 1
21.219 * [backup-simplify]: Simplify (/ PI 1) into PI
21.219 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
21.220 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
21.220 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.220 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
21.220 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
21.221 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
21.221 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
21.222 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
21.223 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
21.223 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
21.223 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.223 * [taylor]: Taking taylor expansion of k in n
21.223 * [backup-simplify]: Simplify k into k
21.223 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.223 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
21.223 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.223 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
21.223 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in n
21.223 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in n
21.223 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
21.223 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
21.223 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
21.223 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
21.223 * [taylor]: Taking taylor expansion of 1/2 in n
21.223 * [backup-simplify]: Simplify 1/2 into 1/2
21.223 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
21.223 * [taylor]: Taking taylor expansion of 1 in n
21.223 * [backup-simplify]: Simplify 1 into 1
21.223 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.223 * [taylor]: Taking taylor expansion of k in n
21.223 * [backup-simplify]: Simplify k into k
21.223 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.223 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
21.223 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
21.223 * [taylor]: Taking taylor expansion of 2 in n
21.223 * [backup-simplify]: Simplify 2 into 2
21.223 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.223 * [taylor]: Taking taylor expansion of PI in n
21.223 * [backup-simplify]: Simplify PI into PI
21.223 * [taylor]: Taking taylor expansion of n in n
21.223 * [backup-simplify]: Simplify 0 into 0
21.223 * [backup-simplify]: Simplify 1 into 1
21.224 * [backup-simplify]: Simplify (/ PI 1) into PI
21.224 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
21.225 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
21.225 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.225 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
21.225 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
21.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
21.227 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
21.227 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
21.228 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
21.228 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
21.228 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.228 * [taylor]: Taking taylor expansion of k in n
21.228 * [backup-simplify]: Simplify k into k
21.228 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.229 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
21.229 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.229 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
21.230 * [backup-simplify]: Simplify (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) into (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
21.230 * [taylor]: Taking taylor expansion of (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) in k
21.230 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) in k
21.230 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
21.230 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
21.230 * [taylor]: Taking taylor expansion of 1/2 in k
21.230 * [backup-simplify]: Simplify 1/2 into 1/2
21.230 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
21.230 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
21.230 * [taylor]: Taking taylor expansion of 1 in k
21.230 * [backup-simplify]: Simplify 1 into 1
21.230 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.230 * [taylor]: Taking taylor expansion of k in k
21.230 * [backup-simplify]: Simplify 0 into 0
21.230 * [backup-simplify]: Simplify 1 into 1
21.231 * [backup-simplify]: Simplify (/ 1 1) into 1
21.231 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
21.231 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
21.231 * [taylor]: Taking taylor expansion of (* 2 PI) in k
21.231 * [taylor]: Taking taylor expansion of 2 in k
21.231 * [backup-simplify]: Simplify 2 into 2
21.231 * [taylor]: Taking taylor expansion of PI in k
21.231 * [backup-simplify]: Simplify PI into PI
21.231 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
21.232 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
21.232 * [taylor]: Taking taylor expansion of (log n) in k
21.232 * [taylor]: Taking taylor expansion of n in k
21.232 * [backup-simplify]: Simplify n into n
21.232 * [backup-simplify]: Simplify (log n) into (log n)
21.233 * [backup-simplify]: Simplify (- 1) into -1
21.233 * [backup-simplify]: Simplify (+ 0 -1) into -1
21.233 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
21.234 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
21.234 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
21.235 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
21.236 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
21.237 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
21.237 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
21.237 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.237 * [taylor]: Taking taylor expansion of k in k
21.237 * [backup-simplify]: Simplify 0 into 0
21.237 * [backup-simplify]: Simplify 1 into 1
21.237 * [backup-simplify]: Simplify (/ 1 1) into 1
21.237 * [backup-simplify]: Simplify (sqrt 0) into 0
21.238 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.239 * [backup-simplify]: Simplify (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 0) into 0
21.239 * [backup-simplify]: Simplify 0 into 0
21.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
21.241 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
21.242 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
21.242 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.242 * [backup-simplify]: Simplify (- 0) into 0
21.243 * [backup-simplify]: Simplify (+ 0 0) into 0
21.244 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
21.246 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
21.247 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
21.249 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.252 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
21.253 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
21.253 * [taylor]: Taking taylor expansion of 0 in k
21.253 * [backup-simplify]: Simplify 0 into 0
21.256 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
21.257 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
21.259 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
21.259 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
21.260 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
21.261 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.262 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
21.266 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
21.266 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
21.266 * [backup-simplify]: Simplify (- 0) into 0
21.267 * [backup-simplify]: Simplify (+ 0 0) into 0
21.268 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
21.269 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
21.270 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
21.272 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
21.274 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
21.275 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
21.275 * [taylor]: Taking taylor expansion of 0 in k
21.275 * [backup-simplify]: Simplify 0 into 0
21.275 * [backup-simplify]: Simplify 0 into 0
21.276 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
21.277 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.279 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
21.281 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
21.281 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
21.281 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
21.282 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
21.283 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.283 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
21.290 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
21.291 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
21.291 * [backup-simplify]: Simplify (- 0) into 0
21.291 * [backup-simplify]: Simplify (+ 0 0) into 0
21.292 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
21.293 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
21.294 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
21.296 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
21.298 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
21.300 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
21.300 * [taylor]: Taking taylor expansion of 0 in k
21.300 * [backup-simplify]: Simplify 0 into 0
21.300 * [backup-simplify]: Simplify 0 into 0
21.300 * [backup-simplify]: Simplify 0 into 0
21.300 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.303 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.308 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
21.310 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
21.312 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
21.316 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (* (/ 1 k) 1)) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))))) into (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))
21.317 * [backup-simplify]: Simplify (/ 1 (/ (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))))
21.317 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in (n k) around 0
21.317 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k
21.317 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.317 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.317 * [taylor]: Taking taylor expansion of -1 in k
21.317 * [backup-simplify]: Simplify -1 into -1
21.317 * [taylor]: Taking taylor expansion of k in k
21.317 * [backup-simplify]: Simplify 0 into 0
21.317 * [backup-simplify]: Simplify 1 into 1
21.317 * [backup-simplify]: Simplify (/ -1 1) into -1
21.318 * [backup-simplify]: Simplify (sqrt 0) into 0
21.319 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.319 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
21.319 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
21.319 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
21.319 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
21.319 * [taylor]: Taking taylor expansion of 1/2 in k
21.319 * [backup-simplify]: Simplify 1/2 into 1/2
21.319 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
21.319 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.320 * [taylor]: Taking taylor expansion of k in k
21.320 * [backup-simplify]: Simplify 0 into 0
21.320 * [backup-simplify]: Simplify 1 into 1
21.320 * [backup-simplify]: Simplify (/ 1 1) into 1
21.320 * [taylor]: Taking taylor expansion of 1 in k
21.320 * [backup-simplify]: Simplify 1 into 1
21.320 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
21.320 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
21.320 * [taylor]: Taking taylor expansion of -2 in k
21.320 * [backup-simplify]: Simplify -2 into -2
21.320 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.320 * [taylor]: Taking taylor expansion of PI in k
21.320 * [backup-simplify]: Simplify PI into PI
21.320 * [taylor]: Taking taylor expansion of n in k
21.320 * [backup-simplify]: Simplify n into n
21.320 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.320 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
21.321 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
21.321 * [backup-simplify]: Simplify (+ 1 0) into 1
21.321 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
21.322 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
21.322 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
21.322 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
21.322 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in n
21.322 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
21.322 * [taylor]: Taking taylor expansion of (/ -1 k) in n
21.322 * [taylor]: Taking taylor expansion of -1 in n
21.322 * [backup-simplify]: Simplify -1 into -1
21.322 * [taylor]: Taking taylor expansion of k in n
21.322 * [backup-simplify]: Simplify k into k
21.322 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
21.322 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
21.323 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
21.323 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
21.323 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
21.323 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
21.323 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
21.323 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
21.323 * [taylor]: Taking taylor expansion of 1/2 in n
21.323 * [backup-simplify]: Simplify 1/2 into 1/2
21.323 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
21.323 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.323 * [taylor]: Taking taylor expansion of k in n
21.323 * [backup-simplify]: Simplify k into k
21.323 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.323 * [taylor]: Taking taylor expansion of 1 in n
21.323 * [backup-simplify]: Simplify 1 into 1
21.323 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
21.323 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
21.323 * [taylor]: Taking taylor expansion of -2 in n
21.323 * [backup-simplify]: Simplify -2 into -2
21.323 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.323 * [taylor]: Taking taylor expansion of PI in n
21.323 * [backup-simplify]: Simplify PI into PI
21.323 * [taylor]: Taking taylor expansion of n in n
21.323 * [backup-simplify]: Simplify 0 into 0
21.323 * [backup-simplify]: Simplify 1 into 1
21.324 * [backup-simplify]: Simplify (/ PI 1) into PI
21.324 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
21.325 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
21.325 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
21.326 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
21.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
21.328 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
21.329 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
21.330 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
21.330 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in n
21.330 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
21.330 * [taylor]: Taking taylor expansion of (/ -1 k) in n
21.330 * [taylor]: Taking taylor expansion of -1 in n
21.330 * [backup-simplify]: Simplify -1 into -1
21.330 * [taylor]: Taking taylor expansion of k in n
21.330 * [backup-simplify]: Simplify k into k
21.330 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
21.331 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
21.331 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
21.331 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
21.331 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
21.331 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
21.331 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
21.331 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
21.331 * [taylor]: Taking taylor expansion of 1/2 in n
21.331 * [backup-simplify]: Simplify 1/2 into 1/2
21.331 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
21.331 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.331 * [taylor]: Taking taylor expansion of k in n
21.331 * [backup-simplify]: Simplify k into k
21.331 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.331 * [taylor]: Taking taylor expansion of 1 in n
21.331 * [backup-simplify]: Simplify 1 into 1
21.331 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
21.331 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
21.331 * [taylor]: Taking taylor expansion of -2 in n
21.331 * [backup-simplify]: Simplify -2 into -2
21.331 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.331 * [taylor]: Taking taylor expansion of PI in n
21.331 * [backup-simplify]: Simplify PI into PI
21.331 * [taylor]: Taking taylor expansion of n in n
21.331 * [backup-simplify]: Simplify 0 into 0
21.331 * [backup-simplify]: Simplify 1 into 1
21.331 * [backup-simplify]: Simplify (/ PI 1) into PI
21.332 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
21.332 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
21.332 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
21.332 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
21.333 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
21.334 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
21.335 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
21.335 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
21.335 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) in k
21.335 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.335 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.335 * [taylor]: Taking taylor expansion of -1 in k
21.335 * [backup-simplify]: Simplify -1 into -1
21.335 * [taylor]: Taking taylor expansion of k in k
21.335 * [backup-simplify]: Simplify 0 into 0
21.335 * [backup-simplify]: Simplify 1 into 1
21.336 * [backup-simplify]: Simplify (/ -1 1) into -1
21.336 * [backup-simplify]: Simplify (sqrt 0) into 0
21.337 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.337 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
21.337 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
21.337 * [taylor]: Taking taylor expansion of 1/2 in k
21.337 * [backup-simplify]: Simplify 1/2 into 1/2
21.337 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
21.337 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
21.337 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.337 * [taylor]: Taking taylor expansion of k in k
21.337 * [backup-simplify]: Simplify 0 into 0
21.337 * [backup-simplify]: Simplify 1 into 1
21.337 * [backup-simplify]: Simplify (/ 1 1) into 1
21.337 * [taylor]: Taking taylor expansion of 1 in k
21.337 * [backup-simplify]: Simplify 1 into 1
21.337 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
21.337 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
21.337 * [taylor]: Taking taylor expansion of (* -2 PI) in k
21.337 * [taylor]: Taking taylor expansion of -2 in k
21.337 * [backup-simplify]: Simplify -2 into -2
21.337 * [taylor]: Taking taylor expansion of PI in k
21.337 * [backup-simplify]: Simplify PI into PI
21.338 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
21.338 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
21.338 * [taylor]: Taking taylor expansion of (log n) in k
21.338 * [taylor]: Taking taylor expansion of n in k
21.338 * [backup-simplify]: Simplify n into n
21.338 * [backup-simplify]: Simplify (log n) into (log n)
21.339 * [backup-simplify]: Simplify (+ 1 0) into 1
21.339 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
21.339 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
21.340 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
21.341 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
21.341 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
21.342 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
21.343 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
21.343 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
21.344 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
21.345 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
21.345 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.345 * [backup-simplify]: Simplify (+ 0 0) into 0
21.346 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
21.347 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
21.347 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
21.348 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.350 * [backup-simplify]: Simplify (- (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (+ (* (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))) into 0
21.350 * [taylor]: Taking taylor expansion of 0 in k
21.351 * [backup-simplify]: Simplify 0 into 0
21.351 * [backup-simplify]: Simplify 0 into 0
21.351 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
21.353 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.355 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
21.356 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
21.356 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
21.356 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
21.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.357 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
21.359 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
21.359 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
21.360 * [backup-simplify]: Simplify (+ 0 0) into 0
21.360 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
21.361 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
21.362 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
21.364 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
21.366 * [backup-simplify]: Simplify (- (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (+ (* (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))) into 0
21.366 * [taylor]: Taking taylor expansion of 0 in k
21.366 * [backup-simplify]: Simplify 0 into 0
21.366 * [backup-simplify]: Simplify 0 into 0
21.366 * [backup-simplify]: Simplify 0 into 0
21.367 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.369 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.373 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
21.374 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
21.376 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (* (/ 1 (- k)) 1)) (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))
21.376 * * * [progress]: simplifying candidates
21.376 * * * * [progress]: [ 1 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))))>
21.376 * * * * [progress]: [ 2 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))))>
21.376 * * * * [progress]: [ 3 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))) (sqrt k)))))>
21.376 * * * * [progress]: [ 4 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 5 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 6 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 7 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 8 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 9 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 10 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 11 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 12 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 13 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 14 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 15 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (sqrt k)))))>
21.377 * * * * [progress]: [ 16 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 17 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 18 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (sqrt k)))))>
21.377 * * * * [progress]: [ 19 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 20 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 21 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))))>
21.377 * * * * [progress]: [ 22 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 23 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 24 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (sqrt k)))))>
21.377 * * * * [progress]: [ 25 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 26 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (sqrt k)))))>
21.377 * * * * [progress]: [ 27 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 28 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))))>
21.378 * * * * [progress]: [ 29 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))))>
21.378 * * * * [progress]: [ 30 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 31 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 32 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (- 1 k)) (/ 1 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 33 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)))))>
21.378 * * * * [progress]: [ 34 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt k)))))>
21.378 * * * * [progress]: [ 35 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (exp (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))))>
21.378 * * * * [progress]: [ 36 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (log (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))))>
21.378 * * * * [progress]: [ 37 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))))>
21.378 * * * * [progress]: [ 38 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))))>
21.378 * * * * [progress]: [ 39 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))))>
21.378 * * * * [progress]: [ 40 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (* 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))))>
21.378 * * * * [progress]: [ 41 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))))>
21.378 * * * * [progress]: [ 42 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))))>
21.378 * * * * [progress]: [ 43 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 44 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 45 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 46 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 47 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 48 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 49 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 50 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (exp (log (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 51 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (log (exp (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.378 * * * * [progress]: [ 52 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 53 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 54 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 55 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 56 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 57 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 58 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 59 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 60 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 61 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 62 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 63 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))))>
21.379 * * * * [progress]: [ 64 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (log1p (expm1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.379 * * * * [progress]: [ 65 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (expm1 (log1p (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.379 * * * * [progress]: [ 66 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (pow (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) 1))))>
