58.157 * [progress]: [Phase 1 of 3] Setting up.
0.003 * * * [progress]: [1/2] Preparing points
0.144 * * * [progress]: [2/2] Setting up program.
0.151 * [progress]: [Phase 2 of 3] Improving.
0.151 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.151 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.151 * * [simplify]: iteration 0: 13 enodes
0.157 * * [simplify]: iteration 1: 31 enodes
0.169 * * [simplify]: iteration 2: 62 enodes
0.225 * * [simplify]: iteration 3: 124 enodes
0.259 * * [simplify]: iteration 4: 327 enodes
0.482 * * [simplify]: iteration 5: 929 enodes
1.945 * * [simplify]: iteration 6: 2719 enodes
2.795 * * [simplify]: iteration complete: 5000 enodes
2.795 * * [simplify]: Extracting #0: cost 1 inf + 0
2.796 * * [simplify]: Extracting #1: cost 61 inf + 0
2.797 * * [simplify]: Extracting #2: cost 488 inf + 1
2.801 * * [simplify]: Extracting #3: cost 953 inf + 92
2.808 * * [simplify]: Extracting #4: cost 921 inf + 18841
2.830 * * [simplify]: Extracting #5: cost 645 inf + 66373
2.905 * * [simplify]: Extracting #6: cost 241 inf + 329522
3.014 * * [simplify]: Extracting #7: cost 5 inf + 560024
3.115 * * [simplify]: Extracting #8: cost 0 inf + 561759
3.216 * * [simplify]: Extracting #9: cost 0 inf + 561250
3.330 * [simplify]: Simplified to:
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
3.338 * * [progress]: iteration 1 / 4
3.338 * * * [progress]: picking best candidate
3.348 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
3.348 * * * [progress]: localizing error
3.372 * * * [progress]: generating rewritten candidates
3.372 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
3.405 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
3.433 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
3.460 * * * [progress]: generating series expansions
3.460 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
3.461 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
3.461 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
3.461 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
3.461 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
3.461 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
3.461 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.461 * [taylor]: Taking taylor expansion of 1/2 in k
3.461 * [backup-simplify]: Simplify 1/2 into 1/2
3.461 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.461 * [taylor]: Taking taylor expansion of 1/2 in k
3.461 * [backup-simplify]: Simplify 1/2 into 1/2
3.461 * [taylor]: Taking taylor expansion of k in k
3.461 * [backup-simplify]: Simplify 0 into 0
3.461 * [backup-simplify]: Simplify 1 into 1
3.461 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
3.461 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
3.461 * [taylor]: Taking taylor expansion of 2 in k
3.461 * [backup-simplify]: Simplify 2 into 2
3.461 * [taylor]: Taking taylor expansion of (* n PI) in k
3.461 * [taylor]: Taking taylor expansion of n in k
3.461 * [backup-simplify]: Simplify n into n
3.461 * [taylor]: Taking taylor expansion of PI in k
3.461 * [backup-simplify]: Simplify PI into PI
3.461 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.461 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
3.462 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
3.462 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.463 * [backup-simplify]: Simplify (- 0) into 0
3.463 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.463 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
3.464 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
3.464 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.464 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.464 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.464 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.464 * [taylor]: Taking taylor expansion of 1/2 in n
3.464 * [backup-simplify]: Simplify 1/2 into 1/2
3.464 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.464 * [taylor]: Taking taylor expansion of 1/2 in n
3.464 * [backup-simplify]: Simplify 1/2 into 1/2
3.464 * [taylor]: Taking taylor expansion of k in n
3.464 * [backup-simplify]: Simplify k into k
3.464 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.464 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.464 * [taylor]: Taking taylor expansion of 2 in n
3.464 * [backup-simplify]: Simplify 2 into 2
3.464 * [taylor]: Taking taylor expansion of (* n PI) in n
3.464 * [taylor]: Taking taylor expansion of n in n
3.464 * [backup-simplify]: Simplify 0 into 0
3.464 * [backup-simplify]: Simplify 1 into 1
3.464 * [taylor]: Taking taylor expansion of PI in n
3.464 * [backup-simplify]: Simplify PI into PI
3.465 * [backup-simplify]: Simplify (* 0 PI) into 0
3.465 * [backup-simplify]: Simplify (* 2 0) into 0
3.467 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.469 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.470 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.470 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.470 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.470 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.471 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.472 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.474 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.474 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.474 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.474 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.474 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.474 * [taylor]: Taking taylor expansion of 1/2 in n
3.474 * [backup-simplify]: Simplify 1/2 into 1/2
3.474 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.474 * [taylor]: Taking taylor expansion of 1/2 in n
3.474 * [backup-simplify]: Simplify 1/2 into 1/2
3.474 * [taylor]: Taking taylor expansion of k in n
3.474 * [backup-simplify]: Simplify k into k
3.474 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.474 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.474 * [taylor]: Taking taylor expansion of 2 in n
3.474 * [backup-simplify]: Simplify 2 into 2
3.474 * [taylor]: Taking taylor expansion of (* n PI) in n
3.474 * [taylor]: Taking taylor expansion of n in n
3.474 * [backup-simplify]: Simplify 0 into 0
3.474 * [backup-simplify]: Simplify 1 into 1
3.474 * [taylor]: Taking taylor expansion of PI in n
3.474 * [backup-simplify]: Simplify PI into PI
3.475 * [backup-simplify]: Simplify (* 0 PI) into 0
3.475 * [backup-simplify]: Simplify (* 2 0) into 0
3.477 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.478 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.479 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.479 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.479 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.479 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.481 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.482 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.483 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.483 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
3.483 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
3.483 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.484 * [taylor]: Taking taylor expansion of 1/2 in k
3.484 * [backup-simplify]: Simplify 1/2 into 1/2
3.484 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.484 * [taylor]: Taking taylor expansion of 1/2 in k
3.484 * [backup-simplify]: Simplify 1/2 into 1/2
3.484 * [taylor]: Taking taylor expansion of k in k
3.484 * [backup-simplify]: Simplify 0 into 0
3.484 * [backup-simplify]: Simplify 1 into 1
3.484 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
3.484 * [taylor]: Taking taylor expansion of (log n) in k
3.484 * [taylor]: Taking taylor expansion of n in k
3.484 * [backup-simplify]: Simplify n into n
3.484 * [backup-simplify]: Simplify (log n) into (log n)
3.484 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.484 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.484 * [taylor]: Taking taylor expansion of 2 in k
3.484 * [backup-simplify]: Simplify 2 into 2
3.484 * [taylor]: Taking taylor expansion of PI in k
3.484 * [backup-simplify]: Simplify PI into PI
3.484 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.486 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.486 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.487 * [backup-simplify]: Simplify (- 0) into 0
3.487 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.488 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.489 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
3.490 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.492 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.493 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.494 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.496 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.497 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
3.497 * [backup-simplify]: Simplify (- 0) into 0
3.498 * [backup-simplify]: Simplify (+ 0 0) into 0
3.499 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.500 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
3.502 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.502 * [taylor]: Taking taylor expansion of 0 in k
3.502 * [backup-simplify]: Simplify 0 into 0
3.503 * [backup-simplify]: Simplify 0 into 0
3.503 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
3.504 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.506 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.507 * [backup-simplify]: Simplify (+ 0 0) into 0
3.507 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
3.508 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.508 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.510 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
3.513 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.515 * [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)))))))
3.519 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.520 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.522 * [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
3.522 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
3.523 * [backup-simplify]: Simplify (- 0) into 0
3.523 * [backup-simplify]: Simplify (+ 0 0) into 0
3.524 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.525 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.526 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.526 * [taylor]: Taking taylor expansion of 0 in k
3.526 * [backup-simplify]: Simplify 0 into 0
3.526 * [backup-simplify]: Simplify 0 into 0
3.526 * [backup-simplify]: Simplify 0 into 0
3.527 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
3.528 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.530 * [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
3.530 * [backup-simplify]: Simplify (+ 0 0) into 0
3.530 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
3.531 * [backup-simplify]: Simplify (- 0) into 0
3.531 * [backup-simplify]: Simplify (+ 0 0) into 0
3.532 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.535 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 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)))))
3.538 * [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)))))
3.546 * [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)))))
3.546 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
3.546 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
3.546 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
3.546 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
3.546 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
3.547 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.547 * [taylor]: Taking taylor expansion of 1/2 in k
3.547 * [backup-simplify]: Simplify 1/2 into 1/2
3.547 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.547 * [taylor]: Taking taylor expansion of 1/2 in k
3.547 * [backup-simplify]: Simplify 1/2 into 1/2
3.547 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.547 * [taylor]: Taking taylor expansion of k in k
3.547 * [backup-simplify]: Simplify 0 into 0
3.547 * [backup-simplify]: Simplify 1 into 1
3.547 * [backup-simplify]: Simplify (/ 1 1) into 1
3.547 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
3.547 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
3.547 * [taylor]: Taking taylor expansion of 2 in k
3.547 * [backup-simplify]: Simplify 2 into 2
3.547 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.547 * [taylor]: Taking taylor expansion of PI in k
3.547 * [backup-simplify]: Simplify PI into PI
3.548 * [taylor]: Taking taylor expansion of n in k
3.548 * [backup-simplify]: Simplify n into n
3.548 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.548 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
3.548 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
3.549 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.549 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.549 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.549 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
3.550 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