21.379 * * * * [progress]: [ 67 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (exp (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.379 * * * * [progress]: [ 68 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (exp (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.379 * * * * [progress]: [ 69 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (exp (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.379 * * * * [progress]: [ 70 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (exp (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.379 * * * * [progress]: [ 71 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (exp (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))))))>
21.379 * * * * [progress]: [ 72 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (exp (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.379 * * * * [progress]: [ 73 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (log (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.379 * * * * [progress]: [ 74 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (cbrt (/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))))>
21.379 * * * * [progress]: [ 75 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.379 * * * * [progress]: [ 76 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (cbrt (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.379 * * * * [progress]: [ 77 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.380 * * * * [progress]: [ 78 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (- (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- (sqrt k))))))>
21.380 * * * * [progress]: [ 79 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 80 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))))>
21.380 * * * * [progress]: [ 81 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 82 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
21.380 * * * * [progress]: [ 83 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 84 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow n (/ (- 1 k) 2)) 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
21.380 * * * * [progress]: [ 85 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 86 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))))>
21.380 * * * * [progress]: [ 87 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 88 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.380 * * * * [progress]: [ 89 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 90 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.380 * * * * [progress]: [ 91 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 92 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))))>
21.380 * * * * [progress]: [ 93 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 94 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.380 * * * * [progress]: [ 95 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 96 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.380 * * * * [progress]: [ 97 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 98 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))))>
21.380 * * * * [progress]: [ 99 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.380 * * * * [progress]: [ 100 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.380 * * * * [progress]: [ 101 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.381 * * * * [progress]: [ 102 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ 1 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.381 * * * * [progress]: [ 103 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))))>
21.381 * * * * [progress]: [ 104 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))))>
21.381 * * * * [progress]: [ 105 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))))>
21.381 * * * * [progress]: [ 106 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))))>
21.381 * * * * [progress]: [ 107 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))))>
21.381 * * * * [progress]: [ 108 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))))>
21.381 * * * * [progress]: [ 109 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.381 * * * * [progress]: [ 110 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))))>
21.381 * * * * [progress]: [ 111 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
21.381 * * * * [progress]: [ 112 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))))>
21.381 * * * * [progress]: [ 113 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))))>
21.381 * * * * [progress]: [ 114 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))))>
21.381 * * * * [progress]: [ 115 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt 1)) (sqrt k)))))>
21.381 * * * * [progress]: [ 116 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))))>
21.381 * * * * [progress]: [ 117 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt k)))))>
21.381 * * * * [progress]: [ 118 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))))))>
21.381 * * * * [progress]: [ 119 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))))>
21.381 * * * * [progress]: [ 120 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))))>
21.381 * * * * [progress]: [ 121 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
21.381 * * * * [progress]: [ 122 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))))>
21.381 * * * * [progress]: [ 123 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))))>
21.381 * * * * [progress]: [ 124 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.381 * * * * [progress]: [ 125 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (log1p (expm1 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.382 * * * * [progress]: [ 126 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (expm1 (log1p (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.382 * * * * [progress]: [ 127 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (pow (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) -1)))>
21.382 * * * * [progress]: [ 128 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (pow (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (- 1))))>
21.382 * * * * [progress]: [ 129 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (pow (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) 1)))>
21.382 * * * * [progress]: [ 130 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 131 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 132 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 133 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 134 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 135 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.382 * * * * [progress]: [ 136 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- 0 (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 137 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- 0 (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 138 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- 0 (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 139 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- 0 (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 140 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- 0 (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 141 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- 0 (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.382 * * * * [progress]: [ 142 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log 1) (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 143 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log 1) (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 144 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log 1) (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 145 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log 1) (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 146 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log 1) (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))))))>
21.382 * * * * [progress]: [ 147 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log 1) (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.382 * * * * [progress]: [ 148 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (log (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.382 * * * * [progress]: [ 149 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (log (exp (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.382 * * * * [progress]: [ 150 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (/ (* (* 1 1) 1) (/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))))>
21.383 * * * * [progress]: [ 151 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (/ (* (* 1 1) 1) (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.383 * * * * [progress]: [ 152 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (cbrt (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.383 * * * * [progress]: [ 153 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (* (* (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.383 * * * * [progress]: [ 154 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.383 * * * * [progress]: [ 155 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (- 1) (- (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.383 * * * * [progress]: [ 156 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))) (/ (cbrt 1) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.383 * * * * [progress]: [ 157 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (/ (cbrt 1) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.383 * * * * [progress]: [ 158 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
21.383 * * * * [progress]: [ 159 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))))>
21.383 * * * * [progress]: [ 160 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (cbrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.383 * * * * [progress]: [ 161 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow n (/ (- 1 k) 2)) (sqrt 1))) (/ (cbrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
21.383 * * * * [progress]: [ 162 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (cbrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.383 * * * * [progress]: [ 163 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow n (/ (- 1 k) 2)) 1)) (/ (cbrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
21.383 * * * * [progress]: [ 164 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
21.383 * * * * [progress]: [ 165 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))))>
21.383 * * * * [progress]: [ 166 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ (cbrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.383 * * * * [progress]: [ 167 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1))) (/ (cbrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.383 * * * * [progress]: [ 168 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ (cbrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.383 * * * * [progress]: [ 169 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1)) (/ (cbrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.383 * * * * [progress]: [ 170 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
21.383 * * * * [progress]: [ 171 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))))>
21.383 * * * * [progress]: [ 172 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (cbrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.384 * * * * [progress]: [ 173 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))) (/ (cbrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.384 * * * * [progress]: [ 174 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (cbrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.384 * * * * [progress]: [ 175 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)) (/ (cbrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.384 * * * * [progress]: [ 176 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
21.384 * * * * [progress]: [ 177 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))))>
21.384 * * * * [progress]: [ 178 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt (sqrt k)))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.384 * * * * [progress]: [ 179 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt 1))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.384 * * * * [progress]: [ 180 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt (sqrt k)))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.384 * * * * [progress]: [ 181 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 1)) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.386 * * * * [progress]: [ 182 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))))>
21.386 * * * * [progress]: [ 183 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))))>
21.386 * * * * [progress]: [ 184 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))))>
21.386 * * * * [progress]: [ 185 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))))>
21.386 * * * * [progress]: [ 186 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))))>
21.386 * * * * [progress]: [ 187 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))))>
21.386 * * * * [progress]: [ 188 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.386 * * * * [progress]: [ 189 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt 1) (cbrt 1)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (cbrt 1) (/ 1 (sqrt k))))))>
21.386 * * * * [progress]: [ 190 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))) (/ (sqrt 1) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.386 * * * * [progress]: [ 191 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (/ (sqrt 1) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.387 * * * * [progress]: [ 192 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 193 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))))>
21.387 * * * * [progress]: [ 194 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (sqrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 195 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow n (/ (- 1 k) 2)) (sqrt 1))) (/ (sqrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
21.387 * * * * [progress]: [ 196 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (sqrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 197 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow n (/ (- 1 k) 2)) 1)) (/ (sqrt 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
21.387 * * * * [progress]: [ 198 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 199 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))))>
21.387 * * * * [progress]: [ 200 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ (sqrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 201 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1))) (/ (sqrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.387 * * * * [progress]: [ 202 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ (sqrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 203 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1)) (/ (sqrt 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.387 * * * * [progress]: [ 204 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 205 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))))>
21.387 * * * * [progress]: [ 206 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 207 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))) (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.387 * * * * [progress]: [ 208 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 209 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)) (/ (sqrt 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.387 * * * * [progress]: [ 210 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 211 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))))>
21.387 * * * * [progress]: [ 212 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ 1 (sqrt (sqrt k)))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.387 * * * * [progress]: [ 213 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ 1 (sqrt 1))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.388 * * * * [progress]: [ 214 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ 1 (sqrt (sqrt k)))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.388 * * * * [progress]: [ 215 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ 1 1)) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.388 * * * * [progress]: [ 216 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))))>
21.388 * * * * [progress]: [ 217 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))))>
21.388 * * * * [progress]: [ 218 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))))>
21.388 * * * * [progress]: [ 219 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))))>
21.388 * * * * [progress]: [ 220 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))))>
21.388 * * * * [progress]: [ 221 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))))>
21.388 * * * * [progress]: [ 222 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) 1) (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.388 * * * * [progress]: [ 223 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (/ 1 (sqrt k))))))>
21.388 * * * * [progress]: [ 224 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))) (/ 1 (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.388 * * * * [progress]: [ 225 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (/ 1 (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.388 * * * * [progress]: [ 226 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
21.388 * * * * [progress]: [ 227 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ 1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))))>
21.388 * * * * [progress]: [ 228 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ 1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.388 * * * * [progress]: [ 229 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt 1))) (/ 1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
21.388 * * * * [progress]: [ 230 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ 1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.388 * * * * [progress]: [ 231 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow n (/ (- 1 k) 2)) 1)) (/ 1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
21.388 * * * * [progress]: [ 232 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
21.388 * * * * [progress]: [ 233 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))) (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))))>
21.388 * * * * [progress]: [ 234 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.388 * * * * [progress]: [ 235 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1))) (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.388 * * * * [progress]: [ 236 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 237 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1)) (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.389 * * * * [progress]: [ 238 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 239 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k))))) (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))))>
21.389 * * * * [progress]: [ 240 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 241 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))) (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.389 * * * * [progress]: [ 242 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 243 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)) (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))))>
21.389 * * * * [progress]: [ 244 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 245 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))))>
21.389 * * * * [progress]: [ 246 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ 1 (sqrt (sqrt k)))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 247 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ 1 (sqrt 1))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.389 * * * * [progress]: [ 248 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ 1 (sqrt (sqrt k)))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 249 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ 1 1)) (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.389 * * * * [progress]: [ 250 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 251 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))))>
21.389 * * * * [progress]: [ 252 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 253 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))))>
21.389 * * * * [progress]: [ 254 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))))>
21.389 * * * * [progress]: [ 255 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)) (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))))>
21.389 * * * * [progress]: [ 256 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 1) (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.389 * * * * [progress]: [ 257 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (/ 1 (sqrt k))))))>
21.389 * * * * [progress]: [ 258 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* 1 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.389 * * * * [progress]: [ 259 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* 1 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.390 * * * * [progress]: [ 260 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) 1))))>
21.390 * * * * [progress]: [ 261 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.390 * * * * [progress]: [ 262 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))))>
21.390 * * * * [progress]: [ 263 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
21.390 * * * * [progress]: [ 264 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k))))))>
21.390 * * * * [progress]: [ 265 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
21.390 * * * * [progress]: [ 266 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt 1))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
21.390 * * * * [progress]: [ 267 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
21.390 * * * * [progress]: [ 268 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow n (/ (- 1 k) 2)) 1)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
21.390 * * * * [progress]: [ 269 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
21.390 * * * * [progress]: [ 270 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k))))))>
21.390 * * * * [progress]: [ 271 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
21.390 * * * * [progress]: [ 272 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))))>
21.390 * * * * [progress]: [ 273 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
21.390 * * * * [progress]: [ 274 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1)) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))))>
21.390 * * * * [progress]: [ 275 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
21.390 * * * * [progress]: [ 276 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k))))))>
21.390 * * * * [progress]: [ 277 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
21.390 * * * * [progress]: [ 278 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))))>
21.390 * * * * [progress]: [ 279 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
21.390 * * * * [progress]: [ 280 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))))>
21.390 * * * * [progress]: [ 281 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
21.390 * * * * [progress]: [ 282 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))))))>
21.391 * * * * [progress]: [ 283 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
21.391 * * * * [progress]: [ 284 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ 1 (sqrt 1))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
21.391 * * * * [progress]: [ 285 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
21.391 * * * * [progress]: [ 286 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ 1 1)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
21.391 * * * * [progress]: [ 287 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k))))))>
21.391 * * * * [progress]: [ 288 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k))))))>
21.391 * * * * [progress]: [ 289 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
21.391 * * * * [progress]: [ 290 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k)))))>
21.391 * * * * [progress]: [ 291 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
21.391 * * * * [progress]: [ 292 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k)))))>
21.391 * * * * [progress]: [ 293 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
21.391 * * * * [progress]: [ 294 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt k)))))>
21.391 * * * * [progress]: [ 295 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (* (cbrt 1) (cbrt 1)) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (cbrt 1)))))>
21.391 * * * * [progress]: [ 296 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt 1) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (sqrt 1)))))>
21.391 * * * * [progress]: [ 297 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) 1))))>
21.391 * * * * [progress]: [ 298 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
21.391 * * * * [progress]: [ 299 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (posit16->real (real->posit16 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
21.391 * * * * [progress]: [ 300 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))))>
21.391 * * * * [progress]: [ 301 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))))>
21.391 * * * * [progress]: [ 302 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))))>
21.391 * * * * [progress]: [ 303 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))))>
21.391 * * * * [progress]: [ 304 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))))>
21.391 * * * * [progress]: [ 305 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))))>
21.391 * * * * [progress]: [ 306 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))))>
21.392 * * * * [progress]: [ 307 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))))>
21.392 * * * * [progress]: [ 308 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))))>
21.392 * * * * [progress]: [ 309 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ k (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (pow (log n) 2) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log (* 2 PI)) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow k 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (pow k 2) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (pow (log (* 2 PI)) 2) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log n) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log (* 2 PI)) (* (log n) (pow k 3))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (pow k 3) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))))))))))))))))))>
21.392 * * * * [progress]: [ 310 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))))>
21.392 * * * * [progress]: [ 311 / 311 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))))>
21.400 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* n (* 2 PI)) (/ 1 2))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (expm1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))
  (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) 1)
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
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  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))
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  (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k))))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))))
  (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1)))
  (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))))
  (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1))
  (/ 1 (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1)))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))
  (/ 1 (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))))
  (/ 1 (/ 1 (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))))
  (/ 1 (/ 1 (sqrt (sqrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
  (/ 1 (/ 1 (sqrt 1)))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ 1 (/ 1 (sqrt (sqrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
  (/ 1 (/ 1 1))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1)))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k)))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k)))
  (/ 1 1)
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ 1 (/ 1 (sqrt k)))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) 1)
  (/ 1 (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))
  (/ 1 (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))
  (/ 1 (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))
  (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt 1)))
  (/ 1 (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))
  (/ 1 (/ (pow n (/ (- 1 k) 2)) 1))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1)))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))))
  (/ 1 (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1)))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (/ 1 (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1))
  (/ 1 (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (/ 1 (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (/ 1 (sqrt (sqrt k))))
  (/ 1 (/ 1 (sqrt 1)))
  (/ 1 (/ 1 (sqrt (sqrt k))))
  (/ 1 (/ 1 1))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1)))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1))
  (/ 1 1)
  (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (cbrt 1))
  (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (sqrt 1))
  (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) 1)
  (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (real->posit16 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
  (- (+ (* +nan.0 (/ k (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (pow (log n) 2) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log (* 2 PI)) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (pow k 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (pow k 2) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (pow (log (* 2 PI)) 2) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log n) (pow k 3)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (/ (* (log (* 2 PI)) (* (log n) (pow k 3))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (* +nan.0 (/ (pow k 3) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))
  (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))
21.408 * * [simplify]: iteration 1: (551 enodes)
21.735 * * [simplify]: iteration 2: (1520 enodes)
22.783 * * [simplify]: Extracting #0: cost 162 inf + 0
22.784 * * [simplify]: Extracting #1: cost 712 inf + 2
22.790 * * [simplify]: Extracting #2: cost 1054 inf + 17161
22.811 * * [simplify]: Extracting #3: cost 783 inf + 174438
22.868 * * [simplify]: Extracting #4: cost 389 inf + 357847
22.955 * * [simplify]: Extracting #5: cost 254 inf + 434713
23.099 * * [simplify]: Extracting #6: cost 175 inf + 483955
23.253 * * [simplify]: Extracting #7: cost 57 inf + 554733
23.374 * * [simplify]: Extracting #8: cost 28 inf + 584584
23.510 * * [simplify]: Extracting #9: cost 6 inf + 606341
23.723 * * [simplify]: Extracting #10: cost 0 inf + 611218
23.934 * [simplify]: Simplified to:
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* PI 2) (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (expm1 (* (* PI 2) n))
  (log1p (* (* PI 2) n))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* (* n (* (* 8 PI) PI)) PI) (* n n))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* 2 (* PI (cbrt n)))
  (* PI (* 2 (sqrt n)))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (expm1 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (/ (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3) (* (sqrt k) k))
  (* (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow n (/ (- 1 k) 2))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow n (/ (- 1 k) 2))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (* (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (fabs (cbrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
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  (+ (fma 1/4 (* (* (sqrt (* (* PI 2) n)) (log (* PI 2))) (* (* k k) (log n))) (fma (* (sqrt (* (* PI 2) n)) (* (log n) (* (log n) (* k k)))) 1/8 (fma 1/8 (* (* (log (* PI 2)) (* (sqrt (* (* PI 2) n)) (log (* PI 2)))) (* k k)) (sqrt (* (* PI 2) n))))) (* -1/2 (* k (+ (* (sqrt (* (* PI 2) n)) (log n)) (* (sqrt (* (* PI 2) n)) (log (* PI 2)))))))
  (exp (* (- 1 k) (* (log (* (* PI 2) n)) 1/2)))
  (exp (* (- 1 k) (* (- (log (* -2 PI)) (log (/ -1 n))) 1/2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (- (+ (- (* (* +nan.0 (log (* PI 2))) (* (sqrt (* (* PI 2) n)) (* (* k k) (log n)))) (* (* (* +nan.0 (log (* PI 2))) (sqrt (* (* PI 2) n))) (* k k))) (- (* (* +nan.0 (sqrt (* (* PI 2) n))) (* (* k (log n)) (* k (log n)))) (+ (- (* k (* +nan.0 (sqrt (* (* PI 2) n)))) (* +nan.0 (sqrt (* (* PI 2) n)))) (+ (- (* +nan.0 (* (* (log (* PI 2)) (* (sqrt (* (* PI 2) n)) (log (* PI 2)))) (* k k))) (* (* +nan.0 (* (* k k) (log n))) (sqrt (* (* PI 2) n)))) (- (* (* +nan.0 (* k k)) (sqrt (* (* PI 2) n))) (* +nan.0 (- (* k (* (sqrt (* (* PI 2) n)) (log (* PI 2)))) (* (* (log n) k) (sqrt (* (* PI 2) n)))))))))))
  (- (- (* +nan.0 (/ (exp (* (- 1 k) (* (log (* (* PI 2) n)) 1/2))) k)) (- (* +nan.0 (/ (exp (* (- 1 k) (* (log (* (* PI 2) n)) 1/2))) (* k k))) (/ (* +nan.0 (/ (exp (* (- 1 k) (* (log (* (* PI 2) n)) 1/2))) (* k k))) k))))
  (+ (- (/ (exp (* (- 1 k) (* (- (log (* -2 PI)) (log (/ -1 n))) 1/2))) (/ k +nan.0))) (* +nan.0 (- (/ (exp (* (- 1 k) (* (- (log (* -2 PI)) (log (/ -1 n))) 1/2))) (* k k)) (exp (* (- 1 k) (* (- (log (* -2 PI)) (log (/ -1 n))) 1/2))))))
  (- (- (* +nan.0 (/ k (sqrt (* (* PI 2) n)))) (- (- (/ (* (* (* (log n) (* (log n) (* k k))) k) +nan.0) (sqrt (* (* PI 2) n))) (/ (* +nan.0 (log (* PI 2))) (/ (/ (sqrt (* (* PI 2) n)) k) (* k k)))) (+ (+ (- (/ (* +nan.0 (* k k)) (/ (sqrt (* (* PI 2) n)) (log (* PI 2)))) (* (/ (* (log (* PI 2)) (log (* PI 2))) (/ (/ (sqrt (* (* PI 2) n)) k) (* k k))) +nan.0)) (- (- (/ (* +nan.0 (* (* k k) (log n))) (sqrt (* (* PI 2) n))) (* +nan.0 (/ (* (* (log n) (* k k)) k) (sqrt (* (* PI 2) n))))) (+ (* (* (/ (log (* PI 2)) (sqrt (* (* PI 2) n))) (* (* (log n) (* k k)) k)) (- +nan.0)) (/ +nan.0 (/ (/ (sqrt (* (* PI 2) n)) k) (* k k)))))) (* (- +nan.0) (/ (* k k) (sqrt (* (* PI 2) n))))))))
  (- (+ (- (/ +nan.0 (exp (* (- 1 k) (* (log (* (* PI 2) n)) 1/2)))) (/ (/ +nan.0 (exp (* (- 1 k) (* (log (* (* PI 2) n)) 1/2)))) (* k k))) (/ (/ +nan.0 (exp (* (- 1 k) (* (log (* (* PI 2) n)) 1/2)))) k)))
  (- (- (* (/ +nan.0 k) (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k))))) (* +nan.0 (- (/ (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (* k k)) (exp (* -1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k))))))))
24.004 * * * [progress]: adding candidates to table
28.111 * * [progress]: iteration 4 / 4
28.111 * * * [progress]: picking best candidate
28.159 * * * * [pick]: Picked  #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
28.159 * * * [progress]: localizing error
28.210 * * * [progress]: generating rewritten candidates
28.210 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
28.215 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
28.222 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
28.230 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
28.261 * * * [progress]: generating series expansions
28.261 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
28.261 * [backup-simplify]: Simplify (pow n (/ (- 1 k) 2)) into (pow n (* 1/2 (- 1 k)))
28.261 * [approximate]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in (n k) around 0
28.261 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in k
28.261 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in k
28.261 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in k
28.261 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
28.261 * [taylor]: Taking taylor expansion of 1/2 in k
28.261 * [backup-simplify]: Simplify 1/2 into 1/2
28.261 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.261 * [taylor]: Taking taylor expansion of 1 in k
28.261 * [backup-simplify]: Simplify 1 into 1
28.261 * [taylor]: Taking taylor expansion of k in k
28.261 * [backup-simplify]: Simplify 0 into 0
28.261 * [backup-simplify]: Simplify 1 into 1
28.261 * [taylor]: Taking taylor expansion of (log n) in k
28.261 * [taylor]: Taking taylor expansion of n in k
28.261 * [backup-simplify]: Simplify n into n
28.261 * [backup-simplify]: Simplify (log n) into (log n)
28.262 * [backup-simplify]: Simplify (- 0) into 0
28.262 * [backup-simplify]: Simplify (+ 1 0) into 1
28.262 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.262 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
28.262 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
28.262 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
28.262 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
28.262 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
28.262 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
28.262 * [taylor]: Taking taylor expansion of 1/2 in n
28.262 * [backup-simplify]: Simplify 1/2 into 1/2
28.262 * [taylor]: Taking taylor expansion of (- 1 k) in n
28.262 * [taylor]: Taking taylor expansion of 1 in n
28.262 * [backup-simplify]: Simplify 1 into 1
28.262 * [taylor]: Taking taylor expansion of k in n
28.263 * [backup-simplify]: Simplify k into k
28.263 * [taylor]: Taking taylor expansion of (log n) in n
28.263 * [taylor]: Taking taylor expansion of n in n
28.263 * [backup-simplify]: Simplify 0 into 0
28.263 * [backup-simplify]: Simplify 1 into 1
28.263 * [backup-simplify]: Simplify (log 1) into 0
28.263 * [backup-simplify]: Simplify (- k) into (- k)
28.263 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
28.263 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
28.263 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
28.263 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
28.263 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
28.263 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
28.263 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
28.263 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
28.263 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
28.263 * [taylor]: Taking taylor expansion of 1/2 in n
28.263 * [backup-simplify]: Simplify 1/2 into 1/2
28.263 * [taylor]: Taking taylor expansion of (- 1 k) in n
28.263 * [taylor]: Taking taylor expansion of 1 in n
28.263 * [backup-simplify]: Simplify 1 into 1
28.264 * [taylor]: Taking taylor expansion of k in n
28.264 * [backup-simplify]: Simplify k into k
28.264 * [taylor]: Taking taylor expansion of (log n) in n
28.264 * [taylor]: Taking taylor expansion of n in n
28.264 * [backup-simplify]: Simplify 0 into 0
28.264 * [backup-simplify]: Simplify 1 into 1
28.264 * [backup-simplify]: Simplify (log 1) into 0
28.264 * [backup-simplify]: Simplify (- k) into (- k)
28.264 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
28.264 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
28.264 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
28.264 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
28.264 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
28.264 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k
28.264 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log n))) in k
28.264 * [taylor]: Taking taylor expansion of 1/2 in k
28.264 * [backup-simplify]: Simplify 1/2 into 1/2
28.264 * [taylor]: Taking taylor expansion of (* (- 1 k) (log n)) in k
28.264 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.264 * [taylor]: Taking taylor expansion of 1 in k
28.265 * [backup-simplify]: Simplify 1 into 1
28.265 * [taylor]: Taking taylor expansion of k in k
28.265 * [backup-simplify]: Simplify 0 into 0
28.265 * [backup-simplify]: Simplify 1 into 1
28.265 * [taylor]: Taking taylor expansion of (log n) in k
28.265 * [taylor]: Taking taylor expansion of n in k
28.265 * [backup-simplify]: Simplify n into n
28.265 * [backup-simplify]: Simplify (log n) into (log n)
28.265 * [backup-simplify]: Simplify (- 0) into 0
28.265 * [backup-simplify]: Simplify (+ 1 0) into 1
28.265 * [backup-simplify]: Simplify (* 1 (log n)) into (log n)
28.265 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
28.265 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
28.265 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2)
28.266 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
28.266 * [backup-simplify]: Simplify (- 0) into 0
28.267 * [backup-simplify]: Simplify (+ 0 0) into 0
28.267 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
28.267 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
28.267 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0
28.268 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
28.268 * [taylor]: Taking taylor expansion of 0 in k
28.268 * [backup-simplify]: Simplify 0 into 0
28.268 * [backup-simplify]: Simplify 0 into 0
28.268 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
28.268 * [backup-simplify]: Simplify (- 1) into -1
28.269 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.269 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log n))) into (- (log n))
28.269 * [backup-simplify]: Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n)))
28.269 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
28.269 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n)))
28.271 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
28.271 * [backup-simplify]: Simplify (- 0) into 0
28.271 * [backup-simplify]: Simplify (+ 0 0) into 0
28.272 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
28.272 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
28.272 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
28.273 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.273 * [taylor]: Taking taylor expansion of 0 in k
28.273 * [backup-simplify]: Simplify 0 into 0
28.273 * [backup-simplify]: Simplify 0 into 0
28.273 * [backup-simplify]: Simplify 0 into 0
28.274 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
28.275 * [backup-simplify]: Simplify (- 0) into 0
28.275 * [backup-simplify]: Simplify (+ 0 0) into 0
28.275 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log n)))) into 0
28.276 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0
28.276 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
28.276 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
28.277 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k))))
28.277 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) into (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k))))
28.277 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
28.277 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in k
28.277 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in k
28.277 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in k
28.277 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
28.277 * [taylor]: Taking taylor expansion of 1/2 in k
28.277 * [backup-simplify]: Simplify 1/2 into 1/2
28.277 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.277 * [taylor]: Taking taylor expansion of 1 in k
28.277 * [backup-simplify]: Simplify 1 into 1
28.277 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.277 * [taylor]: Taking taylor expansion of k in k
28.277 * [backup-simplify]: Simplify 0 into 0
28.277 * [backup-simplify]: Simplify 1 into 1
28.277 * [backup-simplify]: Simplify (/ 1 1) into 1
28.277 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k
28.277 * [taylor]: Taking taylor expansion of (/ 1 n) in k
28.277 * [taylor]: Taking taylor expansion of n in k
28.277 * [backup-simplify]: Simplify n into n
28.277 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
28.277 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n))
28.278 * [backup-simplify]: Simplify (- 1) into -1
28.278 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.278 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
28.278 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
28.278 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))
28.278 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
28.278 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
28.278 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
28.278 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
28.278 * [taylor]: Taking taylor expansion of 1/2 in n
28.278 * [backup-simplify]: Simplify 1/2 into 1/2
28.279 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
28.279 * [taylor]: Taking taylor expansion of 1 in n
28.279 * [backup-simplify]: Simplify 1 into 1
28.279 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.279 * [taylor]: Taking taylor expansion of k in n
28.279 * [backup-simplify]: Simplify k into k
28.279 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.279 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
28.279 * [taylor]: Taking taylor expansion of (/ 1 n) in n
28.279 * [taylor]: Taking taylor expansion of n in n
28.279 * [backup-simplify]: Simplify 0 into 0
28.279 * [backup-simplify]: Simplify 1 into 1
28.279 * [backup-simplify]: Simplify (/ 1 1) into 1
28.279 * [backup-simplify]: Simplify (log 1) into 0
28.279 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
28.279 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
28.279 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
28.280 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
28.280 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
28.280 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
28.280 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
28.280 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
28.280 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
28.280 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
28.280 * [taylor]: Taking taylor expansion of 1/2 in n
28.280 * [backup-simplify]: Simplify 1/2 into 1/2
28.280 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
28.280 * [taylor]: Taking taylor expansion of 1 in n
28.280 * [backup-simplify]: Simplify 1 into 1
28.280 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.280 * [taylor]: Taking taylor expansion of k in n
28.280 * [backup-simplify]: Simplify k into k
28.280 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.280 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
28.280 * [taylor]: Taking taylor expansion of (/ 1 n) in n
28.280 * [taylor]: Taking taylor expansion of n in n
28.280 * [backup-simplify]: Simplify 0 into 0
28.280 * [backup-simplify]: Simplify 1 into 1
28.280 * [backup-simplify]: Simplify (/ 1 1) into 1
28.281 * [backup-simplify]: Simplify (log 1) into 0
28.281 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
28.281 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
28.281 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
28.281 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
28.281 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
28.281 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
28.281 * [taylor]: Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k
28.281 * [taylor]: Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (log n))) in k
28.281 * [taylor]: Taking taylor expansion of -1/2 in k
28.281 * [backup-simplify]: Simplify -1/2 into -1/2
28.281 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log n)) in k
28.281 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.281 * [taylor]: Taking taylor expansion of 1 in k
28.282 * [backup-simplify]: Simplify 1 into 1
28.282 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.282 * [taylor]: Taking taylor expansion of k in k
28.282 * [backup-simplify]: Simplify 0 into 0
28.282 * [backup-simplify]: Simplify 1 into 1
28.282 * [backup-simplify]: Simplify (/ 1 1) into 1
28.282 * [taylor]: Taking taylor expansion of (log n) in k
28.282 * [taylor]: Taking taylor expansion of n in k
28.282 * [backup-simplify]: Simplify n into n
28.282 * [backup-simplify]: Simplify (log n) into (log n)
28.282 * [backup-simplify]: Simplify (- 1) into -1
28.282 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.282 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n))
28.282 * [backup-simplify]: Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n))
28.283 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
28.283 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
28.283 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
28.284 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
28.284 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
28.284 * [backup-simplify]: Simplify (- 0) into 0
28.284 * [backup-simplify]: Simplify (+ 0 0) into 0
28.285 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
28.285 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
28.285 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
28.286 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
28.286 * [taylor]: Taking taylor expansion of 0 in k
28.286 * [backup-simplify]: Simplify 0 into 0
28.286 * [backup-simplify]: Simplify 0 into 0
28.286 * [backup-simplify]: Simplify 0 into 0
28.286 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.288 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
28.288 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.288 * [backup-simplify]: Simplify (- 0) into 0
28.288 * [backup-simplify]: Simplify (+ 0 0) into 0
28.289 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
28.289 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
28.290 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
28.291 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.291 * [taylor]: Taking taylor expansion of 0 in k
28.291 * [backup-simplify]: Simplify 0 into 0
28.291 * [backup-simplify]: Simplify 0 into 0
28.291 * [backup-simplify]: Simplify 0 into 0
28.291 * [backup-simplify]: Simplify 0 into 0
28.291 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.294 * [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
28.294 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.294 * [backup-simplify]: Simplify (- 0) into 0
28.295 * [backup-simplify]: Simplify (+ 0 0) into 0
28.295 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
28.296 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
28.296 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
28.297 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.297 * [taylor]: Taking taylor expansion of 0 in k
28.297 * [backup-simplify]: Simplify 0 into 0
28.297 * [backup-simplify]: Simplify 0 into 0
28.297 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) into (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))
28.298 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1)))
28.298 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
28.298 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in k
28.298 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in k
28.298 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in k
28.298 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
28.298 * [taylor]: Taking taylor expansion of 1/2 in k
28.298 * [backup-simplify]: Simplify 1/2 into 1/2
28.298 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
28.298 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.298 * [taylor]: Taking taylor expansion of k in k
28.298 * [backup-simplify]: Simplify 0 into 0
28.298 * [backup-simplify]: Simplify 1 into 1
28.298 * [backup-simplify]: Simplify (/ 1 1) into 1
28.298 * [taylor]: Taking taylor expansion of 1 in k
28.298 * [backup-simplify]: Simplify 1 into 1
28.298 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k
28.298 * [taylor]: Taking taylor expansion of (/ -1 n) in k
28.298 * [taylor]: Taking taylor expansion of -1 in k
28.298 * [backup-simplify]: Simplify -1 into -1
28.298 * [taylor]: Taking taylor expansion of n in k
28.298 * [backup-simplify]: Simplify n into n
28.298 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n)
28.298 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n))
28.299 * [backup-simplify]: Simplify (+ 1 0) into 1
28.299 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.299 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
28.299 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n)))))
28.299 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
28.299 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
28.299 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
28.299 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
28.299 * [taylor]: Taking taylor expansion of 1/2 in n
28.299 * [backup-simplify]: Simplify 1/2 into 1/2
28.299 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
28.299 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.299 * [taylor]: Taking taylor expansion of k in n
28.299 * [backup-simplify]: Simplify k into k
28.299 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.299 * [taylor]: Taking taylor expansion of 1 in n
28.299 * [backup-simplify]: Simplify 1 into 1
28.299 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
28.299 * [taylor]: Taking taylor expansion of (/ -1 n) in n
28.299 * [taylor]: Taking taylor expansion of -1 in n
28.299 * [backup-simplify]: Simplify -1 into -1
28.299 * [taylor]: Taking taylor expansion of n in n
28.299 * [backup-simplify]: Simplify 0 into 0
28.299 * [backup-simplify]: Simplify 1 into 1
28.300 * [backup-simplify]: Simplify (/ -1 1) into -1
28.300 * [backup-simplify]: Simplify (log -1) into (log -1)
28.300 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
28.300 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
28.301 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
28.301 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
28.301 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
28.301 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
28.301 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
28.301 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
28.301 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
28.301 * [taylor]: Taking taylor expansion of 1/2 in n
28.301 * [backup-simplify]: Simplify 1/2 into 1/2
28.301 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
28.301 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.301 * [taylor]: Taking taylor expansion of k in n
28.301 * [backup-simplify]: Simplify k into k