3.550 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.550 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.550 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.550 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.550 * [taylor]: Taking taylor expansion of 1/2 in n
3.550 * [backup-simplify]: Simplify 1/2 into 1/2
3.550 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.550 * [taylor]: Taking taylor expansion of 1/2 in n
3.550 * [backup-simplify]: Simplify 1/2 into 1/2
3.550 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.550 * [taylor]: Taking taylor expansion of k in n
3.550 * [backup-simplify]: Simplify k into k
3.550 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.550 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.550 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.550 * [taylor]: Taking taylor expansion of 2 in n
3.550 * [backup-simplify]: Simplify 2 into 2
3.550 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.550 * [taylor]: Taking taylor expansion of PI in n
3.550 * [backup-simplify]: Simplify PI into PI
3.550 * [taylor]: Taking taylor expansion of n in n
3.550 * [backup-simplify]: Simplify 0 into 0
3.550 * [backup-simplify]: Simplify 1 into 1
3.551 * [backup-simplify]: Simplify (/ PI 1) into PI
3.551 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.552 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.552 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.553 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.553 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.554 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.555 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
3.556 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.556 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.556 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.557 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.557 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.557 * [taylor]: Taking taylor expansion of 1/2 in n
3.557 * [backup-simplify]: Simplify 1/2 into 1/2
3.557 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.557 * [taylor]: Taking taylor expansion of 1/2 in n
3.557 * [backup-simplify]: Simplify 1/2 into 1/2
3.557 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.557 * [taylor]: Taking taylor expansion of k in n
3.557 * [backup-simplify]: Simplify k into k
3.557 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.557 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.557 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.557 * [taylor]: Taking taylor expansion of 2 in n
3.557 * [backup-simplify]: Simplify 2 into 2
3.557 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.557 * [taylor]: Taking taylor expansion of PI in n
3.557 * [backup-simplify]: Simplify PI into PI
3.557 * [taylor]: Taking taylor expansion of n in n
3.557 * [backup-simplify]: Simplify 0 into 0
3.557 * [backup-simplify]: Simplify 1 into 1
3.558 * [backup-simplify]: Simplify (/ PI 1) into PI
3.558 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.559 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.559 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.559 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.559 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.561 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.562 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
3.564 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.564 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
3.564 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
3.564 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.564 * [taylor]: Taking taylor expansion of 1/2 in k
3.564 * [backup-simplify]: Simplify 1/2 into 1/2
3.564 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.564 * [taylor]: Taking taylor expansion of 1/2 in k
3.564 * [backup-simplify]: Simplify 1/2 into 1/2
3.564 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.564 * [taylor]: Taking taylor expansion of k in k
3.564 * [backup-simplify]: Simplify 0 into 0
3.564 * [backup-simplify]: Simplify 1 into 1
3.564 * [backup-simplify]: Simplify (/ 1 1) into 1
3.564 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
3.564 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.564 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.564 * [taylor]: Taking taylor expansion of 2 in k
3.564 * [backup-simplify]: Simplify 2 into 2
3.564 * [taylor]: Taking taylor expansion of PI in k
3.564 * [backup-simplify]: Simplify PI into PI
3.565 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.566 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.566 * [taylor]: Taking taylor expansion of (log n) in k
3.566 * [taylor]: Taking taylor expansion of n in k
3.566 * [backup-simplify]: Simplify n into n
3.566 * [backup-simplify]: Simplify (log n) into (log n)
3.567 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.567 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.567 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.568 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.569 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
3.570 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
3.571 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.572 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.573 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.574 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.576 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.576 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.576 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.577 * [backup-simplify]: Simplify (- 0) into 0
3.577 * [backup-simplify]: Simplify (+ 0 0) into 0
3.578 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.579 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
3.581 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.582 * [taylor]: Taking taylor expansion of 0 in k
3.582 * [backup-simplify]: Simplify 0 into 0
3.582 * [backup-simplify]: Simplify 0 into 0
3.582 * [backup-simplify]: Simplify 0 into 0
3.583 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.584 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.588 * [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
3.588 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.589 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.589 * [backup-simplify]: Simplify (- 0) into 0
3.590 * [backup-simplify]: Simplify (+ 0 0) into 0
3.591 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.592 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
3.595 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.595 * [taylor]: Taking taylor expansion of 0 in k
3.595 * [backup-simplify]: Simplify 0 into 0
3.595 * [backup-simplify]: Simplify 0 into 0
3.595 * [backup-simplify]: Simplify 0 into 0
3.595 * [backup-simplify]: Simplify 0 into 0
3.596 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.598 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.603 * [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
3.603 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.604 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.605 * [backup-simplify]: Simplify (- 0) into 0
3.605 * [backup-simplify]: Simplify (+ 0 0) into 0
3.606 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.608 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
3.611 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 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
3.611 * [taylor]: Taking taylor expansion of 0 in k
3.611 * [backup-simplify]: Simplify 0 into 0
3.611 * [backup-simplify]: Simplify 0 into 0
3.612 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
3.612 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
3.612 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
3.612 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
3.612 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
3.612 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
3.612 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.612 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.612 * [taylor]: Taking taylor expansion of 1/2 in k
3.612 * [backup-simplify]: Simplify 1/2 into 1/2
3.612 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.612 * [taylor]: Taking taylor expansion of k in k
3.612 * [backup-simplify]: Simplify 0 into 0
3.612 * [backup-simplify]: Simplify 1 into 1
3.613 * [backup-simplify]: Simplify (/ 1 1) into 1
3.613 * [taylor]: Taking taylor expansion of 1/2 in k
3.613 * [backup-simplify]: Simplify 1/2 into 1/2
3.613 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
3.613 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
3.613 * [taylor]: Taking taylor expansion of -2 in k
3.613 * [backup-simplify]: Simplify -2 into -2
3.613 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.613 * [taylor]: Taking taylor expansion of PI in k
3.613 * [backup-simplify]: Simplify PI into PI
3.613 * [taylor]: Taking taylor expansion of n in k
3.613 * [backup-simplify]: Simplify n into n
3.613 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.613 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
3.613 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
3.614 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.614 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.614 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
3.614 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
3.614 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.614 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.614 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.614 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.615 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.615 * [taylor]: Taking taylor expansion of 1/2 in n
3.615 * [backup-simplify]: Simplify 1/2 into 1/2
3.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.615 * [taylor]: Taking taylor expansion of k in n
3.615 * [backup-simplify]: Simplify k into k
3.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.615 * [taylor]: Taking taylor expansion of 1/2 in n
3.615 * [backup-simplify]: Simplify 1/2 into 1/2
3.615 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.615 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.615 * [taylor]: Taking taylor expansion of -2 in n
3.615 * [backup-simplify]: Simplify -2 into -2
3.615 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.615 * [taylor]: Taking taylor expansion of PI in n
3.615 * [backup-simplify]: Simplify PI into PI
3.615 * [taylor]: Taking taylor expansion of n in n
3.615 * [backup-simplify]: Simplify 0 into 0
3.615 * [backup-simplify]: Simplify 1 into 1
3.615 * [backup-simplify]: Simplify (/ PI 1) into PI
3.616 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.617 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.617 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.617 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.620 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
3.621 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.621 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.621 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.621 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.621 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.621 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.621 * [taylor]: Taking taylor expansion of 1/2 in n
3.621 * [backup-simplify]: Simplify 1/2 into 1/2
3.621 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.621 * [taylor]: Taking taylor expansion of k in n
3.621 * [backup-simplify]: Simplify k into k
3.621 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.621 * [taylor]: Taking taylor expansion of 1/2 in n
3.621 * [backup-simplify]: Simplify 1/2 into 1/2
3.621 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.621 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.621 * [taylor]: Taking taylor expansion of -2 in n
3.621 * [backup-simplify]: Simplify -2 into -2
3.621 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.621 * [taylor]: Taking taylor expansion of PI in n
3.621 * [backup-simplify]: Simplify PI into PI
3.621 * [taylor]: Taking taylor expansion of n in n
3.621 * [backup-simplify]: Simplify 0 into 0
3.621 * [backup-simplify]: Simplify 1 into 1
3.622 * [backup-simplify]: Simplify (/ PI 1) into PI
3.622 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.623 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.623 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.624 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.626 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
3.627 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.627 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
3.627 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
3.628 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.628 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.628 * [taylor]: Taking taylor expansion of 1/2 in k
3.628 * [backup-simplify]: Simplify 1/2 into 1/2
3.628 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.628 * [taylor]: Taking taylor expansion of k in k
3.628 * [backup-simplify]: Simplify 0 into 0
3.628 * [backup-simplify]: Simplify 1 into 1
3.628 * [backup-simplify]: Simplify (/ 1 1) into 1
3.628 * [taylor]: Taking taylor expansion of 1/2 in k
3.628 * [backup-simplify]: Simplify 1/2 into 1/2