28.302 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.302 * [taylor]: Taking taylor expansion of 1 in n
28.302 * [backup-simplify]: Simplify 1 into 1
28.302 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
28.302 * [taylor]: Taking taylor expansion of (/ -1 n) in n
28.302 * [taylor]: Taking taylor expansion of -1 in n
28.302 * [backup-simplify]: Simplify -1 into -1
28.302 * [taylor]: Taking taylor expansion of n in n
28.302 * [backup-simplify]: Simplify 0 into 0
28.302 * [backup-simplify]: Simplify 1 into 1
28.302 * [backup-simplify]: Simplify (/ -1 1) into -1
28.302 * [backup-simplify]: Simplify (log -1) into (log -1)
28.302 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
28.302 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
28.303 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
28.303 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
28.304 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
28.304 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) in k
28.304 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) in k
28.304 * [taylor]: Taking taylor expansion of 1/2 in k
28.304 * [backup-simplify]: Simplify 1/2 into 1/2
28.304 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log -1) (log n))) in k
28.304 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
28.304 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.304 * [taylor]: Taking taylor expansion of k in k
28.304 * [backup-simplify]: Simplify 0 into 0
28.304 * [backup-simplify]: Simplify 1 into 1
28.304 * [backup-simplify]: Simplify (/ 1 1) into 1
28.304 * [taylor]: Taking taylor expansion of 1 in k
28.304 * [backup-simplify]: Simplify 1 into 1
28.304 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k
28.304 * [taylor]: Taking taylor expansion of (log -1) in k
28.304 * [taylor]: Taking taylor expansion of -1 in k
28.304 * [backup-simplify]: Simplify -1 into -1
28.305 * [backup-simplify]: Simplify (log -1) into (log -1)
28.305 * [taylor]: Taking taylor expansion of (log n) in k
28.305 * [taylor]: Taking taylor expansion of n in k
28.305 * [backup-simplify]: Simplify n into n
28.305 * [backup-simplify]: Simplify (log n) into (log n)
28.305 * [backup-simplify]: Simplify (+ 1 0) into 1
28.305 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
28.305 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
28.305 * [backup-simplify]: Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n))
28.306 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
28.306 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
28.306 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
28.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
28.308 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
28.308 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
28.308 * [backup-simplify]: Simplify (+ 0 0) into 0
28.308 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
28.309 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
28.309 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log -1) (log n)))) into 0
28.310 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
28.310 * [taylor]: Taking taylor expansion of 0 in k
28.310 * [backup-simplify]: Simplify 0 into 0
28.310 * [backup-simplify]: Simplify 0 into 0
28.310 * [backup-simplify]: Simplify 0 into 0
28.311 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.312 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
28.312 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.313 * [backup-simplify]: Simplify (+ 0 0) into 0
28.313 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
28.314 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
28.314 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
28.315 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.315 * [taylor]: Taking taylor expansion of 0 in k
28.315 * [backup-simplify]: Simplify 0 into 0
28.315 * [backup-simplify]: Simplify 0 into 0
28.315 * [backup-simplify]: Simplify 0 into 0
28.315 * [backup-simplify]: Simplify 0 into 0
28.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.319 * [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
28.319 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.319 * [backup-simplify]: Simplify (+ 0 0) into 0
28.325 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
28.325 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
28.326 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0
28.327 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.327 * [taylor]: Taking taylor expansion of 0 in k
28.327 * [backup-simplify]: Simplify 0 into 0
28.327 * [backup-simplify]: Simplify 0 into 0
28.328 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))
28.328 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
28.328 * [backup-simplify]: Simplify (pow (* 2 PI) (/ (- 1 k) 2)) into (pow (* 2 PI) (* 1/2 (- 1 k)))
28.328 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in (k) around 0
28.328 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
28.328 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
28.328 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
28.328 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
28.328 * [taylor]: Taking taylor expansion of 1/2 in k
28.328 * [backup-simplify]: Simplify 1/2 into 1/2
28.328 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.328 * [taylor]: Taking taylor expansion of 1 in k
28.328 * [backup-simplify]: Simplify 1 into 1
28.328 * [taylor]: Taking taylor expansion of k in k
28.328 * [backup-simplify]: Simplify 0 into 0
28.328 * [backup-simplify]: Simplify 1 into 1
28.328 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.329 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.329 * [taylor]: Taking taylor expansion of 2 in k
28.329 * [backup-simplify]: Simplify 2 into 2
28.329 * [taylor]: Taking taylor expansion of PI in k
28.329 * [backup-simplify]: Simplify PI into PI
28.329 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.329 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.330 * [backup-simplify]: Simplify (- 0) into 0
28.330 * [backup-simplify]: Simplify (+ 1 0) into 1
28.330 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.331 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.333 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
28.333 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
28.333 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
28.333 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
28.333 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
28.333 * [taylor]: Taking taylor expansion of 1/2 in k
28.333 * [backup-simplify]: Simplify 1/2 into 1/2
28.333 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.333 * [taylor]: Taking taylor expansion of 1 in k
28.333 * [backup-simplify]: Simplify 1 into 1
28.333 * [taylor]: Taking taylor expansion of k in k
28.333 * [backup-simplify]: Simplify 0 into 0
28.333 * [backup-simplify]: Simplify 1 into 1
28.333 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.333 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.333 * [taylor]: Taking taylor expansion of 2 in k
28.333 * [backup-simplify]: Simplify 2 into 2
28.333 * [taylor]: Taking taylor expansion of PI in k
28.333 * [backup-simplify]: Simplify PI into PI
28.333 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.334 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.334 * [backup-simplify]: Simplify (- 0) into 0
28.334 * [backup-simplify]: Simplify (+ 1 0) into 1
28.335 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.336 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.337 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
28.338 * [backup-simplify]: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2)
28.338 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
28.340 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
28.340 * [backup-simplify]: Simplify (- 1) into -1
28.340 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.341 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
28.342 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI))))
28.349 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))
28.352 * [backup-simplify]: Simplify (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) into (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))
28.352 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
28.354 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
28.355 * [backup-simplify]: Simplify (- 0) into 0
28.355 * [backup-simplify]: Simplify (+ 0 0) into 0
28.356 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
28.358 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0
28.372 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))
28.377 * [backup-simplify]: Simplify (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))
28.389 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) k) (pow (* 2 PI) 1/2))) into (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))))
28.390 * [backup-simplify]: Simplify (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))
28.390 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in (k) around 0
28.390 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
28.390 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
28.390 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
28.390 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
28.390 * [taylor]: Taking taylor expansion of 1/2 in k
28.390 * [backup-simplify]: Simplify 1/2 into 1/2
28.390 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.390 * [taylor]: Taking taylor expansion of 1 in k
28.390 * [backup-simplify]: Simplify 1 into 1
28.390 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.390 * [taylor]: Taking taylor expansion of k in k
28.390 * [backup-simplify]: Simplify 0 into 0
28.390 * [backup-simplify]: Simplify 1 into 1
28.391 * [backup-simplify]: Simplify (/ 1 1) into 1
28.391 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.391 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.391 * [taylor]: Taking taylor expansion of 2 in k
28.391 * [backup-simplify]: Simplify 2 into 2
28.391 * [taylor]: Taking taylor expansion of PI in k
28.391 * [backup-simplify]: Simplify PI into PI
28.391 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.392 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.393 * [backup-simplify]: Simplify (- 1) into -1
28.393 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.393 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
28.395 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
28.396 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
28.396 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
28.396 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
28.396 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
28.396 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
28.396 * [taylor]: Taking taylor expansion of 1/2 in k
28.396 * [backup-simplify]: Simplify 1/2 into 1/2
28.397 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.397 * [taylor]: Taking taylor expansion of 1 in k
28.397 * [backup-simplify]: Simplify 1 into 1
28.397 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.397 * [taylor]: Taking taylor expansion of k in k
28.397 * [backup-simplify]: Simplify 0 into 0
28.397 * [backup-simplify]: Simplify 1 into 1
28.397 * [backup-simplify]: Simplify (/ 1 1) into 1
28.397 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.397 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.397 * [taylor]: Taking taylor expansion of 2 in k
28.397 * [backup-simplify]: Simplify 2 into 2
28.397 * [taylor]: Taking taylor expansion of PI in k
28.397 * [backup-simplify]: Simplify PI into PI
28.398 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.399 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.399 * [backup-simplify]: Simplify (- 1) into -1
28.399 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.400 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
28.401 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
28.402 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
28.403 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
28.404 * [backup-simplify]: Simplify 0 into 0
28.404 * [backup-simplify]: Simplify 0 into 0
28.404 * [backup-simplify]: Simplify 0 into 0
28.404 * [backup-simplify]: Simplify 0 into 0
28.404 * [backup-simplify]: Simplify 0 into 0
28.404 * [backup-simplify]: Simplify 0 into 0
28.405 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
28.405 * [backup-simplify]: Simplify (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))
28.405 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in (k) around 0
28.406 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
28.406 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
28.406 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
28.406 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
28.406 * [taylor]: Taking taylor expansion of 1/2 in k
28.406 * [backup-simplify]: Simplify 1/2 into 1/2
28.406 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
28.406 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.406 * [taylor]: Taking taylor expansion of k in k
28.406 * [backup-simplify]: Simplify 0 into 0
28.406 * [backup-simplify]: Simplify 1 into 1
28.406 * [backup-simplify]: Simplify (/ 1 1) into 1
28.406 * [taylor]: Taking taylor expansion of 1 in k
28.406 * [backup-simplify]: Simplify 1 into 1
28.406 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.406 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.406 * [taylor]: Taking taylor expansion of 2 in k
28.406 * [backup-simplify]: Simplify 2 into 2
28.406 * [taylor]: Taking taylor expansion of PI in k
28.406 * [backup-simplify]: Simplify PI into PI
28.407 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.408 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.408 * [backup-simplify]: Simplify (+ 1 0) into 1
28.409 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.410 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.412 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
28.412 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
28.412 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
28.412 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
28.412 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
28.412 * [taylor]: Taking taylor expansion of 1/2 in k
28.412 * [backup-simplify]: Simplify 1/2 into 1/2
28.412 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
28.412 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.412 * [taylor]: Taking taylor expansion of k in k
28.412 * [backup-simplify]: Simplify 0 into 0
28.412 * [backup-simplify]: Simplify 1 into 1
28.412 * [backup-simplify]: Simplify (/ 1 1) into 1
28.412 * [taylor]: Taking taylor expansion of 1 in k
28.412 * [backup-simplify]: Simplify 1 into 1
28.412 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.412 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.412 * [taylor]: Taking taylor expansion of 2 in k
28.412 * [backup-simplify]: Simplify 2 into 2
28.412 * [taylor]: Taking taylor expansion of PI in k
28.412 * [backup-simplify]: Simplify PI into PI
28.413 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.414 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.414 * [backup-simplify]: Simplify (+ 1 0) into 1
28.415 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.417 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.418 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
28.419 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
28.420 * [backup-simplify]: Simplify 0 into 0
28.420 * [backup-simplify]: Simplify 0 into 0
28.420 * [backup-simplify]: Simplify 0 into 0
28.420 * [backup-simplify]: Simplify 0 into 0
28.420 * [backup-simplify]: Simplify 0 into 0
28.420 * [backup-simplify]: Simplify 0 into 0
28.421 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
28.421 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
28.422 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) into (* (pow (* 2 PI) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
28.422 * [approximate]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k) around 0
28.422 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
28.422 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
28.422 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
28.422 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
28.422 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
28.422 * [taylor]: Taking taylor expansion of 1/2 in k
28.422 * [backup-simplify]: Simplify 1/2 into 1/2
28.422 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.422 * [taylor]: Taking taylor expansion of 1 in k
28.422 * [backup-simplify]: Simplify 1 into 1
28.422 * [taylor]: Taking taylor expansion of k in k
28.422 * [backup-simplify]: Simplify 0 into 0
28.422 * [backup-simplify]: Simplify 1 into 1
28.422 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.422 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.422 * [taylor]: Taking taylor expansion of 2 in k
28.422 * [backup-simplify]: Simplify 2 into 2
28.422 * [taylor]: Taking taylor expansion of PI in k
28.422 * [backup-simplify]: Simplify PI into PI
28.423 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.424 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.424 * [backup-simplify]: Simplify (- 0) into 0
28.425 * [backup-simplify]: Simplify (+ 1 0) into 1
28.425 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.427 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.429 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
28.429 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
28.429 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.429 * [taylor]: Taking taylor expansion of k in k
28.429 * [backup-simplify]: Simplify 0 into 0
28.429 * [backup-simplify]: Simplify 1 into 1
28.430 * [backup-simplify]: Simplify (/ 1 1) into 1
28.430 * [backup-simplify]: Simplify (sqrt 0) into 0
28.432 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.432 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
28.432 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
28.432 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
28.432 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
28.432 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
28.432 * [taylor]: Taking taylor expansion of 1/2 in k
28.432 * [backup-simplify]: Simplify 1/2 into 1/2
28.432 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.432 * [taylor]: Taking taylor expansion of 1 in k
28.432 * [backup-simplify]: Simplify 1 into 1
28.432 * [taylor]: Taking taylor expansion of k in k
28.432 * [backup-simplify]: Simplify 0 into 0
28.432 * [backup-simplify]: Simplify 1 into 1
28.432 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.432 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.432 * [taylor]: Taking taylor expansion of 2 in k
28.432 * [backup-simplify]: Simplify 2 into 2
28.432 * [taylor]: Taking taylor expansion of PI in k
28.432 * [backup-simplify]: Simplify PI into PI
28.433 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.434 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.435 * [backup-simplify]: Simplify (- 0) into 0
28.435 * [backup-simplify]: Simplify (+ 1 0) into 1
28.436 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.438 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.440 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
28.440 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
28.440 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.440 * [taylor]: Taking taylor expansion of k in k
28.440 * [backup-simplify]: Simplify 0 into 0
28.441 * [backup-simplify]: Simplify 1 into 1
28.441 * [backup-simplify]: Simplify (/ 1 1) into 1
28.441 * [backup-simplify]: Simplify (sqrt 0) into 0
28.443 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.444 * [backup-simplify]: Simplify (* (pow (* 2 PI) 1/2) 0) into 0
28.444 * [backup-simplify]: Simplify 0 into 0
28.450 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
28.452 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
28.453 * [backup-simplify]: Simplify (- 1) into -1
28.453 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.454 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
28.457 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI))))
28.466 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))
28.469 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt PI))))
28.471 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (sqrt PI)))) into (- (* +nan.0 (* (sqrt 2) (sqrt PI))))
28.472 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
28.474 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
28.474 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
28.476 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
28.476 * [backup-simplify]: Simplify (- 0) into 0
28.477 * [backup-simplify]: Simplify (+ 0 0) into 0
28.477 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
28.478 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0
28.486 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))
28.495 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) +nan.0) (* (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) 0))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))))))
28.508 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))))))
28.509 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.513 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
28.514 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
28.520 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
28.520 * [backup-simplify]: Simplify (- 0) into 0
28.521 * [backup-simplify]: Simplify (+ 0 0) into 0
28.522 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
28.524 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
28.543 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3)))
28.565 * [backup-simplify]: Simplify (+ (* (pow (* 2 PI) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3))) 0)))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))))))))
28.586 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))))))))
28.635 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))))) k) (- (* +nan.0 (* (sqrt 2) (sqrt PI)))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI))))))))))))))
28.636 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) into (* (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
28.636 * [approximate]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k) around 0
28.636 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
28.636 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
28.636 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
28.636 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
28.636 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
28.636 * [taylor]: Taking taylor expansion of 1/2 in k
28.636 * [backup-simplify]: Simplify 1/2 into 1/2
28.636 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.636 * [taylor]: Taking taylor expansion of 1 in k
28.636 * [backup-simplify]: Simplify 1 into 1
28.636 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.636 * [taylor]: Taking taylor expansion of k in k
28.636 * [backup-simplify]: Simplify 0 into 0
28.636 * [backup-simplify]: Simplify 1 into 1
28.637 * [backup-simplify]: Simplify (/ 1 1) into 1
28.637 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.637 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.637 * [taylor]: Taking taylor expansion of 2 in k
28.637 * [backup-simplify]: Simplify 2 into 2
28.637 * [taylor]: Taking taylor expansion of PI in k
28.637 * [backup-simplify]: Simplify PI into PI
28.637 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.638 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.639 * [backup-simplify]: Simplify (- 1) into -1
28.639 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.639 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
28.640 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
28.641 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
28.641 * [taylor]: Taking taylor expansion of (sqrt k) in k
28.641 * [taylor]: Taking taylor expansion of k in k
28.641 * [backup-simplify]: Simplify 0 into 0
28.641 * [backup-simplify]: Simplify 1 into 1
28.641 * [backup-simplify]: Simplify (sqrt 0) into 0
28.642 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.642 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
28.642 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
28.642 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
28.642 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
28.642 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
28.642 * [taylor]: Taking taylor expansion of 1/2 in k
28.642 * [backup-simplify]: Simplify 1/2 into 1/2
28.642 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.642 * [taylor]: Taking taylor expansion of 1 in k
28.642 * [backup-simplify]: Simplify 1 into 1
28.642 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.642 * [taylor]: Taking taylor expansion of k in k
28.642 * [backup-simplify]: Simplify 0 into 0
28.642 * [backup-simplify]: Simplify 1 into 1
28.643 * [backup-simplify]: Simplify (/ 1 1) into 1
28.643 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.643 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.643 * [taylor]: Taking taylor expansion of 2 in k
28.643 * [backup-simplify]: Simplify 2 into 2
28.643 * [taylor]: Taking taylor expansion of PI in k
28.643 * [backup-simplify]: Simplify PI into PI
28.643 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.644 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.644 * [backup-simplify]: Simplify (- 1) into -1
28.644 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.644 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
28.645 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
28.646 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
28.646 * [taylor]: Taking taylor expansion of (sqrt k) in k
28.646 * [taylor]: Taking taylor expansion of k in k
28.646 * [backup-simplify]: Simplify 0 into 0
28.646 * [backup-simplify]: Simplify 1 into 1
28.646 * [backup-simplify]: Simplify (sqrt 0) into 0
28.647 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.648 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) 0) into 0
28.648 * [backup-simplify]: Simplify 0 into 0
28.649 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
28.650 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
28.651 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
28.653 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
28.653 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
28.656 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
28.657 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
28.658 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
28.660 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))))))))
28.660 * [backup-simplify]: Simplify (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) into (/ (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
28.660 * [approximate]: Taking taylor expansion of (/ (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k) around 0
28.660 * [taylor]: Taking taylor expansion of (/ (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
28.660 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
28.660 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
28.660 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
28.660 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
28.660 * [taylor]: Taking taylor expansion of 1/2 in k
28.660 * [backup-simplify]: Simplify 1/2 into 1/2
28.661 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
28.661 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.661 * [taylor]: Taking taylor expansion of k in k
28.661 * [backup-simplify]: Simplify 0 into 0
28.661 * [backup-simplify]: Simplify 1 into 1
28.661 * [backup-simplify]: Simplify (/ 1 1) into 1
28.661 * [taylor]: Taking taylor expansion of 1 in k
28.661 * [backup-simplify]: Simplify 1 into 1
28.661 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.661 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.661 * [taylor]: Taking taylor expansion of 2 in k
28.661 * [backup-simplify]: Simplify 2 into 2
28.661 * [taylor]: Taking taylor expansion of PI in k
28.661 * [backup-simplify]: Simplify PI into PI
28.661 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.662 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.662 * [backup-simplify]: Simplify (+ 1 0) into 1
28.663 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.664 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.664 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
28.664 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
28.664 * [taylor]: Taking taylor expansion of (/ -1 k) in k
28.664 * [taylor]: Taking taylor expansion of -1 in k
28.664 * [backup-simplify]: Simplify -1 into -1
28.664 * [taylor]: Taking taylor expansion of k in k
28.664 * [backup-simplify]: Simplify 0 into 0
28.664 * [backup-simplify]: Simplify 1 into 1
28.665 * [backup-simplify]: Simplify (/ -1 1) into -1
28.665 * [backup-simplify]: Simplify (sqrt 0) into 0
28.666 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
28.666 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))
28.666 * [taylor]: Taking taylor expansion of (/ (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
28.667 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
28.667 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
28.667 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
28.667 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
28.667 * [taylor]: Taking taylor expansion of 1/2 in k
28.667 * [backup-simplify]: Simplify 1/2 into 1/2
28.667 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
28.667 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.667 * [taylor]: Taking taylor expansion of k in k
28.667 * [backup-simplify]: Simplify 0 into 0
28.667 * [backup-simplify]: Simplify 1 into 1
28.667 * [backup-simplify]: Simplify (/ 1 1) into 1
28.667 * [taylor]: Taking taylor expansion of 1 in k
28.667 * [backup-simplify]: Simplify 1 into 1
28.667 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.667 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.667 * [taylor]: Taking taylor expansion of 2 in k
28.667 * [backup-simplify]: Simplify 2 into 2
28.667 * [taylor]: Taking taylor expansion of PI in k
28.667 * [backup-simplify]: Simplify PI into PI
28.667 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.668 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.668 * [backup-simplify]: Simplify (+ 1 0) into 1
28.668 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.669 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.670 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
28.670 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
28.670 * [taylor]: Taking taylor expansion of (/ -1 k) in k
28.670 * [taylor]: Taking taylor expansion of -1 in k
28.670 * [backup-simplify]: Simplify -1 into -1
28.670 * [taylor]: Taking taylor expansion of k in k
28.670 * [backup-simplify]: Simplify 0 into 0
28.670 * [backup-simplify]: Simplify 1 into 1
28.671 * [backup-simplify]: Simplify (/ -1 1) into -1
28.671 * [backup-simplify]: Simplify (sqrt 0) into 0
28.672 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
28.672 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))
28.673 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))
28.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
28.680 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
28.681 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
28.682 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
28.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.687 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
28.691 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
28.692 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
28.696 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))))) (/ 1 (- k))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))))))
28.696 * * * * [progress]: [ 4 / 4 ] generating series at (2)
28.697 * [backup-simplify]: Simplify (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) into (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))))
28.697 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in (n k) around 0
28.697 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in k
28.697 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
28.697 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.697 * [taylor]: Taking taylor expansion of k in k
28.697 * [backup-simplify]: Simplify 0 into 0
28.697 * [backup-simplify]: Simplify 1 into 1
28.698 * [backup-simplify]: Simplify (/ 1 1) into 1
28.698 * [backup-simplify]: Simplify (sqrt 0) into 0
28.699 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.699 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))) in k
28.699 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in k
28.699 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in k
28.699 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in k
28.699 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
28.700 * [taylor]: Taking taylor expansion of 1/2 in k
28.700 * [backup-simplify]: Simplify 1/2 into 1/2
28.700 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.700 * [taylor]: Taking taylor expansion of 1 in k
28.700 * [backup-simplify]: Simplify 1 into 1
28.700 * [taylor]: Taking taylor expansion of k in k
28.700 * [backup-simplify]: Simplify 0 into 0
28.700 * [backup-simplify]: Simplify 1 into 1
28.700 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.700 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.700 * [taylor]: Taking taylor expansion of 2 in k
28.700 * [backup-simplify]: Simplify 2 into 2
28.700 * [taylor]: Taking taylor expansion of PI in k
28.700 * [backup-simplify]: Simplify PI into PI
28.700 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.701 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.702 * [backup-simplify]: Simplify (- 0) into 0
28.702 * [backup-simplify]: Simplify (+ 1 0) into 1
28.703 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.705 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.707 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
28.707 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in k
28.707 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in k
28.707 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in k
28.707 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
28.707 * [taylor]: Taking taylor expansion of 1/2 in k
28.707 * [backup-simplify]: Simplify 1/2 into 1/2
28.707 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.707 * [taylor]: Taking taylor expansion of 1 in k
28.707 * [backup-simplify]: Simplify 1 into 1
28.707 * [taylor]: Taking taylor expansion of k in k
28.708 * [backup-simplify]: Simplify 0 into 0
28.708 * [backup-simplify]: Simplify 1 into 1
28.708 * [taylor]: Taking taylor expansion of (log n) in k
28.708 * [taylor]: Taking taylor expansion of n in k
28.708 * [backup-simplify]: Simplify n into n
28.708 * [backup-simplify]: Simplify (log n) into (log n)
28.708 * [backup-simplify]: Simplify (- 0) into 0
28.709 * [backup-simplify]: Simplify (+ 1 0) into 1
28.709 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
28.709 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
28.709 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
28.709 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in n
28.709 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
28.709 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.709 * [taylor]: Taking taylor expansion of k in n
28.709 * [backup-simplify]: Simplify k into k
28.709 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.709 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
28.710 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
28.710 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
28.710 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))) in n
28.710 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in n
28.710 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in n
28.710 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in n
28.710 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
28.710 * [taylor]: Taking taylor expansion of 1/2 in n
28.710 * [backup-simplify]: Simplify 1/2 into 1/2
28.710 * [taylor]: Taking taylor expansion of (- 1 k) in n
28.710 * [taylor]: Taking taylor expansion of 1 in n
28.710 * [backup-simplify]: Simplify 1 into 1
28.710 * [taylor]: Taking taylor expansion of k in n
28.710 * [backup-simplify]: Simplify k into k
28.710 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
28.710 * [taylor]: Taking taylor expansion of (* 2 PI) in n
28.710 * [taylor]: Taking taylor expansion of 2 in n
28.710 * [backup-simplify]: Simplify 2 into 2
28.710 * [taylor]: Taking taylor expansion of PI in n
28.710 * [backup-simplify]: Simplify PI into PI
28.711 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.712 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.712 * [backup-simplify]: Simplify (- k) into (- k)
28.712 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
28.712 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
28.713 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI))))
28.714 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
28.714 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
28.714 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
28.715 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
28.715 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
28.715 * [taylor]: Taking taylor expansion of 1/2 in n
28.715 * [backup-simplify]: Simplify 1/2 into 1/2
28.715 * [taylor]: Taking taylor expansion of (- 1 k) in n
28.715 * [taylor]: Taking taylor expansion of 1 in n
28.715 * [backup-simplify]: Simplify 1 into 1
28.715 * [taylor]: Taking taylor expansion of k in n
28.715 * [backup-simplify]: Simplify k into k
28.715 * [taylor]: Taking taylor expansion of (log n) in n
28.715 * [taylor]: Taking taylor expansion of n in n
28.715 * [backup-simplify]: Simplify 0 into 0
28.715 * [backup-simplify]: Simplify 1 into 1
28.715 * [backup-simplify]: Simplify (log 1) into 0
28.715 * [backup-simplify]: Simplify (- k) into (- k)
28.715 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
28.715 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
28.716 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
28.716 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
28.716 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
28.716 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k))))) in n
28.716 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
28.716 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.716 * [taylor]: Taking taylor expansion of k in n
28.716 * [backup-simplify]: Simplify k into k
28.716 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.716 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
28.717 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
28.717 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
28.717 * [taylor]: Taking taylor expansion of (* (pow (* 2 PI) (* 1/2 (- 1 k))) (pow n (* 1/2 (- 1 k)))) in n
28.717 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 k))) in n
28.717 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 PI)))) in n
28.717 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 PI))) in n
28.717 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
28.717 * [taylor]: Taking taylor expansion of 1/2 in n
28.717 * [backup-simplify]: Simplify 1/2 into 1/2
28.717 * [taylor]: Taking taylor expansion of (- 1 k) in n
28.717 * [taylor]: Taking taylor expansion of 1 in n
28.717 * [backup-simplify]: Simplify 1 into 1
28.717 * [taylor]: Taking taylor expansion of k in n
28.717 * [backup-simplify]: Simplify k into k
28.717 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
28.717 * [taylor]: Taking taylor expansion of (* 2 PI) in n
28.717 * [taylor]: Taking taylor expansion of 2 in n
28.717 * [backup-simplify]: Simplify 2 into 2
28.717 * [taylor]: Taking taylor expansion of PI in n
28.717 * [backup-simplify]: Simplify PI into PI
28.718 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.719 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.719 * [backup-simplify]: Simplify (- k) into (- k)
28.719 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
28.719 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
28.720 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI))))
28.721 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
28.721 * [taylor]: Taking taylor expansion of (pow n (* 1/2 (- 1 k))) in n
28.721 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log n))) in n
28.721 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log n)) in n
28.721 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
28.721 * [taylor]: Taking taylor expansion of 1/2 in n
28.721 * [backup-simplify]: Simplify 1/2 into 1/2
28.721 * [taylor]: Taking taylor expansion of (- 1 k) in n
28.721 * [taylor]: Taking taylor expansion of 1 in n
28.721 * [backup-simplify]: Simplify 1 into 1
28.721 * [taylor]: Taking taylor expansion of k in n
28.721 * [backup-simplify]: Simplify k into k
28.722 * [taylor]: Taking taylor expansion of (log n) in n
28.722 * [taylor]: Taking taylor expansion of n in n
28.722 * [backup-simplify]: Simplify 0 into 0
28.722 * [backup-simplify]: Simplify 1 into 1
28.722 * [backup-simplify]: Simplify (log 1) into 0
28.722 * [backup-simplify]: Simplify (- k) into (- k)
28.722 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
28.722 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
28.723 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
28.723 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
28.723 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
28.724 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (log n))))) into (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))
28.725 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) into (* (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (sqrt (/ 1 k)))
28.725 * [taylor]: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
28.725 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) in k
28.725 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k
28.726 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log n))) in k
28.726 * [taylor]: Taking taylor expansion of 1/2 in k
28.726 * [backup-simplify]: Simplify 1/2 into 1/2
28.726 * [taylor]: Taking taylor expansion of (* (- 1 k) (log n)) in k
28.726 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.726 * [taylor]: Taking taylor expansion of 1 in k
28.726 * [backup-simplify]: Simplify 1 into 1
28.726 * [taylor]: Taking taylor expansion of k in k
28.726 * [backup-simplify]: Simplify 0 into 0
28.726 * [backup-simplify]: Simplify 1 into 1
28.726 * [taylor]: Taking taylor expansion of (log n) in k
28.726 * [taylor]: Taking taylor expansion of n in k
28.726 * [backup-simplify]: Simplify n into n
28.726 * [backup-simplify]: Simplify (log n) into (log n)
28.726 * [backup-simplify]: Simplify (- 0) into 0
28.727 * [backup-simplify]: Simplify (+ 1 0) into 1
28.727 * [backup-simplify]: Simplify (* 1 (log n)) into (log n)
28.727 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
28.727 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
28.727 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) in k
28.727 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (log (* 2 PI)))) in k
28.727 * [taylor]: Taking taylor expansion of 1/2 in k
28.727 * [backup-simplify]: Simplify 1/2 into 1/2
28.727 * [taylor]: Taking taylor expansion of (* (- 1 k) (log (* 2 PI))) in k
28.727 * [taylor]: Taking taylor expansion of (- 1 k) in k
28.727 * [taylor]: Taking taylor expansion of 1 in k
28.727 * [backup-simplify]: Simplify 1 into 1
28.727 * [taylor]: Taking taylor expansion of k in k
28.727 * [backup-simplify]: Simplify 0 into 0
28.727 * [backup-simplify]: Simplify 1 into 1
28.727 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.727 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.727 * [taylor]: Taking taylor expansion of 2 in k
28.727 * [backup-simplify]: Simplify 2 into 2
28.727 * [taylor]: Taking taylor expansion of PI in k
28.727 * [backup-simplify]: Simplify PI into PI
28.728 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.729 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.729 * [backup-simplify]: Simplify (- 0) into 0
28.730 * [backup-simplify]: Simplify (+ 1 0) into 1
28.731 * [backup-simplify]: Simplify (* 1 (log (* 2 PI))) into (log (* 2 PI))
28.733 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
28.735 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
28.735 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
28.735 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.735 * [taylor]: Taking taylor expansion of k in k
28.736 * [backup-simplify]: Simplify 0 into 0
28.736 * [backup-simplify]: Simplify 1 into 1
28.736 * [backup-simplify]: Simplify (/ 1 1) into 1
28.736 * [backup-simplify]: Simplify (sqrt 0) into 0
28.738 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.739 * [backup-simplify]: Simplify (* (pow n 1/2) (pow (* 2 PI) 1/2)) into (sqrt (* PI (* n 2)))
28.739 * [backup-simplify]: Simplify (* (sqrt (* PI (* n 2))) 0) into 0
28.739 * [backup-simplify]: Simplify 0 into 0
28.741 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
28.741 * [backup-simplify]: Simplify (- 0) into 0
28.742 * [backup-simplify]: Simplify (+ 0 0) into 0
28.742 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
28.743 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
28.743 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0
28.744 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
28.744 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
28.746 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
28.746 * [backup-simplify]: Simplify (- 0) into 0
28.747 * [backup-simplify]: Simplify (+ 0 0) into 0
28.747 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
28.748 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log (* 2 PI)))) into 0
28.750 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
28.751 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) 0) (* 0 (exp (* 1/2 (* (- 1 k) (log n)))))) into 0
28.752 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))) into 0
28.752 * [taylor]: Taking taylor expansion of 0 in k
28.752 * [backup-simplify]: Simplify 0 into 0
28.752 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
28.753 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
28.753 * [backup-simplify]: Simplify (- 1) into -1
28.753 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.755 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log (* 2 PI)))) into (- (log (* 2 PI)))
28.758 * [backup-simplify]: Simplify (+ (* 1/2 (- (log (* 2 PI)))) (* 0 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI))))
28.765 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))
28.765 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
28.766 * [backup-simplify]: Simplify (- 1) into -1
28.766 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.766 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (log n))) into (- (log n))
28.766 * [backup-simplify]: Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n)))
28.767 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
28.770 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* -1/2 (* (sqrt n) (log n))) (pow (* 2 PI) 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))
28.772 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
28.772 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
28.774 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
28.774 * [backup-simplify]: Simplify (- 0) into 0
28.774 * [backup-simplify]: Simplify (+ 0 0) into 0
28.775 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
28.775 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
28.775 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
28.776 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.777 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
28.779 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
28.779 * [backup-simplify]: Simplify (- 0) into 0
28.779 * [backup-simplify]: Simplify (+ 0 0) into 0
28.780 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
28.780 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
28.782 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.783 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 k) (log n))))))) into 0
28.783 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.784 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
28.785 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))))) into 0
28.785 * [taylor]: Taking taylor expansion of 0 in k
28.785 * [backup-simplify]: Simplify 0 into 0
28.785 * [backup-simplify]: Simplify 0 into 0
28.786 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
28.788 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
28.790 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
28.793 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
28.793 * [backup-simplify]: Simplify (- 0) into 0
28.794 * [backup-simplify]: Simplify (+ 0 0) into 0
28.801 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log (* 2 PI))))) into 0
28.803 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log (* 2 PI)))) (* 0 (log (* 2 PI))))) into 0
28.818 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))
28.820 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
28.820 * [backup-simplify]: Simplify (- 0) into 0
28.820 * [backup-simplify]: Simplify (+ 0 0) into 0
28.821 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log n)))) into 0
28.822 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0
28.823 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
28.834 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* 2 PI) 1/2)))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))
28.843 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))
28.847 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))
28.854 * [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
28.854 * [backup-simplify]: Simplify (- 0) into 0
28.855 * [backup-simplify]: Simplify (+ 0 0) into 0
28.856 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
28.857 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
28.858 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0
28.859 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.861 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
28.867 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
28.867 * [backup-simplify]: Simplify (- 0) into 0
28.868 * [backup-simplify]: Simplify (+ 0 0) into 0
28.869 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
28.871 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
28.873 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.875 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 k) (log n)))))))) into 0
28.876 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.877 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
28.879 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))))) into 0
28.879 * [taylor]: Taking taylor expansion of 0 in k
28.879 * [backup-simplify]: Simplify 0 into 0
28.879 * [backup-simplify]: Simplify 0 into 0
28.879 * [backup-simplify]: Simplify 0 into 0
28.880 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.885 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
28.887 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
28.891 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
28.892 * [backup-simplify]: Simplify (- 0) into 0
28.892 * [backup-simplify]: Simplify (+ 0 0) into 0
28.893 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
28.894 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log (* 2 PI)))) (* 0 (log (* 2 PI)))))) into 0
28.904 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3)))
28.906 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
28.906 * [backup-simplify]: Simplify (- 0) into 0
28.907 * [backup-simplify]: Simplify (+ 0 0) into 0
28.907 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log n))))) into 0
28.908 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log n))) (* 0 (log n))))) into 0
28.909 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3)))
28.918 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (* -1/48 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 3)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (pow (* 2 PI) 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log n) (pow (log (* 2 PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log n) 2) (log (* 2 PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* 2 PI)) 3)) (sqrt (* n PI))))))))
28.940 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (* 1/4 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))) +nan.0) (* (- (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log n) (pow (log (* 2 PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log n) 2) (log (* 2 PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* 2 PI)) 3)) (sqrt (* n PI)))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))))))))))))
28.951 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI)))))))))))))))
28.961 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (* (log n) (log (* 2 PI)))) (sqrt (* n PI))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) (* k 1)) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))))))))))))))))))))))
28.962 * [backup-simplify]: Simplify (* (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) (/ (pow (* 2 PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) into (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k))
28.962 * [approximate]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in (n k) around 0
28.962 * [taylor]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in k
28.962 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) in k
28.962 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in k
28.962 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in k
28.962 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in k
28.962 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
28.962 * [taylor]: Taking taylor expansion of 1/2 in k
28.962 * [backup-simplify]: Simplify 1/2 into 1/2
28.962 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.962 * [taylor]: Taking taylor expansion of 1 in k
28.962 * [backup-simplify]: Simplify 1 into 1
28.962 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.962 * [taylor]: Taking taylor expansion of k in k
28.962 * [backup-simplify]: Simplify 0 into 0
28.962 * [backup-simplify]: Simplify 1 into 1
28.962 * [backup-simplify]: Simplify (/ 1 1) into 1