3.628 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
3.628 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
3.628 * [taylor]: Taking taylor expansion of (* -2 PI) in k
3.628 * [taylor]: Taking taylor expansion of -2 in k
3.628 * [backup-simplify]: Simplify -2 into -2
3.629 * [taylor]: Taking taylor expansion of PI in k
3.629 * [backup-simplify]: Simplify PI into PI
3.629 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.630 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.630 * [taylor]: Taking taylor expansion of (log n) in k
3.630 * [taylor]: Taking taylor expansion of n in k
3.630 * [backup-simplify]: Simplify n into n
3.630 * [backup-simplify]: Simplify (log n) into (log n)
3.631 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.631 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.631 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.632 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
3.633 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
3.635 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.636 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.637 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.638 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
3.640 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
3.640 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.640 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.641 * [backup-simplify]: Simplify (+ 0 0) into 0
3.642 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.643 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
3.648 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.648 * [taylor]: Taking taylor expansion of 0 in k
3.648 * [backup-simplify]: Simplify 0 into 0
3.648 * [backup-simplify]: Simplify 0 into 0
3.648 * [backup-simplify]: Simplify 0 into 0
3.649 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.651 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
3.654 * [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
3.654 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.655 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.656 * [backup-simplify]: Simplify (+ 0 0) into 0
3.657 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.659 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
3.661 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.661 * [taylor]: Taking taylor expansion of 0 in k
3.661 * [backup-simplify]: Simplify 0 into 0
3.661 * [backup-simplify]: Simplify 0 into 0
3.661 * [backup-simplify]: Simplify 0 into 0
3.661 * [backup-simplify]: Simplify 0 into 0
3.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.664 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.670 * [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
3.670 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.671 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.672 * [backup-simplify]: Simplify (+ 0 0) into 0
3.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.675 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
3.678 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
3.678 * [taylor]: Taking taylor expansion of 0 in k
3.678 * [backup-simplify]: Simplify 0 into 0
3.678 * [backup-simplify]: Simplify 0 into 0
3.679 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
3.679 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
3.680 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
3.680 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
3.680 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.680 * [taylor]: Taking taylor expansion of 2 in n
3.680 * [backup-simplify]: Simplify 2 into 2
3.680 * [taylor]: Taking taylor expansion of (* n PI) in n
3.680 * [taylor]: Taking taylor expansion of n in n
3.680 * [backup-simplify]: Simplify 0 into 0
3.680 * [backup-simplify]: Simplify 1 into 1
3.680 * [taylor]: Taking taylor expansion of PI in n
3.680 * [backup-simplify]: Simplify PI into PI
3.680 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.680 * [taylor]: Taking taylor expansion of 2 in n
3.680 * [backup-simplify]: Simplify 2 into 2
3.680 * [taylor]: Taking taylor expansion of (* n PI) in n
3.680 * [taylor]: Taking taylor expansion of n in n
3.680 * [backup-simplify]: Simplify 0 into 0
3.680 * [backup-simplify]: Simplify 1 into 1
3.680 * [taylor]: Taking taylor expansion of PI in n
3.680 * [backup-simplify]: Simplify PI into PI
3.681 * [backup-simplify]: Simplify (* 0 PI) into 0
3.681 * [backup-simplify]: Simplify (* 2 0) into 0
3.681 * [backup-simplify]: Simplify 0 into 0
3.682 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.683 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.683 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.684 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.684 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.684 * [backup-simplify]: Simplify 0 into 0
3.685 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.686 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.686 * [backup-simplify]: Simplify 0 into 0
3.687 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.688 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
3.688 * [backup-simplify]: Simplify 0 into 0
3.689 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.689 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
3.689 * [backup-simplify]: Simplify 0 into 0
3.690 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.691 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
3.691 * [backup-simplify]: Simplify 0 into 0
3.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
3.694 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
3.694 * [backup-simplify]: Simplify 0 into 0
3.694 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
3.694 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
3.694 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
3.694 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.694 * [taylor]: Taking taylor expansion of 2 in n
3.694 * [backup-simplify]: Simplify 2 into 2
3.694 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.694 * [taylor]: Taking taylor expansion of PI in n
3.694 * [backup-simplify]: Simplify PI into PI
3.694 * [taylor]: Taking taylor expansion of n in n
3.694 * [backup-simplify]: Simplify 0 into 0
3.694 * [backup-simplify]: Simplify 1 into 1
3.694 * [backup-simplify]: Simplify (/ PI 1) into PI
3.695 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.695 * [taylor]: Taking taylor expansion of 2 in n
3.695 * [backup-simplify]: Simplify 2 into 2
3.695 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.695 * [taylor]: Taking taylor expansion of PI in n
3.695 * [backup-simplify]: Simplify PI into PI
3.695 * [taylor]: Taking taylor expansion of n in n
3.695 * [backup-simplify]: Simplify 0 into 0
3.695 * [backup-simplify]: Simplify 1 into 1
3.695 * [backup-simplify]: Simplify (/ PI 1) into PI
3.695 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.696 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.696 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.697 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.697 * [backup-simplify]: Simplify 0 into 0
3.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.698 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.698 * [backup-simplify]: Simplify 0 into 0
3.699 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.699 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.699 * [backup-simplify]: Simplify 0 into 0
3.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.701 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.701 * [backup-simplify]: Simplify 0 into 0
3.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.702 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.702 * [backup-simplify]: Simplify 0 into 0
3.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.704 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.704 * [backup-simplify]: Simplify 0 into 0
3.705 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
3.705 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
3.705 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
3.705 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.705 * [taylor]: Taking taylor expansion of -2 in n
3.705 * [backup-simplify]: Simplify -2 into -2
3.705 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.705 * [taylor]: Taking taylor expansion of PI in n
3.705 * [backup-simplify]: Simplify PI into PI
3.705 * [taylor]: Taking taylor expansion of n in n
3.705 * [backup-simplify]: Simplify 0 into 0
3.705 * [backup-simplify]: Simplify 1 into 1
3.705 * [backup-simplify]: Simplify (/ PI 1) into PI
3.705 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.705 * [taylor]: Taking taylor expansion of -2 in n
3.705 * [backup-simplify]: Simplify -2 into -2
3.705 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.705 * [taylor]: Taking taylor expansion of PI in n
3.705 * [backup-simplify]: Simplify PI into PI
3.705 * [taylor]: Taking taylor expansion of n in n
3.705 * [backup-simplify]: Simplify 0 into 0
3.705 * [backup-simplify]: Simplify 1 into 1
3.706 * [backup-simplify]: Simplify (/ PI 1) into PI
3.706 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.706 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.707 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.707 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
3.707 * [backup-simplify]: Simplify 0 into 0
3.708 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.709 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
3.709 * [backup-simplify]: Simplify 0 into 0
3.709 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.710 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.710 * [backup-simplify]: Simplify 0 into 0
3.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.712 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.712 * [backup-simplify]: Simplify 0 into 0
3.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.713 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.713 * [backup-simplify]: Simplify 0 into 0
3.714 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.715 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.715 * [backup-simplify]: Simplify 0 into 0
3.716 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
3.716 * * * * [progress]: [ 3 / 3 ] generating series at (2)
3.716 * [backup-simplify]: Simplify (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
3.716 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
3.716 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
3.716 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.716 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.716 * [taylor]: Taking taylor expansion of k in k
3.716 * [backup-simplify]: Simplify 0 into 0
3.716 * [backup-simplify]: Simplify 1 into 1
3.716 * [backup-simplify]: Simplify (/ 1 1) into 1
3.716 * [backup-simplify]: Simplify (sqrt 0) into 0
3.718 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.718 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
3.718 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
3.718 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
3.718 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.718 * [taylor]: Taking taylor expansion of 1/2 in k
3.718 * [backup-simplify]: Simplify 1/2 into 1/2
3.718 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.718 * [taylor]: Taking taylor expansion of 1/2 in k
3.718 * [backup-simplify]: Simplify 1/2 into 1/2
3.718 * [taylor]: Taking taylor expansion of k in k
3.718 * [backup-simplify]: Simplify 0 into 0
3.718 * [backup-simplify]: Simplify 1 into 1
3.718 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
3.718 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
3.718 * [taylor]: Taking taylor expansion of 2 in k
3.718 * [backup-simplify]: Simplify 2 into 2
3.718 * [taylor]: Taking taylor expansion of (* n PI) in k
3.718 * [taylor]: Taking taylor expansion of n in k
3.718 * [backup-simplify]: Simplify n into n
3.718 * [taylor]: Taking taylor expansion of PI in k
3.719 * [backup-simplify]: Simplify PI into PI
3.719 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.719 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
3.719 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
3.719 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.720 * [backup-simplify]: Simplify (- 0) into 0
3.720 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.720 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
3.720 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
3.720 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
3.720 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
3.720 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.720 * [taylor]: Taking taylor expansion of k in n
3.721 * [backup-simplify]: Simplify k into k
3.721 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.721 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
3.721 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.721 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
3.721 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.721 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.721 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.721 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.721 * [taylor]: Taking taylor expansion of 1/2 in n