28.962 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k
28.962 * [taylor]: Taking taylor expansion of (/ 1 n) in k
28.962 * [taylor]: Taking taylor expansion of n in k
28.963 * [backup-simplify]: Simplify n into n
28.963 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
28.963 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n))
28.963 * [backup-simplify]: Simplify (- 1) into -1
28.963 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.963 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
28.963 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
28.964 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))
28.964 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in k
28.964 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in k
28.964 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in k
28.964 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
28.964 * [taylor]: Taking taylor expansion of 1/2 in k
28.964 * [backup-simplify]: Simplify 1/2 into 1/2
28.964 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.964 * [taylor]: Taking taylor expansion of 1 in k
28.964 * [backup-simplify]: Simplify 1 into 1
28.964 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.964 * [taylor]: Taking taylor expansion of k in k
28.964 * [backup-simplify]: Simplify 0 into 0
28.964 * [backup-simplify]: Simplify 1 into 1
28.964 * [backup-simplify]: Simplify (/ 1 1) into 1
28.964 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.964 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.964 * [taylor]: Taking taylor expansion of 2 in k
28.964 * [backup-simplify]: Simplify 2 into 2
28.964 * [taylor]: Taking taylor expansion of PI in k
28.964 * [backup-simplify]: Simplify PI into PI
28.964 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.965 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.965 * [backup-simplify]: Simplify (- 1) into -1
28.966 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.966 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
28.967 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
28.968 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
28.968 * [taylor]: Taking taylor expansion of (sqrt k) in k
28.968 * [taylor]: Taking taylor expansion of k in k
28.968 * [backup-simplify]: Simplify 0 into 0
28.968 * [backup-simplify]: Simplify 1 into 1
28.968 * [backup-simplify]: Simplify (sqrt 0) into 0
28.969 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.969 * [taylor]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in n
28.969 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) in n
28.969 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
28.969 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
28.969 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
28.969 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
28.969 * [taylor]: Taking taylor expansion of 1/2 in n
28.969 * [backup-simplify]: Simplify 1/2 into 1/2
28.969 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
28.969 * [taylor]: Taking taylor expansion of 1 in n
28.969 * [backup-simplify]: Simplify 1 into 1
28.969 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.969 * [taylor]: Taking taylor expansion of k in n
28.969 * [backup-simplify]: Simplify k into k
28.969 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.969 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
28.969 * [taylor]: Taking taylor expansion of (/ 1 n) in n
28.969 * [taylor]: Taking taylor expansion of n in n
28.969 * [backup-simplify]: Simplify 0 into 0
28.969 * [backup-simplify]: Simplify 1 into 1
28.970 * [backup-simplify]: Simplify (/ 1 1) into 1
28.970 * [backup-simplify]: Simplify (log 1) into 0
28.970 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
28.970 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
28.970 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
28.970 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
28.971 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
28.971 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
28.971 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in n
28.971 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in n
28.971 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in n
28.971 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
28.971 * [taylor]: Taking taylor expansion of 1/2 in n
28.971 * [backup-simplify]: Simplify 1/2 into 1/2
28.971 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
28.971 * [taylor]: Taking taylor expansion of 1 in n
28.971 * [backup-simplify]: Simplify 1 into 1
28.971 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.971 * [taylor]: Taking taylor expansion of k in n
28.971 * [backup-simplify]: Simplify k into k
28.971 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.971 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
28.971 * [taylor]: Taking taylor expansion of (* 2 PI) in n
28.971 * [taylor]: Taking taylor expansion of 2 in n
28.971 * [backup-simplify]: Simplify 2 into 2
28.971 * [taylor]: Taking taylor expansion of PI in n
28.971 * [backup-simplify]: Simplify PI into PI
28.972 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.973 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.973 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
28.973 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
28.973 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
28.974 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))
28.975 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
28.975 * [taylor]: Taking taylor expansion of (sqrt k) in n
28.975 * [taylor]: Taking taylor expansion of k in n
28.975 * [backup-simplify]: Simplify k into k
28.975 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
28.975 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
28.975 * [taylor]: Taking taylor expansion of (* (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) (sqrt k)) in n
28.975 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k))))) in n
28.975 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 1/2 (- 1 (/ 1 k)))) in n
28.975 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n)))) in n
28.976 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (/ 1 n))) in n
28.976 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
28.976 * [taylor]: Taking taylor expansion of 1/2 in n
28.976 * [backup-simplify]: Simplify 1/2 into 1/2
28.976 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
28.976 * [taylor]: Taking taylor expansion of 1 in n
28.976 * [backup-simplify]: Simplify 1 into 1
28.976 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.976 * [taylor]: Taking taylor expansion of k in n
28.976 * [backup-simplify]: Simplify k into k
28.976 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.976 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
28.976 * [taylor]: Taking taylor expansion of (/ 1 n) in n
28.976 * [taylor]: Taking taylor expansion of n in n
28.976 * [backup-simplify]: Simplify 0 into 0
28.976 * [backup-simplify]: Simplify 1 into 1
28.976 * [backup-simplify]: Simplify (/ 1 1) into 1
28.977 * [backup-simplify]: Simplify (log 1) into 0
28.977 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
28.977 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
28.977 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
28.977 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
28.978 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
28.978 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
28.978 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (- 1 (/ 1 k)))) in n
28.978 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI)))) in n
28.978 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) in n
28.978 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
28.978 * [taylor]: Taking taylor expansion of 1/2 in n
28.978 * [backup-simplify]: Simplify 1/2 into 1/2
28.978 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
28.978 * [taylor]: Taking taylor expansion of 1 in n
28.978 * [backup-simplify]: Simplify 1 into 1
28.978 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.978 * [taylor]: Taking taylor expansion of k in n
28.978 * [backup-simplify]: Simplify k into k
28.978 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.978 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
28.978 * [taylor]: Taking taylor expansion of (* 2 PI) in n
28.978 * [taylor]: Taking taylor expansion of 2 in n
28.978 * [backup-simplify]: Simplify 2 into 2
28.978 * [taylor]: Taking taylor expansion of PI in n
28.978 * [backup-simplify]: Simplify PI into PI
28.979 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.980 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.980 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
28.980 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
28.980 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
28.981 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))
28.982 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
28.983 * [taylor]: Taking taylor expansion of (sqrt k) in n
28.983 * [taylor]: Taking taylor expansion of k in n
28.983 * [backup-simplify]: Simplify k into k
28.983 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
28.983 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
28.984 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
28.985 * [backup-simplify]: Simplify (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt k)) into (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt k))
28.985 * [taylor]: Taking taylor expansion of (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt k)) in k
28.985 * [taylor]: Taking taylor expansion of (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) in k
28.985 * [taylor]: Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k
28.985 * [taylor]: Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (log n))) in k
28.986 * [taylor]: Taking taylor expansion of -1/2 in k
28.986 * [backup-simplify]: Simplify -1/2 into -1/2
28.986 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log n)) in k
28.986 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.986 * [taylor]: Taking taylor expansion of 1 in k
28.986 * [backup-simplify]: Simplify 1 into 1
28.986 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.986 * [taylor]: Taking taylor expansion of k in k
28.986 * [backup-simplify]: Simplify 0 into 0
28.986 * [backup-simplify]: Simplify 1 into 1
28.986 * [backup-simplify]: Simplify (/ 1 1) into 1
28.986 * [taylor]: Taking taylor expansion of (log n) in k
28.986 * [taylor]: Taking taylor expansion of n in k
28.986 * [backup-simplify]: Simplify n into n
28.986 * [backup-simplify]: Simplify (log n) into (log n)
28.987 * [backup-simplify]: Simplify (- 1) into -1
28.987 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.987 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n))
28.987 * [backup-simplify]: Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n))
28.987 * [backup-simplify]: Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
28.987 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in k
28.987 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) in k
28.988 * [taylor]: Taking taylor expansion of 1/2 in k
28.988 * [backup-simplify]: Simplify 1/2 into 1/2
28.988 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 PI))) in k
28.988 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
28.988 * [taylor]: Taking taylor expansion of 1 in k
28.988 * [backup-simplify]: Simplify 1 into 1
28.988 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.988 * [taylor]: Taking taylor expansion of k in k
28.988 * [backup-simplify]: Simplify 0 into 0
28.988 * [backup-simplify]: Simplify 1 into 1
28.988 * [backup-simplify]: Simplify (/ 1 1) into 1
28.988 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
28.988 * [taylor]: Taking taylor expansion of (* 2 PI) in k
28.988 * [taylor]: Taking taylor expansion of 2 in k
28.988 * [backup-simplify]: Simplify 2 into 2
28.988 * [taylor]: Taking taylor expansion of PI in k
28.988 * [backup-simplify]: Simplify PI into PI
28.989 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
28.990 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
28.990 * [backup-simplify]: Simplify (- 1) into -1
28.991 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.992 * [backup-simplify]: Simplify (* -1 (log (* 2 PI))) into (* -1 (log (* 2 PI)))
28.995 * [backup-simplify]: Simplify (* 1/2 (* -1 (log (* 2 PI)))) into (* -1/2 (log (* 2 PI)))
28.996 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
28.996 * [taylor]: Taking taylor expansion of (sqrt k) in k
28.996 * [taylor]: Taking taylor expansion of k in k
28.996 * [backup-simplify]: Simplify 0 into 0
28.996 * [backup-simplify]: Simplify 1 into 1
28.996 * [backup-simplify]: Simplify (sqrt 0) into 0
28.998 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.999 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
29.000 * [backup-simplify]: Simplify (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) into 0
29.000 * [backup-simplify]: Simplify 0 into 0
29.001 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
29.003 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
29.003 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
29.004 * [backup-simplify]: Simplify (- 0) into 0
29.004 * [backup-simplify]: Simplify (+ 0 0) into 0
29.005 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
29.006 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0
29.007 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
29.008 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
29.009 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
29.010 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
29.010 * [backup-simplify]: Simplify (- 0) into 0
29.010 * [backup-simplify]: Simplify (+ 0 0) into 0
29.011 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
29.011 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
29.011 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
29.012 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
29.014 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into 0
29.015 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) (* 0 (sqrt k))) into 0
29.015 * [taylor]: Taking taylor expansion of 0 in k
29.015 * [backup-simplify]: Simplify 0 into 0
29.015 * [backup-simplify]: Simplify 0 into 0
29.016 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into 0
29.018 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
29.019 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
29.020 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
29.021 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
29.024 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
29.024 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.025 * [backup-simplify]: Simplify (- 0) into 0
29.025 * [backup-simplify]: Simplify (+ 0 0) into 0
29.026 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
29.027 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
29.029 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
29.030 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.033 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
29.033 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.034 * [backup-simplify]: Simplify (- 0) into 0
29.034 * [backup-simplify]: Simplify (+ 0 0) into 0
29.035 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
29.036 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
29.036 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
29.037 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
29.039 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into 0
29.041 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
29.041 * [taylor]: Taking taylor expansion of 0 in k
29.041 * [backup-simplify]: Simplify 0 into 0
29.042 * [backup-simplify]: Simplify 0 into 0
29.042 * [backup-simplify]: Simplify 0 into 0
29.045 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
29.052 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into 0
29.054 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
29.055 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
29.056 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
29.057 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
29.061 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
29.061 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.061 * [backup-simplify]: Simplify (- 0) into 0
29.061 * [backup-simplify]: Simplify (+ 0 0) into 0
29.062 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
29.063 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
29.065 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
29.065 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.068 * [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
29.068 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.071 * [backup-simplify]: Simplify (- 0) into 0
29.071 * [backup-simplify]: Simplify (+ 0 0) into 0
29.072 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
29.072 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
29.073 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
29.074 * [backup-simplify]: Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
29.075 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))) into 0
29.076 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
29.076 * [taylor]: Taking taylor expansion of 0 in k
29.076 * [backup-simplify]: Simplify 0 into 0
29.076 * [backup-simplify]: Simplify 0 into 0
29.076 * [backup-simplify]: Simplify 0 into 0
29.076 * [backup-simplify]: Simplify 0 into 0
29.079 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
29.080 * [backup-simplify]: Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))) into 0
29.082 * [backup-simplify]: Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
29.082 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
29.085 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 3))))))))
29.086 * [backup-simplify]: Simplify (* (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) (/ (pow (* 2 PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k)))
29.086 * [approximate]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in (n k) around 0
29.086 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in k
29.086 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) in k
29.086 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in k
29.086 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in k
29.086 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in k
29.086 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
29.086 * [taylor]: Taking taylor expansion of 1/2 in k
29.086 * [backup-simplify]: Simplify 1/2 into 1/2
29.086 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
29.086 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.086 * [taylor]: Taking taylor expansion of k in k
29.086 * [backup-simplify]: Simplify 0 into 0
29.086 * [backup-simplify]: Simplify 1 into 1
29.086 * [backup-simplify]: Simplify (/ 1 1) into 1
29.086 * [taylor]: Taking taylor expansion of 1 in k
29.086 * [backup-simplify]: Simplify 1 into 1
29.086 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k
29.086 * [taylor]: Taking taylor expansion of (/ -1 n) in k
29.086 * [taylor]: Taking taylor expansion of -1 in k
29.086 * [backup-simplify]: Simplify -1 into -1
29.086 * [taylor]: Taking taylor expansion of n in k
29.086 * [backup-simplify]: Simplify n into n
29.086 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n)
29.086 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n))
29.087 * [backup-simplify]: Simplify (+ 1 0) into 1
29.087 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
29.087 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
29.087 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n)))))
29.087 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in k
29.087 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in k
29.087 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in k
29.087 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
29.087 * [taylor]: Taking taylor expansion of 1/2 in k
29.087 * [backup-simplify]: Simplify 1/2 into 1/2
29.087 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
29.087 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.087 * [taylor]: Taking taylor expansion of k in k
29.087 * [backup-simplify]: Simplify 0 into 0
29.087 * [backup-simplify]: Simplify 1 into 1
29.087 * [backup-simplify]: Simplify (/ 1 1) into 1
29.087 * [taylor]: Taking taylor expansion of 1 in k
29.087 * [backup-simplify]: Simplify 1 into 1
29.087 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
29.087 * [taylor]: Taking taylor expansion of (* 2 PI) in k
29.087 * [taylor]: Taking taylor expansion of 2 in k
29.087 * [backup-simplify]: Simplify 2 into 2
29.087 * [taylor]: Taking taylor expansion of PI in k
29.087 * [backup-simplify]: Simplify PI into PI
29.088 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
29.088 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
29.089 * [backup-simplify]: Simplify (+ 1 0) into 1
29.089 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
29.090 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
29.091 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
29.091 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
29.091 * [taylor]: Taking taylor expansion of (/ -1 k) in k
29.091 * [taylor]: Taking taylor expansion of -1 in k
29.091 * [backup-simplify]: Simplify -1 into -1
29.091 * [taylor]: Taking taylor expansion of k in k
29.091 * [backup-simplify]: Simplify 0 into 0
29.091 * [backup-simplify]: Simplify 1 into 1
29.091 * [backup-simplify]: Simplify (/ -1 1) into -1
29.091 * [backup-simplify]: Simplify (sqrt 0) into 0
29.092 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
29.093 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))
29.093 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (/ -1 n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))
29.093 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in n
29.093 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) in n
29.093 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
29.093 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
29.094 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
29.094 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
29.094 * [taylor]: Taking taylor expansion of 1/2 in n
29.094 * [backup-simplify]: Simplify 1/2 into 1/2
29.094 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
29.094 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.094 * [taylor]: Taking taylor expansion of k in n
29.094 * [backup-simplify]: Simplify k into k
29.094 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.094 * [taylor]: Taking taylor expansion of 1 in n
29.094 * [backup-simplify]: Simplify 1 into 1
29.094 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
29.094 * [taylor]: Taking taylor expansion of (/ -1 n) in n
29.094 * [taylor]: Taking taylor expansion of -1 in n
29.094 * [backup-simplify]: Simplify -1 into -1
29.094 * [taylor]: Taking taylor expansion of n in n
29.094 * [backup-simplify]: Simplify 0 into 0
29.094 * [backup-simplify]: Simplify 1 into 1
29.094 * [backup-simplify]: Simplify (/ -1 1) into -1
29.094 * [backup-simplify]: Simplify (log -1) into (log -1)
29.094 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
29.094 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
29.095 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
29.095 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
29.096 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
29.096 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in n
29.096 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in n
29.096 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in n
29.096 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
29.096 * [taylor]: Taking taylor expansion of 1/2 in n
29.096 * [backup-simplify]: Simplify 1/2 into 1/2
29.096 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
29.096 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.096 * [taylor]: Taking taylor expansion of k in n
29.096 * [backup-simplify]: Simplify k into k
29.096 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.096 * [taylor]: Taking taylor expansion of 1 in n
29.096 * [backup-simplify]: Simplify 1 into 1
29.096 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
29.096 * [taylor]: Taking taylor expansion of (* 2 PI) in n
29.096 * [taylor]: Taking taylor expansion of 2 in n
29.096 * [backup-simplify]: Simplify 2 into 2
29.096 * [taylor]: Taking taylor expansion of PI in n
29.096 * [backup-simplify]: Simplify PI into PI
29.096 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
29.097 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
29.097 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
29.097 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
29.097 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))
29.098 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
29.098 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
29.098 * [taylor]: Taking taylor expansion of (/ -1 k) in n
29.098 * [taylor]: Taking taylor expansion of -1 in n
29.098 * [backup-simplify]: Simplify -1 into -1
29.098 * [taylor]: Taking taylor expansion of k in n
29.098 * [backup-simplify]: Simplify k into k
29.098 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
29.098 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
29.098 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
29.098 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
29.099 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))
29.100 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k)))
29.100 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) (sqrt (/ -1 k))) in n
29.100 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1)))) in n
29.100 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 1/2 (+ (/ 1 k) 1))) in n
29.100 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n)))) in n
29.101 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (/ -1 n))) in n
29.101 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
29.101 * [taylor]: Taking taylor expansion of 1/2 in n
29.101 * [backup-simplify]: Simplify 1/2 into 1/2
29.101 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
29.101 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.101 * [taylor]: Taking taylor expansion of k in n
29.101 * [backup-simplify]: Simplify k into k
29.101 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.101 * [taylor]: Taking taylor expansion of 1 in n
29.101 * [backup-simplify]: Simplify 1 into 1
29.101 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
29.101 * [taylor]: Taking taylor expansion of (/ -1 n) in n
29.101 * [taylor]: Taking taylor expansion of -1 in n
29.101 * [backup-simplify]: Simplify -1 into -1
29.101 * [taylor]: Taking taylor expansion of n in n
29.101 * [backup-simplify]: Simplify 0 into 0
29.101 * [backup-simplify]: Simplify 1 into 1
29.101 * [backup-simplify]: Simplify (/ -1 1) into -1
29.101 * [backup-simplify]: Simplify (log -1) into (log -1)
29.101 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
29.101 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
29.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
29.102 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log -1) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))
29.103 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
29.103 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (* 1/2 (+ (/ 1 k) 1))) in n
29.103 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI)))) in n
29.103 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) in n
29.103 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
29.103 * [taylor]: Taking taylor expansion of 1/2 in n
29.103 * [backup-simplify]: Simplify 1/2 into 1/2
29.103 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
29.103 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.103 * [taylor]: Taking taylor expansion of k in n
29.103 * [backup-simplify]: Simplify k into k
29.103 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.103 * [taylor]: Taking taylor expansion of 1 in n
29.103 * [backup-simplify]: Simplify 1 into 1
29.103 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in n
29.103 * [taylor]: Taking taylor expansion of (* 2 PI) in n
29.103 * [taylor]: Taking taylor expansion of 2 in n
29.103 * [backup-simplify]: Simplify 2 into 2
29.103 * [taylor]: Taking taylor expansion of PI in n
29.104 * [backup-simplify]: Simplify PI into PI
29.104 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
29.105 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
29.105 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
29.105 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
29.106 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log (* 2 PI))) into (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))
29.107 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
29.107 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
29.107 * [taylor]: Taking taylor expansion of (/ -1 k) in n
29.107 * [taylor]: Taking taylor expansion of -1 in n
29.107 * [backup-simplify]: Simplify -1 into -1
29.107 * [taylor]: Taking taylor expansion of k in n
29.107 * [backup-simplify]: Simplify k into k
29.107 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
29.108 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
29.108 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
29.108 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
29.109 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))
29.111 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k)))
29.111 * [taylor]: Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) in k
29.111 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) in k
29.111 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) in k
29.111 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))) in k
29.111 * [taylor]: Taking taylor expansion of 1/2 in k
29.111 * [backup-simplify]: Simplify 1/2 into 1/2
29.111 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (log (* 2 PI))) in k
29.111 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
29.111 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.111 * [taylor]: Taking taylor expansion of k in k
29.111 * [backup-simplify]: Simplify 0 into 0
29.111 * [backup-simplify]: Simplify 1 into 1
29.112 * [backup-simplify]: Simplify (/ 1 1) into 1
29.112 * [taylor]: Taking taylor expansion of 1 in k
29.112 * [backup-simplify]: Simplify 1 into 1
29.112 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
29.112 * [taylor]: Taking taylor expansion of (* 2 PI) in k
29.112 * [taylor]: Taking taylor expansion of 2 in k
29.112 * [backup-simplify]: Simplify 2 into 2
29.112 * [taylor]: Taking taylor expansion of PI in k
29.112 * [backup-simplify]: Simplify PI into PI
29.112 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
29.114 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
29.114 * [backup-simplify]: Simplify (+ 1 0) into 1
29.116 * [backup-simplify]: Simplify (* 1 (log (* 2 PI))) into (log (* 2 PI))
29.117 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
29.118 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))
29.119 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) in k
29.119 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))) in k
29.119 * [taylor]: Taking taylor expansion of 1/2 in k
29.119 * [backup-simplify]: Simplify 1/2 into 1/2
29.119 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log -1) (log n))) in k
29.119 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
29.119 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.119 * [taylor]: Taking taylor expansion of k in k
29.119 * [backup-simplify]: Simplify 0 into 0
29.119 * [backup-simplify]: Simplify 1 into 1
29.119 * [backup-simplify]: Simplify (/ 1 1) into 1
29.119 * [taylor]: Taking taylor expansion of 1 in k
29.119 * [backup-simplify]: Simplify 1 into 1
29.119 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k
29.119 * [taylor]: Taking taylor expansion of (log -1) in k
29.119 * [taylor]: Taking taylor expansion of -1 in k
29.119 * [backup-simplify]: Simplify -1 into -1
29.120 * [backup-simplify]: Simplify (log -1) into (log -1)
29.120 * [taylor]: Taking taylor expansion of (log n) in k
29.120 * [taylor]: Taking taylor expansion of n in k
29.120 * [backup-simplify]: Simplify n into n
29.120 * [backup-simplify]: Simplify (log n) into (log n)
29.120 * [backup-simplify]: Simplify (+ 1 0) into 1
29.120 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
29.121 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
29.121 * [backup-simplify]: Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n))
29.122 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
29.122 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))
29.122 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
29.122 * [taylor]: Taking taylor expansion of (/ -1 k) in k
29.122 * [taylor]: Taking taylor expansion of -1 in k
29.122 * [backup-simplify]: Simplify -1 into -1
29.122 * [taylor]: Taking taylor expansion of k in k
29.122 * [backup-simplify]: Simplify 0 into 0
29.122 * [backup-simplify]: Simplify 1 into 1
29.123 * [backup-simplify]: Simplify (/ -1 1) into -1
29.123 * [backup-simplify]: Simplify (sqrt 0) into 0
29.125 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
29.126 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))
29.128 * [backup-simplify]: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))
29.130 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))
29.131 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
29.132 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
29.132 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
29.133 * [backup-simplify]: Simplify (+ 0 0) into 0
29.133 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
29.134 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (log (* 2 PI)))) into 0
29.136 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
29.137 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
29.138 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
29.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
29.139 * [backup-simplify]: Simplify (+ 0 0) into 0
29.140 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
29.140 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
29.141 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log -1) (log n)))) into 0
29.142 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
29.144 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))))) into 0
29.146 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
29.146 * [taylor]: Taking taylor expansion of 0 in k
29.146 * [backup-simplify]: Simplify 0 into 0
29.146 * [backup-simplify]: Simplify 0 into 0
29.148 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) into 0
29.148 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
29.151 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
29.154 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
29.156 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
29.157 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
29.160 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
29.160 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.161 * [backup-simplify]: Simplify (+ 0 0) into 0
29.162 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
29.163 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
29.172 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
29.173 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.175 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
29.176 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.176 * [backup-simplify]: Simplify (+ 0 0) into 0
29.177 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
29.178 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
29.178 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
29.180 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
29.181 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI)))))))) into 0
29.181 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.181 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
29.182 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
29.182 * [taylor]: Taking taylor expansion of 0 in k
29.182 * [backup-simplify]: Simplify 0 into 0
29.182 * [backup-simplify]: Simplify 0 into 0
29.183 * [backup-simplify]: Simplify 0 into 0
29.184 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into 0
29.184 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.187 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
29.189 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
29.191 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log -1) (log n))))))))
29.194 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n)))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n)))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log (* 2 PI))))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log -1) (log (/ 1 (- n))))))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)))))))
29.194 * * * [progress]: simplifying candidates
29.194 * * * * [progress]: [ 1 / 239 ] simplifiying candidate #<alt (λ (k n) (* (log1p (expm1 (pow n (/ (- 1 k) 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.194 * * * * [progress]: [ 2 / 239 ] simplifiying candidate #<alt (λ (k n) (* (expm1 (log1p (pow n (/ (- 1 k) 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.194 * * * * [progress]: [ 3 / 239 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (log n) (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.194 * * * * [progress]: [ 4 / 239 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (log n) (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.194 * * * * [progress]: [ 5 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (* 1 (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.194 * * * * [progress]: [ 6 / 239 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.194 * * * * [progress]: [ 7 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.194 * * * * [progress]: [ 8 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 9 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 10 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 11 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 12 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 13 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 14 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 15 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 16 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 17 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ 1 1)) (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 18 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 19 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 20 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 21 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 22 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 23 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 24 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 25 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 26 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ 1 1)) (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 27 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n 1) (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 28 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (- 1 k)) (/ 1 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 29 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* (cbrt n) (cbrt n)) (/ (- 1 k) 2)) (pow (cbrt n) (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 30 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (/ (- 1 k) 2)) (pow (sqrt n) (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.195 * * * * [progress]: [ 31 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 1 (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 32 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow n (/ (- 1 k) 2)) 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 33 / 239 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (pow n (/ (- 1 k) 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 34 / 239 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (pow n (/ (- 1 k) 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 35 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) (cbrt (pow n (/ (- 1 k) 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 36 / 239 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 37 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (pow n (/ (- 1 k) 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 38 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (pow n (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 39 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (/ (- 1 k) 2) 2)) (pow n (/ (/ (- 1 k) 2) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 40 / 239 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (pow n (/ (- 1 k) 2)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 41 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (log1p (expm1 (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt k))))>
29.196 * * * * [progress]: [ 42 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (expm1 (log1p (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt k))))>
29.196 * * * * [progress]: [ 43 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (* (+ (log 2) (log PI)) (/ (- 1 k) 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 44 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (* (log (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 45 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (* (log (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 46 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (* 1 (/ (- 1 k) 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 47 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (* 1 (/ (- 1 k) 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 48 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* 2 PI) (/ 1 2)) (pow (* 2 PI) (/ k 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 49 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 50 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 51 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 52 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 53 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (sqrt k))))>
29.196 * * * * [progress]: [ 54 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (sqrt k))))>
29.196 * * * * [progress]: [ 55 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 56 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (sqrt k))))>
29.197 * * * * [progress]: [ 57 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 58 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 59 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k))))>
29.197 * * * * [progress]: [ 60 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 61 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 62 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (sqrt k))))>
29.197 * * * * [progress]: [ 63 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 64 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 65 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k))))>
29.197 * * * * [progress]: [ 66 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 67 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 68 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k))))>
29.197 * * * * [progress]: [ 69 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) 1) (/ (- 1 k) 2)) (sqrt k))))>
29.197 * * * * [progress]: [ 70 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (- 1 k)) (/ 1 2)) (sqrt k))))>
29.197 * * * * [progress]: [ 71 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (sqrt k))))>
29.197 * * * * [progress]: [ 72 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* 2 PI) (/ (- 1 k) 2)) 1) (sqrt k))))>
29.197 * * * * [progress]: [ 73 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (log (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt k))))>
29.197 * * * * [progress]: [ 74 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (log (exp (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt k))))>
29.198 * * * * [progress]: [ 75 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt k))))>
29.198 * * * * [progress]: [ 76 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (cbrt (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt k))))>
29.198 * * * * [progress]: [ 77 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt k))))>
29.198 * * * * [progress]: [ 78 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* 1 (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))))>
29.198 * * * * [progress]: [ 79 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (sqrt k))))>
29.198 * * * * [progress]: [ 80 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (posit16->real (real->posit16 (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt k))))>
29.198 * * * * [progress]: [ 81 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (log1p (expm1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.198 * * * * [progress]: [ 82 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (expm1 (log1p (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.198 * * * * [progress]: [ 83 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (pow (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) 1)))>
29.198 * * * * [progress]: [ 84 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (exp (- (* (+ (log 2) (log PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.198 * * * * [progress]: [ 85 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (exp (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.198 * * * * [progress]: [ 86 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (exp (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.198 * * * * [progress]: [ 87 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (exp (- (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (sqrt k))))))>
29.198 * * * * [progress]: [ 88 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (exp (log (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.198 * * * * [progress]: [ 89 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (log (exp (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.198 * * * * [progress]: [ 90 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (cbrt (/ (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
29.198 * * * * [progress]: [ 91 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.198 * * * * [progress]: [ 92 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (cbrt (* (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.198 * * * * [progress]: [ 93 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.198 * * * * [progress]: [ 94 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (- (pow (* 2 PI) (/ (- 1 k) 2))) (- (sqrt k)))))>
29.198 * * * * [progress]: [ 95 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
29.198 * * * * [progress]: [ 96 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt k))))))>
29.198 * * * * [progress]: [ 97 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
29.198 * * * * [progress]: [ 98 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt 1)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))))>
29.198 * * * * [progress]: [ 99 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
29.199 * * * * [progress]: [ 100 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow 2 (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))))>
29.199 * * * * [progress]: [ 101 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
29.199 * * * * [progress]: [ 102 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (cbrt k))))))>
29.199 * * * * [progress]: [ 103 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.199 * * * * [progress]: [ 104 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)))))>
29.199 * * * * [progress]: [ 105 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.199 * * * * [progress]: [ 106 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)))))>
29.199 * * * * [progress]: [ 107 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
29.199 * * * * [progress]: [ 108 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (cbrt k))))))>
29.199 * * * * [progress]: [ 109 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.199 * * * * [progress]: [ 110 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)))))>
29.199 * * * * [progress]: [ 111 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.199 * * * * [progress]: [ 112 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)))))>
29.199 * * * * [progress]: [ 113 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
29.199 * * * * [progress]: [ 114 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k))))))>
29.199 * * * * [progress]: [ 115 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
29.199 * * * * [progress]: [ 116 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ 1 (sqrt 1)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.199 * * * * [progress]: [ 117 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
29.199 * * * * [progress]: [ 118 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ 1 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.199 * * * * [progress]: [ 119 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k))))))>
29.199 * * * * [progress]: [ 120 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k))))))>
29.199 * * * * [progress]: [ 121 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
29.199 * * * * [progress]: [ 122 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt 1)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt k)))))>
29.199 * * * * [progress]: [ 123 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
29.200 * * * * [progress]: [ 124 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) 1) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt k)))))>
29.200 * * * * [progress]: [ 125 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* 1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.200 * * * * [progress]: [ 126 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))))>
29.200 * * * * [progress]: [ 127 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
29.200 * * * * [progress]: [ 128 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))>
29.200 * * * * [progress]: [ 129 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k)))))>
29.200 * * * * [progress]: [ 130 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
29.200 * * * * [progress]: [ 131 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt 1)) (sqrt k))))>
29.200 * * * * [progress]: [ 132 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
29.200 * * * * [progress]: [ 133 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* 2 PI) (/ (- 1 k) 2)) 1) (sqrt k))))>
29.200 * * * * [progress]: [ 134 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))))>
29.200 * * * * [progress]: [ 135 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))))))>
29.200 * * * * [progress]: [ 136 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))))))>
29.200 * * * * [progress]: [ 137 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
29.200 * * * * [progress]: [ 138 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))))))>
29.200 * * * * [progress]: [ 139 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ 1 2)) (* (sqrt k) (pow (* 2 PI) (/ k 2))))))>
29.200 * * * * [progress]: [ 140 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (posit16->real (real->posit16 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.200 * * * * [progress]: [ 141 / 239 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.200 * * * * [progress]: [ 142 / 239 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.200 * * * * [progress]: [ 143 / 239 ] simplifiying candidate #<alt (λ (k n) (pow (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) 1))>
29.200 * * * * [progress]: [ 144 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (* (+ (log 2) (log PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.200 * * * * [progress]: [ 145 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.200 * * * * [progress]: [ 146 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.200 * * * * [progress]: [ 147 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (sqrt k))))))>
29.200 * * * * [progress]: [ 148 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (log (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 149 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (* (+ (log 2) (log PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.201 * * * * [progress]: [ 150 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.201 * * * * [progress]: [ 151 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.201 * * * * [progress]: [ 152 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (sqrt k))))))>
29.201 * * * * [progress]: [ 153 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (log (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 154 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (/ (- 1 k) 2))) (- (* (+ (log 2) (log PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.201 * * * * [progress]: [ 155 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (/ (- 1 k) 2))) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.201 * * * * [progress]: [ 156 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (/ (- 1 k) 2))) (- (* (log (* 2 PI)) (/ (- 1 k) 2)) (log (sqrt k))))))>
29.201 * * * * [progress]: [ 157 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (/ (- 1 k) 2))) (- (log (pow (* 2 PI) (/ (- 1 k) 2))) (log (sqrt k))))))>
29.201 * * * * [progress]: [ 158 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow n (/ (- 1 k) 2))) (log (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 159 / 239 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 160 / 239 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 161 / 239 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (/ (* (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
29.201 * * * * [progress]: [ 162 / 239 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 163 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 164 / 239 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 165 / 239 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 166 / 239 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ 1 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (* (pow n (/ k 2)) (sqrt k))))>