3.721 * [backup-simplify]: Simplify 1/2 into 1/2
3.721 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.721 * [taylor]: Taking taylor expansion of 1/2 in n
3.721 * [backup-simplify]: Simplify 1/2 into 1/2
3.721 * [taylor]: Taking taylor expansion of k in n
3.721 * [backup-simplify]: Simplify k into k
3.721 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.721 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.721 * [taylor]: Taking taylor expansion of 2 in n
3.721 * [backup-simplify]: Simplify 2 into 2
3.721 * [taylor]: Taking taylor expansion of (* n PI) in n
3.721 * [taylor]: Taking taylor expansion of n in n
3.721 * [backup-simplify]: Simplify 0 into 0
3.721 * [backup-simplify]: Simplify 1 into 1
3.721 * [taylor]: Taking taylor expansion of PI in n
3.721 * [backup-simplify]: Simplify PI into PI
3.722 * [backup-simplify]: Simplify (* 0 PI) into 0
3.723 * [backup-simplify]: Simplify (* 2 0) into 0
3.725 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.726 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.728 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.728 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.728 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.728 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.729 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.730 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.732 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.732 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
3.732 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
3.732 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.732 * [taylor]: Taking taylor expansion of k in n
3.732 * [backup-simplify]: Simplify k into k
3.732 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.732 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
3.732 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.732 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
3.732 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.732 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.732 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.732 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.732 * [taylor]: Taking taylor expansion of 1/2 in n
3.732 * [backup-simplify]: Simplify 1/2 into 1/2
3.732 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.732 * [taylor]: Taking taylor expansion of 1/2 in n
3.732 * [backup-simplify]: Simplify 1/2 into 1/2
3.733 * [taylor]: Taking taylor expansion of k in n
3.733 * [backup-simplify]: Simplify k into k
3.733 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.733 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.733 * [taylor]: Taking taylor expansion of 2 in n
3.733 * [backup-simplify]: Simplify 2 into 2
3.733 * [taylor]: Taking taylor expansion of (* n PI) in n
3.733 * [taylor]: Taking taylor expansion of n in n
3.733 * [backup-simplify]: Simplify 0 into 0
3.733 * [backup-simplify]: Simplify 1 into 1
3.733 * [taylor]: Taking taylor expansion of PI in n
3.733 * [backup-simplify]: Simplify PI into PI
3.733 * [backup-simplify]: Simplify (* 0 PI) into 0
3.734 * [backup-simplify]: Simplify (* 2 0) into 0
3.735 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.737 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.738 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.738 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.739 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.739 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.740 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.741 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.743 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.744 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k)))
3.744 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
3.744 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
3.744 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
3.744 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.744 * [taylor]: Taking taylor expansion of 1/2 in k
3.744 * [backup-simplify]: Simplify 1/2 into 1/2
3.744 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.744 * [taylor]: Taking taylor expansion of 1/2 in k
3.744 * [backup-simplify]: Simplify 1/2 into 1/2
3.744 * [taylor]: Taking taylor expansion of k in k
3.744 * [backup-simplify]: Simplify 0 into 0
3.744 * [backup-simplify]: Simplify 1 into 1
3.744 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
3.744 * [taylor]: Taking taylor expansion of (log n) in k
3.744 * [taylor]: Taking taylor expansion of n in k
3.744 * [backup-simplify]: Simplify n into n
3.744 * [backup-simplify]: Simplify (log n) into (log n)
3.744 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.744 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.745 * [taylor]: Taking taylor expansion of 2 in k
3.745 * [backup-simplify]: Simplify 2 into 2
3.745 * [taylor]: Taking taylor expansion of PI in k
3.745 * [backup-simplify]: Simplify PI into PI
3.745 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.746 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.747 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.747 * [backup-simplify]: Simplify (- 0) into 0
3.747 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.748 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.750 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
3.751 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.751 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.751 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.751 * [taylor]: Taking taylor expansion of k in k
3.751 * [backup-simplify]: Simplify 0 into 0
3.751 * [backup-simplify]: Simplify 1 into 1
3.751 * [backup-simplify]: Simplify (/ 1 1) into 1
3.752 * [backup-simplify]: Simplify (sqrt 0) into 0
3.753 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.754 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
3.754 * [backup-simplify]: Simplify 0 into 0
3.756 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.757 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.759 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.759 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
3.760 * [backup-simplify]: Simplify (- 0) into 0
3.760 * [backup-simplify]: Simplify (+ 0 0) into 0
3.761 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.763 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
3.765 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.766 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
3.766 * [taylor]: Taking taylor expansion of 0 in k
3.766 * [backup-simplify]: Simplify 0 into 0
3.767 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
3.768 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.770 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.770 * [backup-simplify]: Simplify (+ 0 0) into 0
3.771 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
3.771 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.771 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.776 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
3.779 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.783 * [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)))))))
3.785 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.785 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.786 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.788 * [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
3.789 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
3.789 * [backup-simplify]: Simplify (- 0) into 0
3.790 * [backup-simplify]: Simplify (+ 0 0) into 0
3.790 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.791 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.793 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.793 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.793 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
3.794 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
3.794 * [taylor]: Taking taylor expansion of 0 in k
3.794 * [backup-simplify]: Simplify 0 into 0
3.794 * [backup-simplify]: Simplify 0 into 0
3.795 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
3.797 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.798 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
3.798 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.800 * [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
3.800 * [backup-simplify]: Simplify (+ 0 0) into 0
3.801 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
3.801 * [backup-simplify]: Simplify (- 0) into 0
3.801 * [backup-simplify]: Simplify (+ 0 0) into 0
3.803 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.805 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 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)))))
3.811 * [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))))))))
3.814 * [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))))))))
3.815 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.816 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
3.819 * [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
3.820 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
3.820 * [backup-simplify]: Simplify (- 0) into 0
3.820 * [backup-simplify]: Simplify (+ 0 0) into 0
3.821 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.822 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
3.824 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
3.824 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.824 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
3.826 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
3.826 * [taylor]: Taking taylor expansion of 0 in k
3.826 * [backup-simplify]: Simplify 0 into 0
3.826 * [backup-simplify]: Simplify 0 into 0
3.826 * [backup-simplify]: Simplify 0 into 0
3.826 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.829 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.830 * [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
3.831 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.834 * [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
3.834 * [backup-simplify]: Simplify (+ 0 0) into 0
3.835 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
3.835 * [backup-simplify]: Simplify (- 0) into 0
3.836 * [backup-simplify]: Simplify (+ 0 0) into 0
3.837 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
3.841 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 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)))))))
3.857 * [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))))))))))))))
3.870 * [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))))))))))))))
3.892 * [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))))))))))))))))))))))
3.892 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
3.892 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
3.892 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
3.892 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.892 * [taylor]: Taking taylor expansion of k in k
3.892 * [backup-simplify]: Simplify 0 into 0
3.892 * [backup-simplify]: Simplify 1 into 1
3.893 * [backup-simplify]: Simplify (sqrt 0) into 0
3.894 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.894 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
3.894 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
3.894 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
3.894 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.894 * [taylor]: Taking taylor expansion of 1/2 in k
3.894 * [backup-simplify]: Simplify 1/2 into 1/2
3.894 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.894 * [taylor]: Taking taylor expansion of 1/2 in k
3.894 * [backup-simplify]: Simplify 1/2 into 1/2
3.894 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.894 * [taylor]: Taking taylor expansion of k in k
3.894 * [backup-simplify]: Simplify 0 into 0
3.894 * [backup-simplify]: Simplify 1 into 1
3.894 * [backup-simplify]: Simplify (/ 1 1) into 1
3.894 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
3.894 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
3.894 * [taylor]: Taking taylor expansion of 2 in k
3.894 * [backup-simplify]: Simplify 2 into 2
3.894 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.894 * [taylor]: Taking taylor expansion of PI in k
3.894 * [backup-simplify]: Simplify PI into PI
3.894 * [taylor]: Taking taylor expansion of n in k
3.894 * [backup-simplify]: Simplify n into n
3.894 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.894 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
3.894 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
3.895 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.895 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.895 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.895 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
3.895 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
3.895 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
3.895 * [taylor]: Taking taylor expansion of (sqrt k) in n
3.895 * [taylor]: Taking taylor expansion of k in n
3.895 * [backup-simplify]: Simplify k into k
3.895 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
3.895 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
3.895 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.895 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.896 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.896 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.896 * [taylor]: Taking taylor expansion of 1/2 in n
3.896 * [backup-simplify]: Simplify 1/2 into 1/2
3.896 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.896 * [taylor]: Taking taylor expansion of 1/2 in n
3.896 * [backup-simplify]: Simplify 1/2 into 1/2
3.896 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.896 * [taylor]: Taking taylor expansion of k in n
3.896 * [backup-simplify]: Simplify k into k
3.896 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.896 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.896 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.896 * [taylor]: Taking taylor expansion of 2 in n
3.896 * [backup-simplify]: Simplify 2 into 2
3.896 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.896 * [taylor]: Taking taylor expansion of PI in n
3.896 * [backup-simplify]: Simplify PI into PI
3.896 * [taylor]: Taking taylor expansion of n in n
3.896 * [backup-simplify]: Simplify 0 into 0
3.896 * [backup-simplify]: Simplify 1 into 1
3.896 * [backup-simplify]: Simplify (/ PI 1) into PI
3.896 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.897 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.897 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.897 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.897 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.898 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.899 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
3.900 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.900 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
3.900 * [taylor]: Taking taylor expansion of (sqrt k) in n
3.900 * [taylor]: Taking taylor expansion of k in n
3.900 * [backup-simplify]: Simplify k into k
3.900 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
3.900 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
3.900 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.900 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.900 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.900 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.900 * [taylor]: Taking taylor expansion of 1/2 in n
3.900 * [backup-simplify]: Simplify 1/2 into 1/2
3.900 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.900 * [taylor]: Taking taylor expansion of 1/2 in n
3.900 * [backup-simplify]: Simplify 1/2 into 1/2
3.900 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.900 * [taylor]: Taking taylor expansion of k in n
3.900 * [backup-simplify]: Simplify k into k
3.900 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.900 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.900 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.900 * [taylor]: Taking taylor expansion of 2 in n
3.900 * [backup-simplify]: Simplify 2 into 2
3.900 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.900 * [taylor]: Taking taylor expansion of PI in n
3.900 * [backup-simplify]: Simplify PI into PI
3.900 * [taylor]: Taking taylor expansion of n in n
3.900 * [backup-simplify]: Simplify 0 into 0
3.900 * [backup-simplify]: Simplify 1 into 1
3.901 * [backup-simplify]: Simplify (/ PI 1) into PI
3.901 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.902 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.902 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.902 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.902 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.903 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.903 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
3.904 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.905 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
3.905 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
3.905 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
3.905 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
3.905 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.905 * [taylor]: Taking taylor expansion of 1/2 in k
3.905 * [backup-simplify]: Simplify 1/2 into 1/2
3.905 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.905 * [taylor]: Taking taylor expansion of 1/2 in k
3.905 * [backup-simplify]: Simplify 1/2 into 1/2
3.905 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.905 * [taylor]: Taking taylor expansion of k in k
3.905 * [backup-simplify]: Simplify 0 into 0
3.905 * [backup-simplify]: Simplify 1 into 1
3.905 * [backup-simplify]: Simplify (/ 1 1) into 1
3.906 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
3.906 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.906 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.906 * [taylor]: Taking taylor expansion of 2 in k
3.906 * [backup-simplify]: Simplify 2 into 2
3.906 * [taylor]: Taking taylor expansion of PI in k
3.906 * [backup-simplify]: Simplify PI into PI
3.906 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.907 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.907 * [taylor]: Taking taylor expansion of (log n) in k
3.907 * [taylor]: Taking taylor expansion of n in k
3.907 * [backup-simplify]: Simplify n into n
3.907 * [backup-simplify]: Simplify (log n) into (log n)
3.907 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.907 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.907 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.907 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.908 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
3.909 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
3.910 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.910 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.910 * [taylor]: Taking taylor expansion of k in k
3.910 * [backup-simplify]: Simplify 0 into 0
3.910 * [backup-simplify]: Simplify 1 into 1
3.910 * [backup-simplify]: Simplify (sqrt 0) into 0
3.911 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.911 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
3.911 * [backup-simplify]: Simplify 0 into 0
3.912 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.912 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.914 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.914 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.914 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.914 * [backup-simplify]: Simplify (- 0) into 0
3.914 * [backup-simplify]: Simplify (+ 0 0) into 0
3.915 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.916 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
3.917 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.918 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
3.918 * [taylor]: Taking taylor expansion of 0 in k
3.918 * [backup-simplify]: Simplify 0 into 0
3.918 * [backup-simplify]: Simplify 0 into 0
3.919 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
3.920 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
3.921 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.921 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.925 * [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
3.925 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.926 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.926 * [backup-simplify]: Simplify (- 0) into 0
3.927 * [backup-simplify]: Simplify (+ 0 0) into 0
3.928 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.930 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
3.932 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.933 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
3.935 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
3.935 * [taylor]: Taking taylor expansion of 0 in k
3.935 * [backup-simplify]: Simplify 0 into 0
3.935 * [backup-simplify]: Simplify 0 into 0
3.935 * [backup-simplify]: Simplify 0 into 0
3.938 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.940 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
3.941 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
3.942 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.943 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.950 * [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
3.950 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.951 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.952 * [backup-simplify]: Simplify (- 0) into 0
3.952 * [backup-simplify]: Simplify (+ 0 0) into 0
3.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.956 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
3.959 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 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
3.960 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
3.962 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
3.962 * [taylor]: Taking taylor expansion of 0 in k
3.962 * [backup-simplify]: Simplify 0 into 0
3.962 * [backup-simplify]: Simplify 0 into 0
3.962 * [backup-simplify]: Simplify 0 into 0
3.962 * [backup-simplify]: Simplify 0 into 0
3.966 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.968 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
3.969 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
3.974 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
3.974 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
3.974 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
3.974 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
3.974 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
3.974 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
3.974 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
3.974 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.974 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.975 * [taylor]: Taking taylor expansion of 1/2 in k
3.975 * [backup-simplify]: Simplify 1/2 into 1/2
3.975 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.975 * [taylor]: Taking taylor expansion of k in k
3.975 * [backup-simplify]: Simplify 0 into 0
3.975 * [backup-simplify]: Simplify 1 into 1
3.975 * [backup-simplify]: Simplify (/ 1 1) into 1
3.975 * [taylor]: Taking taylor expansion of 1/2 in k
3.975 * [backup-simplify]: Simplify 1/2 into 1/2
3.975 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
3.975 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
3.975 * [taylor]: Taking taylor expansion of -2 in k
3.975 * [backup-simplify]: Simplify -2 into -2
3.975 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.975 * [taylor]: Taking taylor expansion of PI in k
3.975 * [backup-simplify]: Simplify PI into PI
3.975 * [taylor]: Taking taylor expansion of n in k
3.976 * [backup-simplify]: Simplify n into n
3.976 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.976 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
3.976 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
3.976 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.977 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.977 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
3.977 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
3.977 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.977 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.977 * [taylor]: Taking taylor expansion of -1 in k
3.977 * [backup-simplify]: Simplify -1 into -1
3.977 * [taylor]: Taking taylor expansion of k in k
3.977 * [backup-simplify]: Simplify 0 into 0
3.978 * [backup-simplify]: Simplify 1 into 1
3.978 * [backup-simplify]: Simplify (/ -1 1) into -1
3.978 * [backup-simplify]: Simplify (sqrt 0) into 0
3.980 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.980 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
3.980 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
3.980 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.981 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.981 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.981 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.981 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.981 * [taylor]: Taking taylor expansion of 1/2 in n
3.981 * [backup-simplify]: Simplify 1/2 into 1/2
3.981 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.981 * [taylor]: Taking taylor expansion of k in n
3.981 * [backup-simplify]: Simplify k into k
3.981 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.981 * [taylor]: Taking taylor expansion of 1/2 in n
3.981 * [backup-simplify]: Simplify 1/2 into 1/2
3.981 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.981 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.981 * [taylor]: Taking taylor expansion of -2 in n
3.981 * [backup-simplify]: Simplify -2 into -2
3.981 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.981 * [taylor]: Taking taylor expansion of PI in n
3.981 * [backup-simplify]: Simplify PI into PI
3.981 * [taylor]: Taking taylor expansion of n in n
3.981 * [backup-simplify]: Simplify 0 into 0
3.981 * [backup-simplify]: Simplify 1 into 1
3.982 * [backup-simplify]: Simplify (/ PI 1) into PI
3.982 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.983 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.983 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.984 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.985 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.986 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