29.201 * * * * [progress]: [ 167 / 239 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.201 * * * * [progress]: [ 168 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (/ (- 1 k) 2)) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (* (pow (sqrt n) (/ (- 1 k) 2)) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.201 * * * * [progress]: [ 169 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.201 * * * * [progress]: [ 170 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.201 * * * * [progress]: [ 171 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
29.201 * * * * [progress]: [ 172 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
29.202 * * * * [progress]: [ 173 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.202 * * * * [progress]: [ 174 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (* (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.202 * * * * [progress]: [ 175 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (* (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.202 * * * * [progress]: [ 176 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (* (sqrt (pow n (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
29.202 * * * * [progress]: [ 177 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow n (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (* (sqrt (pow n (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
29.202 * * * * [progress]: [ 178 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (/ (- 1 k) 2) 2)) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (* (pow n (/ (/ (- 1 k) 2) 2)) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.202 * * * * [progress]: [ 179 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (/ (- 1 k) 2) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (* (pow n (/ (/ (- 1 k) 2) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.202 * * * * [progress]: [ 180 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (/ (- 1 k) 2) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (* (pow n (/ (/ (- 1 k) 2) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
29.202 * * * * [progress]: [ 181 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (/ (- 1 k) 2) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (* (pow n (/ (/ (- 1 k) 2) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
29.202 * * * * [progress]: [ 182 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (/ (- 1 k) 2) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (* (pow n (/ (/ (- 1 k) 2) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))))>
29.202 * * * * [progress]: [ 183 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.202 * * * * [progress]: [ 184 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.202 * * * * [progress]: [ 185 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
29.202 * * * * [progress]: [ 186 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
29.202 * * * * [progress]: [ 187 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
29.202 * * * * [progress]: [ 188 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt 1))) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))>
29.202 * * * * [progress]: [ 189 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
29.202 * * * * [progress]: [ 190 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) 1)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))>
29.202 * * * * [progress]: [ 191 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
29.202 * * * * [progress]: [ 192 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
29.202 * * * * [progress]: [ 193 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
29.202 * * * * [progress]: [ 194 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt 1))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))))>
29.202 * * * * [progress]: [ 195 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
29.203 * * * * [progress]: [ 196 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))) 1)) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))))>
29.203 * * * * [progress]: [ 197 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
29.203 * * * * [progress]: [ 198 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
29.203 * * * * [progress]: [ 199 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
29.203 * * * * [progress]: [ 200 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt 1))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))))>
29.203 * * * * [progress]: [ 201 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
29.203 * * * * [progress]: [ 202 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) 1)) (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))))>
29.203 * * * * [progress]: [ 203 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
29.203 * * * * [progress]: [ 204 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
29.203 * * * * [progress]: [ 205 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ 1 (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
29.203 * * * * [progress]: [ 206 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ 1 (sqrt 1))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.203 * * * * [progress]: [ 207 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ 1 (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
29.203 * * * * [progress]: [ 208 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ 1 1)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.203 * * * * [progress]: [ 209 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))>
29.203 * * * * [progress]: [ 210 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))>
29.203 * * * * [progress]: [ 211 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
29.203 * * * * [progress]: [ 212 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt 1))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
29.203 * * * * [progress]: [ 213 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
29.203 * * * * [progress]: [ 214 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) 1)) (/ (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
29.203 * * * * [progress]: [ 215 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.203 * * * * [progress]: [ 216 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
29.203 * * * * [progress]: [ 217 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (cbrt n) (cbrt n)) (/ (- 1 k) 2)) (* (pow (cbrt n) (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.203 * * * * [progress]: [ 218 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt n) (/ (- 1 k) 2)) (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.203 * * * * [progress]: [ 219 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow 1 (/ (- 1 k) 2)) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.204 * * * * [progress]: [ 220 / 239 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) (* (cbrt (pow n (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.204 * * * * [progress]: [ 221 / 239 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow n (/ (- 1 k) 2))) (* (sqrt (pow n (/ (- 1 k) 2))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.204 * * * * [progress]: [ 222 / 239 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.204 * * * * [progress]: [ 223 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (/ (- 1 k) 2) 2)) (* (pow n (/ (/ (- 1 k) 2) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))))>
29.204 * * * * [progress]: [ 224 / 239 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)))>
29.204 * * * * [progress]: [ 225 / 239 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ 1 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (pow n (/ k 2))))>
29.204 * * * * [progress]: [ 226 / 239 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))))>
29.204 * * * * [progress]: [ 227 / 239 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))>
29.204 * * * * [progress]: [ 228 / 239 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.204 * * * * [progress]: [ 229 / 239 ] simplifiying candidate #<alt (λ (k n) (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.204 * * * * [progress]: [ 230 / 239 ] simplifiying candidate #<alt (λ (k n) (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
29.204 * * * * [progress]: [ 231 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))) (sqrt k))))>
29.204 * * * * [progress]: [ 232 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))))>
29.204 * * * * [progress]: [ 233 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))))>
29.204 * * * * [progress]: [ 234 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI))))))))))))))))>
29.204 * * * * [progress]: [ 235 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))))))))))>
29.204 * * * * [progress]: [ 236 / 239 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))))))))>
29.204 * * * * [progress]: [ 237 / 239 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt (* n PI))))))))))))))))))))))))>
29.204 * * * * [progress]: [ 238 / 239 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 3)))))))))>
29.204 * * * * [progress]: [ 239 / 239 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k))))))))>
29.207 * [simplify]: Simplifying:
  (expm1 (pow n (/ (- 1 k) 2)))
  (log1p (pow n (/ (- 1 k) 2)))
  (* (log n) (/ (- 1 k) 2))
  (* (log n) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow n (/ 1 2))
  (pow n (/ k 2))
  (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow n (sqrt (/ (- 1 k) 2)))
  (pow n (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow n (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow n (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow n (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow n (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow n (/ (sqrt (- 1 k)) 1))
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  (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
  (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt PI))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt PI))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))) (- (* +nan.0 (* (* (sqrt 2) k) (sqrt PI))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))))))))
  (- (+ (* +nan.0 (* (* (sqrt 2) (pow k 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) k) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 PI)) 2) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log n) 2) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) k)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log n) (pow k 2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (* (log n) (pow k 2)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log (* 2 PI)) (* (sqrt 2) (pow k 2))) (sqrt (* n PI)))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)) (- (* +nan.0 (/ (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) k)))))))
29.218 * * [simplify]: iteration 1: (427 enodes)
29.405 * * [simplify]: iteration 2: (1190 enodes)
30.227 * * [simplify]: Extracting #0: cost 178 inf + 0
30.228 * * [simplify]: Extracting #1: cost 711 inf + 2
30.235 * * [simplify]: Extracting #2: cost 1036 inf + 16090
30.249 * * [simplify]: Extracting #3: cost 970 inf + 137643
30.318 * * [simplify]: Extracting #4: cost 494 inf + 373399
30.432 * * [simplify]: Extracting #5: cost 257 inf + 495620
30.555 * * [simplify]: Extracting #6: cost 143 inf + 559112
30.656 * * [simplify]: Extracting #7: cost 70 inf + 592091
30.781 * * [simplify]: Extracting #8: cost 27 inf + 629892
30.964 * * [simplify]: Extracting #9: cost 3 inf + 649104
31.149 * * [simplify]: Extracting #10: cost 0 inf + 651038
31.305 * * [simplify]: Extracting #11: cost 0 inf + 650938
31.475 * * [simplify]: Extracting #12: cost 0 inf + 650913
31.661 * [simplify]: Simplified to:
  (expm1 (pow n (/ (- 1 k) 2)))
  (log1p (pow n (/ (- 1 k) 2)))
  (* (log n) (/ (- 1 k) 2))
  (* (log n) (/ (- 1 k) 2))
  (/ (- 1 k) 2)
  (sqrt n)
  (pow n (/ k 2))
  (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow n (sqrt (/ (- 1 k) 2)))
  (pow n (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow n (* (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt (- 1 k))))
  (pow n (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow n (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow n (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow n (sqrt (- 1 k)))
  (pow n (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow n (/ 1 (sqrt 2)))
  n
  (pow n (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow n (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow n (+ (sqrt k) 1))
  (pow n (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow n (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow n (+ (sqrt k) 1))
  (pow n (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow n (/ 1 (sqrt 2)))
  n
  n
  (pow n (- 1 k))
  (pow (* (cbrt n) (cbrt n)) (/ (- 1 k) 2))
  (pow (cbrt n) (/ (- 1 k) 2))
  (pow (sqrt n) (/ (- 1 k) 2))
  (pow (sqrt n) (/ (- 1 k) 2))
  1
  (pow n (/ (- 1 k) 2))
  (* (log n) (/ (- 1 k) 2))
  (exp (pow n (/ (- 1 k) 2)))
  (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2))))
  (cbrt (pow n (/ (- 1 k) 2)))
  (pow (pow n (/ (- 1 k) 2)) 3)
  (sqrt (pow n (/ (- 1 k) 2)))
  (sqrt (pow n (/ (- 1 k) 2)))
  (pow n (/ (- 1 k) 4))
  (pow n (/ (- 1 k) 4))
  (real->posit16 (pow n (/ (- 1 k) 2)))
  (expm1 (pow (* PI 2) (/ (- 1 k) 2)))
  (log1p (pow (* PI 2) (/ (- 1 k) 2)))
  (* (/ (- 1 k) 2) (log (* PI 2)))
  (* (/ (- 1 k) 2) (log (* PI 2)))
  (* (/ (- 1 k) 2) (log (* PI 2)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* PI 2))
  (pow (* PI 2) (/ k 2))
  (pow (* PI 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* PI 2) (sqrt (/ (- 1 k) 2)))
  (pow (* PI 2) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* PI 2) (* (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt (- 1 k))))
  (pow (* PI 2) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* PI 2) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* PI 2) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* PI 2) (sqrt (- 1 k)))
  (pow (* PI 2) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* PI 2) (/ 1 (sqrt 2)))
  (* PI 2)
  (pow (* PI 2) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* PI 2) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI 2) (+ (sqrt k) 1))
  (pow (* PI 2) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* PI 2) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI 2) (+ (sqrt k) 1))
  (pow (* PI 2) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* PI 2) (/ 1 (sqrt 2)))
  (* PI 2)
  (* PI 2)
  (pow (* PI 2) (- 1 k))
  (pow 2 (/ (- 1 k) 2))
  (pow PI (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* PI 2)))
  (exp (pow (* PI 2) (/ (- 1 k) 2)))
  (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
  (cbrt (pow (* PI 2) (/ (- 1 k) 2)))
  (pow (pow (* PI 2) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* PI 2) (/ (- 1 k) 2)))
  (sqrt (pow (* PI 2) (/ (- 1 k) 2)))
  (pow (* PI 2) (/ (- 1 k) 4))
  (pow (* PI 2) (/ (- 1 k) 4))
  (real->posit16 (pow (* PI 2) (/ (- 1 k) 2)))
  (expm1 (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* PI 2))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* PI 2))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* PI 2))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* PI 2))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* PI 2))) (log (sqrt k)))
  (exp (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
  (/ (/ (pow (pow (* PI 2) (/ (- 1 k) 2)) 3) k) (sqrt k))
  (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
  (pow (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) 3)
  (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* PI 2) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow 2 (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow PI (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow 2 (/ (- 1 k) 2))
  (/ (pow PI (/ (- 1 k) 2)) (sqrt k))
  (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow 2 (/ (- 1 k) 2))
  (/ (pow PI (/ (- 1 k) 2)) (sqrt k))
  (* (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (fabs (cbrt k)) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))))
  (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))))
  (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k))
  (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))))
  (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k))
  (/ (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (fabs (cbrt k)))
  (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (cbrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (fabs (cbrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (sqrt (cbrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* PI 2) (/ (- 1 k) 4))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (sqrt k))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* PI 2) (/ (- 1 k) 4))
  (/ (pow (* PI 2) (/ (- 1 k) 4)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* PI 2) (/ (- 1 k) 2))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* PI 2) (/ (- 1 k) 2))
  (/ (sqrt k) (pow PI (/ (- 1 k) 2)))
  (/ (sqrt k) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* PI 2) (/ (- 1 k) 2))))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 4)))
  (* (pow (* PI 2) (/ k 2)) (sqrt k))
  (real->posit16 (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
  (expm1 (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))
  (log1p (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (+ (log n) (log (* PI 2)))) (log (sqrt k)))
  (exp (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))
  (* (pow n (/ (- 1 k) 2)) (* (pow n (/ (- 1 k) 2)) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (pow (* PI 2) (/ (- 1 k) 2)) 3) k) (sqrt k)))))
  (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))))
  (* (cbrt (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))) (cbrt (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))))
  (cbrt (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))
  (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))))
  (sqrt (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))
  (sqrt (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))
  (* (sqrt n) (pow (* PI 2) (/ (- 1 k) 2)))
  (* (pow n (/ k 2)) (sqrt k))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))))
  (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
  (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
  (/ (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))))
  (/ (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))))
  (/ (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))))
  (/ (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))))
  (/ (* (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (pow n (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (* (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (pow n (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (* (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (pow n (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (* (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (pow n (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (* (pow n (/ (/ (- 1 k) 2) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
  (* (pow n (/ (/ (- 1 k) 2) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
  (/ (* (pow n (/ (/ (- 1 k) 2) 2)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (* (pow n (/ (/ (- 1 k) 2) 2)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (* (pow n (/ (/ (- 1 k) 2) 2)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (* (pow n (/ (/ (- 1 k) 2) 2)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 4)) (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 4))))
  (/ (pow n (/ (- 1 k) 4)) (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 4))))
  (/ (pow n (/ (- 1 k) 4)) (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 4))))
  (/ (pow n (/ (- 1 k) 4)) (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 4))))
  (* (pow n (/ (- 1 k) 2)) (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))))
  (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
  (/ (/ (* (pow n (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (* (/ (pow 2 (/ (- 1 k) 2)) (fabs (cbrt k))) (pow n (/ (- 1 k) 2)))
  (/ (* (pow n (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (pow n (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))
  (/ (* (pow n (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (pow n (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))
  (* (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (* (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))))
  (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (/ (fabs (cbrt k)) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))))
  (/ (* (* (pow n (/ (- 1 k) 2)) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (* (* (pow n (/ (- 1 k) 2)) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
  (/ (* (* (pow n (/ (- 1 k) 2)) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (* (* (pow n (/ (- 1 k) 2)) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
  (/ (/ (* (pow n (/ (- 1 k) 2)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (fabs (cbrt k))))
  (/ (* (pow n (/ (- 1 k) 2)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (* (pow n (/ (- 1 k) 2)) (sqrt (pow (* PI 2) (/ (- 1 k) 2))))
  (/ (* (pow n (/ (- 1 k) 2)) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (* (pow n (/ (- 1 k) 2)) (sqrt (pow (* PI 2) (/ (- 1 k) 2))))
  (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow n (/ (- 1 k) 2))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow n (/ (- 1 k) 2))
  (/ (* (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (fabs (cbrt k))))
  (* (/ (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (pow n (/ (- 1 k) 2)))
  (* (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2)))
  (* (/ (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (pow n (/ (- 1 k) 2)))
  (* (pow (* PI 2) (/ (/ (- 1 k) 2) 2)) (pow n (/ (- 1 k) 2)))
  (pow n (/ (- 1 k) 2))
  (* (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
  (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow (cbrt n) (/ (- 1 k) 2)))
  (* (pow (sqrt n) (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
  (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))
  (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (cbrt (pow n (/ (- 1 k) 2))))
  (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (sqrt (pow n (/ (- 1 k) 2))))
  (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2)))
  (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (/ (- 1 k) 2) 2))) (sqrt k))
  (* (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
  (* (sqrt n) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
  (real->posit16 (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))
  (+ (fma (* (* (* (log n) k) (* (log n) k)) (sqrt n)) 1/8 (sqrt n)) (* -1/2 (* (* k (log n)) (sqrt n))))
  (exp (* (* (- (log n)) (- 1 k)) -1/2))
  (exp (* (+ (- (log -1) (log -1)) (log n)) (* 1/2 (- 1 k))))
  (fma (* 1/8 (* (sqrt 2) (* (* (log (* PI 2)) k) (* (log (* PI 2)) k)))) (sqrt PI) (- (sqrt (* PI 2)) (* (* (sqrt 2) (* (log (* PI 2)) k)) (* (sqrt PI) 1/2))))
  (exp (* (* (- 1 k) (log (* PI 2))) 1/2))
  (exp (* (* (- 1 k) (log (* PI 2))) 1/2))
  (- (fma (* (* (sqrt 2) (* k k)) +nan.0) (sqrt PI) (+ (* (* (sqrt PI) (sqrt 2)) (- +nan.0)) (fma (* (* (* (sqrt 2) (* k k)) +nan.0) (log (* PI 2))) (sqrt PI) (+ (fma (* (* k (sqrt 2)) (* (log (* PI 2)) (sqrt PI))) +nan.0 (* (- +nan.0) (* (* k (sqrt 2)) (sqrt PI)))) (* (* +nan.0 (* (* (sqrt 2) (* k k)) (* (log (* PI 2)) (log (* PI 2))))) (- (sqrt PI))))))))
  (- (- (* (/ +nan.0 (* k k)) (/ (exp (* (* (- 1 k) (log (* PI 2))) 1/2)) k)) (* +nan.0 (- (/ (exp (* (* (- 1 k) (log (* PI 2))) 1/2)) k) (/ (/ (exp (* (* (- 1 k) (log (* PI 2))) 1/2)) k) k)))))
  (+ (* (- +nan.0) (/ (exp (* (* (- 1 k) (log (* PI 2))) 1/2)) k)) (* +nan.0 (- (/ (/ (exp (* (* (- 1 k) (log (* PI 2))) 1/2)) k) k) (exp (* (* (- 1 k) (log (* PI 2))) 1/2)))))
  (- (fma +nan.0 (* (* (sqrt (* PI n)) (sqrt 2)) (* k k)) (+ (* (- (* (* k (sqrt 2)) +nan.0)) (sqrt (* PI n))) (- (* (* +nan.0 (* (sqrt 2) (* (* (log (* PI 2)) k) (* (log (* PI 2)) k)))) (sqrt (* PI n))) (fma (* (* (sqrt 2) +nan.0) (* (* (log n) k) (* (log n) k))) (sqrt (* PI n)) (+ (* (- (* (* (sqrt 2) +nan.0) (* k (log n)))) (sqrt (* PI n))) (+ (- (* (sqrt (* PI n)) (* (* (sqrt 2) +nan.0) (* (* k k) (log n)))) (* (log (* PI 2)) (* (sqrt (* PI n)) (* (* (sqrt 2) +nan.0) (* (* k k) (log n)))))) (- (* (* (sqrt (* PI n)) (sqrt 2)) +nan.0) (* +nan.0 (- (* (* (sqrt 2) (* (log (* PI 2)) k)) (sqrt (* PI n))) (* (* (log (* PI 2)) (sqrt 2)) (* k (* k (sqrt (* PI n)))))))))))))))
  (- (- (* (/ (/ (exp (fma -1/2 (* (- (log n)) (- 1 k)) (* (* (- 1 k) (log (* PI 2))) 1/2))) k) k) +nan.0) (* +nan.0 (- (/ (exp (fma -1/2 (* (- (log n)) (- 1 k)) (* (* (- 1 k) (log (* PI 2))) 1/2))) k) (/ (/ (/ (exp (fma -1/2 (* (- (log n)) (- 1 k)) (* (* (- 1 k) (log (* PI 2))) 1/2))) k) k) k)))))
  (+ (/ (* (- +nan.0) (exp (* (* 1/2 (- 1 k)) (+ (+ (- (log -1) (log -1)) (log n)) (log (* PI 2)))))) (* k k)) (* +nan.0 (- (exp (* (* 1/2 (- 1 k)) (+ (+ (- (log -1) (log -1)) (log n)) (log (* PI 2))))) (/ (exp (* (* 1/2 (- 1 k)) (+ (+ (- (log -1) (log -1)) (log n)) (log (* PI 2))))) k))))
31.698 * * * [progress]: adding candidates to table
34.416 * [progress]: [Phase 3 of 3] Extracting.
34.416 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))> #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))))> #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k)))))> #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2))))))> #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))))> #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))>)
34.417 * * * [regime-changes]: Trying 2 branch expressions: (n k)
34.417 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))> #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))))> #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k)))))> #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2))))))> #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))))> #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))>)
34.482 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))> #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))))> #<alt (λ (k n) (/ 1 (/ (/ 1 (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k)))))> #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2))))))> #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))))> #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))>)
34.562 * * * [regime]: Found split indices: #<option (#s(si 5 255))>
34.562 * [simplify]: Simplifying:
  (* (pow n (/ (- 1 k) 2)) (* (pow 2 (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))
34.562 * * [simplify]: iteration 1: (14 enodes)
34.563 * * [simplify]: iteration 2: (18 enodes)
34.563 * * [simplify]: Extracting #0: cost 1 inf + 0
34.563 * * [simplify]: Extracting #1: cost 3 inf + 0
34.563 * * [simplify]: Extracting #2: cost 7 inf + 0
34.563 * * [simplify]: Extracting #3: cost 10 inf + 1
34.563 * * [simplify]: Extracting #4: cost 12 inf + 2
34.563 * * [simplify]: Extracting #5: cost 3 inf + 1132
34.564 * * [simplify]: Extracting #6: cost 0 inf + 2925
34.564 * [simplify]: Simplified to:
  (* (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (pow 2 (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))
42.308 * [regime-testing]: Baseline error score: 0.4339793468069403
42.310 * [regime-testing]: Oracle error score: 0.04092504063152125
42.315 * [regime-testing]: End program error score: 0.4339793468069403