3.988 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.988 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
3.988 * [taylor]: Taking taylor expansion of (/ -1 k) in n
3.988 * [taylor]: Taking taylor expansion of -1 in n
3.988 * [backup-simplify]: Simplify -1 into -1
3.988 * [taylor]: Taking taylor expansion of k in n
3.988 * [backup-simplify]: Simplify k into k
3.988 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
3.988 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
3.988 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
3.988 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
3.989 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
3.990 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
3.990 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.990 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.990 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.990 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.990 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.990 * [taylor]: Taking taylor expansion of 1/2 in n
3.990 * [backup-simplify]: Simplify 1/2 into 1/2
3.990 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.990 * [taylor]: Taking taylor expansion of k in n
3.990 * [backup-simplify]: Simplify k into k
3.990 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.990 * [taylor]: Taking taylor expansion of 1/2 in n
3.990 * [backup-simplify]: Simplify 1/2 into 1/2
3.990 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.990 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.990 * [taylor]: Taking taylor expansion of -2 in n
3.990 * [backup-simplify]: Simplify -2 into -2
3.990 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.990 * [taylor]: Taking taylor expansion of PI in n
3.990 * [backup-simplify]: Simplify PI into PI
3.990 * [taylor]: Taking taylor expansion of n in n
3.990 * [backup-simplify]: Simplify 0 into 0
3.990 * [backup-simplify]: Simplify 1 into 1
3.991 * [backup-simplify]: Simplify (/ PI 1) into PI
3.991 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.992 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.992 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.993 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.994 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.994 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
3.995 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.995 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
3.995 * [taylor]: Taking taylor expansion of (/ -1 k) in n
3.995 * [taylor]: Taking taylor expansion of -1 in n
3.995 * [backup-simplify]: Simplify -1 into -1
3.995 * [taylor]: Taking taylor expansion of k in n
3.995 * [backup-simplify]: Simplify k into k
3.995 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
3.995 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
3.995 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
3.995 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
3.996 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
3.996 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
3.996 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
3.996 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
3.996 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.996 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.996 * [taylor]: Taking taylor expansion of 1/2 in k
3.996 * [backup-simplify]: Simplify 1/2 into 1/2
3.996 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.996 * [taylor]: Taking taylor expansion of k in k
3.996 * [backup-simplify]: Simplify 0 into 0
3.996 * [backup-simplify]: Simplify 1 into 1
3.999 * [backup-simplify]: Simplify (/ 1 1) into 1
3.999 * [taylor]: Taking taylor expansion of 1/2 in k
3.999 * [backup-simplify]: Simplify 1/2 into 1/2
3.999 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
3.999 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
3.999 * [taylor]: Taking taylor expansion of (* -2 PI) in k
3.999 * [taylor]: Taking taylor expansion of -2 in k
3.999 * [backup-simplify]: Simplify -2 into -2
3.999 * [taylor]: Taking taylor expansion of PI in k
3.999 * [backup-simplify]: Simplify PI into PI
3.999 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
4.000 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
4.000 * [taylor]: Taking taylor expansion of (log n) in k
4.000 * [taylor]: Taking taylor expansion of n in k
4.000 * [backup-simplify]: Simplify n into n
4.000 * [backup-simplify]: Simplify (log n) into (log n)
4.000 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.001 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
4.001 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.001 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
4.002 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
4.003 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
4.003 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
4.003 * [taylor]: Taking taylor expansion of (/ -1 k) in k
4.003 * [taylor]: Taking taylor expansion of -1 in k
4.003 * [backup-simplify]: Simplify -1 into -1
4.003 * [taylor]: Taking taylor expansion of k in k
4.003 * [backup-simplify]: Simplify 0 into 0
4.003 * [backup-simplify]: Simplify 1 into 1
4.003 * [backup-simplify]: Simplify (/ -1 1) into -1
4.003 * [backup-simplify]: Simplify (sqrt 0) into 0
4.004 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
4.005 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
4.006 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
4.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.007 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
4.008 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
4.008 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.008 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
4.009 * [backup-simplify]: Simplify (+ 0 0) into 0
4.010 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.010 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
4.011 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
4.012 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
4.012 * [taylor]: Taking taylor expansion of 0 in k
4.012 * [backup-simplify]: Simplify 0 into 0
4.012 * [backup-simplify]: Simplify 0 into 0
4.013 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
4.015 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.016 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
4.017 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
4.017 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.018 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
4.020 * [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
4.020 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.021 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
4.021 * [backup-simplify]: Simplify (+ 0 0) into 0
4.022 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.023 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
4.024 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.024 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.025 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
4.026 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
4.026 * [taylor]: Taking taylor expansion of 0 in k
4.026 * [backup-simplify]: Simplify 0 into 0
4.027 * [backup-simplify]: Simplify 0 into 0
4.027 * [backup-simplify]: Simplify 0 into 0
4.028 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.032 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.035 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
4.037 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
4.039 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
4.040 * * * [progress]: simplifying candidates
4.040 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
4.040 * * * * [progress]: [ 9 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 10 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.040 * * * * [progress]: [ 12 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 13 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.040 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))>
4.040 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
4.040 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.040 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.040 * * * * [progress]: [ 21 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.040 * * * * [progress]: [ 22 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.041 * * * * [progress]: [ 23 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.041 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))>
4.041 * * * * [progress]: [ 25 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.041 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log (* n 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 34 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 36 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 37 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* (* n 2) PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) 1) PI) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))>
4.041 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) 1))>
4.041 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
4.041 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
4.042 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
4.042 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
4.042 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
4.042 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.042 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.042 * * * * [progress]: [ 54 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
4.042 * * * * [progress]: [ 55 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.042 * * * * [progress]: [ 56 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.042 * * * * [progress]: [ 57 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.042 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (- (sqrt k))))>
4.042 * * * * [progress]: [ 59 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))>
4.042 * * * * [progress]: [ 60 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))>
4.042 * * * * [progress]: [ 61 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
4.042 * * * * [progress]: [ 62 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
4.042 * * * * [progress]: [ 63 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
4.042 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
4.042 * * * * [progress]: [ 65 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))>
4.042 * * * * [progress]: [ 66 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))>
4.042 * * * * [progress]: [ 67 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
4.042 * * * * [progress]: [ 68 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
4.042 * * * * [progress]: [ 69 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
4.042 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
4.042 * * * * [progress]: [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
4.042 * * * * [progress]: [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
4.042 * * * * [progress]: [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
4.043 * * * * [progress]: [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
4.043 * * * * [progress]: [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
4.043 * * * * [progress]: [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
4.043 * * * * [progress]: [ 77 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
4.043 * * * * [progress]: [ 78 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
4.043 * * * * [progress]: [ 79 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
4.043 * * * * [progress]: [ 80 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
4.043 * * * * [progress]: [ 81 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
4.043 * * * * [progress]: [ 82 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
4.043 * * * * [progress]: [ 83 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
4.043 * * * * [progress]: [ 84 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
4.043 * * * * [progress]: [ 85 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
4.043 * * * * [progress]: [ 86 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
4.043 * * * * [progress]: [ 87 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
4.043 * * * * [progress]: [ 88 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
4.043 * * * * [progress]: [ 89 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
4.043 * * * * [progress]: [ 90 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
4.043 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
4.043 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
4.043 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
4.043 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
4.043 * * * * [progress]: [ 95 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
4.043 * * * * [progress]: [ 96 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
4.043 * * * * [progress]: [ 97 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
4.043 * * * * [progress]: [ 98 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
4.044 * * * * [progress]: [ 99 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
4.044 * * * * [progress]: [ 100 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
4.044 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
4.044 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
4.044 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
4.044 * * * * [progress]: [ 104 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
4.044 * * * * [progress]: [ 105 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
4.044 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
4.044 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
4.044 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
4.044 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
4.044 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
4.044 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
4.044 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))>
4.044 * * * * [progress]: [ 113 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))))>
4.044 * * * * [progress]: [ 114 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))))>
4.044 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
4.044 * * * * [progress]: [ 116 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))))>
4.044 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))>
4.044 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.044 * * * * [progress]: [ 119 / 127 ] 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)))>
4.044 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
4.044 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
4.044 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.044 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.045 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.045 * * * * [progress]: [ 125 / 127 ] 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)))))))))))))))))))))))>
4.045 * * * * [progress]: [ 126 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
4.045 * * * * [progress]: [ 127 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
4.046 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (+ (log n) (log 2)) (log PI))
  (+ (log (* n 2)) (log PI))
  (log (* (* n 2) PI))
  (exp (* (* n 2) PI))
  (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))
  (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) 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 PI) (cbrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) 1)
  (* 2 PI)
  (real->posit16 (* (* n 2) PI))
  (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) 1)
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) 1)
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) 1)
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1)
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1)
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1)
  (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))
  (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))
  (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))
  (real->posit16 (/ (pow (* (* n 2) PI) (- 1/2 (/ 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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
4.049 * * [simplify]: iteration 0: 271 enodes
4.139 * * [simplify]: iteration 1: 662 enodes
4.450 * * [simplify]: iteration 2: 2241 enodes
5.191 * * [simplify]: iteration complete: 5008 enodes
5.192 * * [simplify]: Extracting #0: cost 96 inf + 0
5.193 * * [simplify]: Extracting #1: cost 556 inf + 1
5.197 * * [simplify]: Extracting #2: cost 1197 inf + 932
5.206 * * [simplify]: Extracting #3: cost 1527 inf + 33350
5.246 * * [simplify]: Extracting #4: cost 1063 inf + 205576
5.370 * * [simplify]: Extracting #5: cost 381 inf + 501395
5.556 * * [simplify]: Extracting #6: cost 148 inf + 646155
5.776 * * [simplify]: Extracting #7: cost 56 inf + 693103
5.966 * * [simplify]: Extracting #8: cost 3 inf + 723366
6.179 * * [simplify]: Extracting #9: cost 0 inf + 713906
6.361 * * [simplify]: Extracting #10: cost 0 inf + 709106
6.602 * * [simplify]: Extracting #11: cost 0 inf + 708436
6.791 * [simplify]: Simplified to:
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (- 1/2 (* 1/2 k))
  (- 1/2 (* 1/2 k))
  (- 1/2 (* 1/2 k))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k)))))
  (pow (* (* 2 PI) n) (sqrt (- 1/2 (* 1/2 k))))
  (* (* 2 PI) n)
  (pow (* (* 2 PI) n) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* 2 PI) n) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* 2 PI) n)
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (* -1/2 k))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (* -1/2 k))
  (pow (* n 2) (- 1/2 (* 1/2 k)))
  (pow PI (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (exp (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (* (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (* (* (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (real->posit16 (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* (cbrt PI) (* n 2)) (cbrt PI))
  (* 2 (* n (sqrt PI)))
  (* n 2)
  (* 2 PI)
  (real->posit16 (* (* 2 PI) n))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (exp (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (* (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) k) (* (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))))
  (* (cbrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))) (cbrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))))
  (cbrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (* (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)) (* (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))))
  (sqrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (sqrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (- (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (- (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (cbrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (fabs (cbrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (cbrt k)))
  (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/2 (* 1/2 k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/2 (* 1/2 k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))
  (* (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k))) (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k)))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (/ (fabs (cbrt k)) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (cbrt k)))
  (* (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (* (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (* (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (* (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (fabs (cbrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (cbrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  1
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  1
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (fabs (cbrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (* -1/2 k)))
  (/ (sqrt k) (pow (* (* 2 PI) n) (* -1/2 k)))
  (/ (sqrt k) (pow PI (- 1/2 (* 1/2 k))))
  (/ (sqrt k) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (sqrt k) (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (sqrt k) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- 1/4 (/ k 4))))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (real->posit16 (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (- (+ (+ (* (log (* 2 PI)) (* (* (* (* k k) (log n)) (sqrt (* (* 2 PI) n))) 1/4)) (sqrt (* (* 2 PI) n))) (* (* (* k k) 1/8) (+ (* (sqrt (* (* 2 PI) n)) (* (log (* 2 PI)) (log (* 2 PI)))) (* (sqrt (* (* 2 PI) n)) (* (log n) (log n)))))) (/ (* (* k (sqrt (* (* 2 PI) n))) (log (* (* 2 PI) n))) 2))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (+ (+ (* (- (log (* 2 PI))) (* (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (log n))) (* (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (- (log (* 2 PI)) (* (log n) (log n))))) (+ (+ (- (* k (* +nan.0 (sqrt (* (* 2 PI) n)))) (* +nan.0 (sqrt (* (* 2 PI) n)))) (* (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (- (* (log (* 2 PI)) (log (* 2 PI))) (log n)))) (- (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (* +nan.0 (* (* k (sqrt (* (* 2 PI) n))) (- (log (* 2 PI)) (log n)))))))
  (+ (/ (* (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (- +nan.0)) (* (* k k) k)) (* +nan.0 (- (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) k) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (* k k)))))
  (+ (- (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) k) +nan.0)) (* +nan.0 (- (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))))))
6.804 * * * [progress]: adding candidates to table
7.413 * * [progress]: iteration 2 / 4
7.413 * * * [progress]: picking best candidate
7.441 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
7.441 * * * [progress]: localizing error
7.493 * * * [progress]: generating rewritten candidates
7.493 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
7.525 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
7.535 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1)
7.569 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
7.633 * * * [progress]: generating series expansions
7.634 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
7.635 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
7.635 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
7.635 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
7.635 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
7.635 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
7.635 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
7.635 * [taylor]: Taking taylor expansion of 1/2 in k
7.635 * [backup-simplify]: Simplify 1/2 into 1/2
7.635 * [taylor]: Taking taylor expansion of (- 1 k) in k
7.635 * [taylor]: Taking taylor expansion of 1 in k
7.635 * [backup-simplify]: Simplify 1 into 1
7.635 * [taylor]: Taking taylor expansion of k in k
7.635 * [backup-simplify]: Simplify 0 into 0
7.635 * [backup-simplify]: Simplify 1 into 1
7.635 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
7.635 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
7.635 * [taylor]: Taking taylor expansion of 2 in k
7.635 * [backup-simplify]: Simplify 2 into 2
7.635 * [taylor]: Taking taylor expansion of (* n PI) in k
7.635 * [taylor]: Taking taylor expansion of n in k
7.635 * [backup-simplify]: Simplify n into n
7.635 * [taylor]: Taking taylor expansion of PI in k
7.635 * [backup-simplify]: Simplify PI into PI
7.635 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.636 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
7.636 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
7.636 * [backup-simplify]: Simplify (- 0) into 0
7.637 * [backup-simplify]: Simplify (+ 1 0) into 1
7.638 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.638 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
7.638 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
7.638 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
7.638 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
7.638 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
7.638 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
7.638 * [taylor]: Taking taylor expansion of 1/2 in n
7.638 * [backup-simplify]: Simplify 1/2 into 1/2
7.638 * [taylor]: Taking taylor expansion of (- 1 k) in n
7.638 * [taylor]: Taking taylor expansion of 1 in n
7.638 * [backup-simplify]: Simplify 1 into 1
7.638 * [taylor]: Taking taylor expansion of k in n
7.638 * [backup-simplify]: Simplify k into k
7.638 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.638 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.638 * [taylor]: Taking taylor expansion of 2 in n
7.638 * [backup-simplify]: Simplify 2 into 2
7.638 * [taylor]: Taking taylor expansion of (* n PI) in n
7.638 * [taylor]: Taking taylor expansion of n in n
7.638 * [backup-simplify]: Simplify 0 into 0
7.638 * [backup-simplify]: Simplify 1 into 1
7.638 * [taylor]: Taking taylor expansion of PI in n
7.638 * [backup-simplify]: Simplify PI into PI
7.639 * [backup-simplify]: Simplify (* 0 PI) into 0
7.640 * [backup-simplify]: Simplify (* 2 0) into 0
7.641 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.643 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.644 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.644 * [backup-simplify]: Simplify (- k) into (- k)
7.644 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
7.644 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
7.646 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.647 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
7.648 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
7.648 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
7.648 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
7.648 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
7.648 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
7.648 * [taylor]: Taking taylor expansion of 1/2 in n
7.648 * [backup-simplify]: Simplify 1/2 into 1/2
7.648 * [taylor]: Taking taylor expansion of (- 1 k) in n
7.648 * [taylor]: Taking taylor expansion of 1 in n
7.648 * [backup-simplify]: Simplify 1 into 1
7.648 * [taylor]: Taking taylor expansion of k in n
7.648 * [backup-simplify]: Simplify k into k
7.648 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.649 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.649 * [taylor]: Taking taylor expansion of 2 in n
7.649 * [backup-simplify]: Simplify 2 into 2
7.649 * [taylor]: Taking taylor expansion of (* n PI) in n
7.649 * [taylor]: Taking taylor expansion of n in n
7.649 * [backup-simplify]: Simplify 0 into 0
7.649 * [backup-simplify]: Simplify 1 into 1
7.649 * [taylor]: Taking taylor expansion of PI in n
7.649 * [backup-simplify]: Simplify PI into PI
7.649 * [backup-simplify]: Simplify (* 0 PI) into 0
7.650 * [backup-simplify]: Simplify (* 2 0) into 0
7.651 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.653 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.654 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.654 * [backup-simplify]: Simplify (- k) into (- k)
7.654 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
7.654 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
7.656 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.657 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
7.658 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
7.658 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
7.659 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
7.659 * [taylor]: Taking taylor expansion of 1/2 in k
7.659 * [backup-simplify]: Simplify 1/2 into 1/2
7.659 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
7.659 * [taylor]: Taking taylor expansion of (- 1 k) in k
7.659 * [taylor]: Taking taylor expansion of 1 in k
7.659 * [backup-simplify]: Simplify 1 into 1
7.659 * [taylor]: Taking taylor expansion of k in k
7.659 * [backup-simplify]: Simplify 0 into 0
7.659 * [backup-simplify]: Simplify 1 into 1
7.659 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
7.659 * [taylor]: Taking taylor expansion of (log n) in k
7.659 * [taylor]: Taking taylor expansion of n in k
7.659 * [backup-simplify]: Simplify n into n
7.659 * [backup-simplify]: Simplify (log n) into (log n)
7.659 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.659 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.659 * [taylor]: Taking taylor expansion of 2 in k
7.659 * [backup-simplify]: Simplify 2 into 2
7.659 * [taylor]: Taking taylor expansion of PI in k
7.659 * [backup-simplify]: Simplify PI into PI
7.660 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.661 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.661 * [backup-simplify]: Simplify (- 0) into 0
7.662 * [backup-simplify]: Simplify (+ 1 0) into 1
7.663 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.664 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
7.665 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
7.666 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
7.667 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
7.669 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.670 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
7.672 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.672 * [backup-simplify]: Simplify (- 0) into 0
7.673 * [backup-simplify]: Simplify (+ 0 0) into 0
7.673 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
7.675 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.676 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
7.678 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.678 * [taylor]: Taking taylor expansion of 0 in k
7.678 * [backup-simplify]: Simplify 0 into 0
7.678 * [backup-simplify]: Simplify 0 into 0
7.679 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.680 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.682 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.682 * [backup-simplify]: Simplify (+ 0 0) into 0
7.683 * [backup-simplify]: Simplify (- 1) into -1
7.683 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.685 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
7.687 * [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)))))
7.690 * [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)))))))
7.693 * [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)))))))
7.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.702 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.706 * [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
7.706 * [backup-simplify]: Simplify (- 0) into 0
7.707 * [backup-simplify]: Simplify (+ 0 0) into 0
7.708 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
7.709 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.711 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.713 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.713 * [taylor]: Taking taylor expansion of 0 in k
7.713 * [backup-simplify]: Simplify 0 into 0
7.713 * [backup-simplify]: Simplify 0 into 0
7.713 * [backup-simplify]: Simplify 0 into 0
7.715 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.716 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.720 * [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
7.720 * [backup-simplify]: Simplify (+ 0 0) into 0
7.720 * [backup-simplify]: Simplify (- 0) into 0
7.721 * [backup-simplify]: Simplify (+ 0 0) into 0
7.723 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.725 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.730 * [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)))))
7.735 * [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)))))
7.745 * [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)))))
7.746 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
7.746 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
7.746 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
7.746 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
7.746 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
7.746 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
7.746 * [taylor]: Taking taylor expansion of 1/2 in k
7.746 * [backup-simplify]: Simplify 1/2 into 1/2
7.746 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
7.746 * [taylor]: Taking taylor expansion of 1 in k
7.746 * [backup-simplify]: Simplify 1 into 1
7.746 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.747 * [taylor]: Taking taylor expansion of k in k
7.747 * [backup-simplify]: Simplify 0 into 0
7.747 * [backup-simplify]: Simplify 1 into 1
7.747 * [backup-simplify]: Simplify (/ 1 1) into 1
7.747 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
7.747 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
7.747 * [taylor]: Taking taylor expansion of 2 in k
7.747 * [backup-simplify]: Simplify 2 into 2
7.747 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.747 * [taylor]: Taking taylor expansion of PI in k
7.747 * [backup-simplify]: Simplify PI into PI
7.747 * [taylor]: Taking taylor expansion of n in k
7.747 * [backup-simplify]: Simplify n into n
7.747 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.747 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
7.747 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
7.748 * [backup-simplify]: Simplify (- 1) into -1
7.748 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.749 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
7.749 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
7.749 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
7.749 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
7.749 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.749 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.749 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
7.749 * [taylor]: Taking taylor expansion of 1/2 in n
7.749 * [backup-simplify]: Simplify 1/2 into 1/2
7.749 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
7.749 * [taylor]: Taking taylor expansion of 1 in n
7.749 * [backup-simplify]: Simplify 1 into 1
7.749 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.749 * [taylor]: Taking taylor expansion of k in n
7.749 * [backup-simplify]: Simplify k into k
7.750 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.750 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.750 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.750 * [taylor]: Taking taylor expansion of 2 in n
7.750 * [backup-simplify]: Simplify 2 into 2
7.750 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.750 * [taylor]: Taking taylor expansion of PI in n
7.750 * [backup-simplify]: Simplify PI into PI
7.750 * [taylor]: Taking taylor expansion of n in n
7.750 * [backup-simplify]: Simplify 0 into 0
7.750 * [backup-simplify]: Simplify 1 into 1
7.750 * [backup-simplify]: Simplify (/ PI 1) into PI
7.751 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.752 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.752 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.752 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
7.752 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
7.754 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.755 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
7.756 * [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)))))
7.756 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
7.756 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.756 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.756 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
7.756 * [taylor]: Taking taylor expansion of 1/2 in n
7.756 * [backup-simplify]: Simplify 1/2 into 1/2
7.756 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
7.756 * [taylor]: Taking taylor expansion of 1 in n
7.756 * [backup-simplify]: Simplify 1 into 1
7.756 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.757 * [taylor]: Taking taylor expansion of k in n
7.757 * [backup-simplify]: Simplify k into k
7.757 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.757 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.757 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.757 * [taylor]: Taking taylor expansion of 2 in n
7.757 * [backup-simplify]: Simplify 2 into 2
7.757 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.757 * [taylor]: Taking taylor expansion of PI in n
7.757 * [backup-simplify]: Simplify PI into PI
7.757 * [taylor]: Taking taylor expansion of n in n
7.757 * [backup-simplify]: Simplify 0 into 0
7.757 * [backup-simplify]: Simplify 1 into 1
7.757 * [backup-simplify]: Simplify (/ PI 1) into PI
7.758 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.759 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.759 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.759 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
7.759 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
7.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.762 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
7.763 * [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)))))
7.763 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
7.763 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
7.763 * [taylor]: Taking taylor expansion of 1/2 in k
7.764 * [backup-simplify]: Simplify 1/2 into 1/2
7.764 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
7.764 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
7.764 * [taylor]: Taking taylor expansion of 1 in k
7.764 * [backup-simplify]: Simplify 1 into 1
7.764 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.764 * [taylor]: Taking taylor expansion of k in k
7.764 * [backup-simplify]: Simplify 0 into 0
7.764 * [backup-simplify]: Simplify 1 into 1
7.764 * [backup-simplify]: Simplify (/ 1 1) into 1
7.764 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
7.764 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.764 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.764 * [taylor]: Taking taylor expansion of 2 in k
7.764 * [backup-simplify]: Simplify 2 into 2
7.764 * [taylor]: Taking taylor expansion of PI in k
7.764 * [backup-simplify]: Simplify PI into PI
7.765 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.766 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.766 * [taylor]: Taking taylor expansion of (log n) in k
7.766 * [taylor]: Taking taylor expansion of n in k
7.766 * [backup-simplify]: Simplify n into n
7.766 * [backup-simplify]: Simplify (log n) into (log n)
7.766 * [backup-simplify]: Simplify (- 1) into -1
7.767 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.767 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.768 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
7.769 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
7.770 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
7.772 * [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)))))
7.773 * [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)))))
7.774 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.775 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.777 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.777 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.778 * [backup-simplify]: Simplify (- 0) into 0
7.778 * [backup-simplify]: Simplify (+ 0 0) into 0
7.779 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
7.780 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.781 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
7.783 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.783 * [taylor]: Taking taylor expansion of 0 in k
7.783 * [backup-simplify]: Simplify 0 into 0
7.784 * [backup-simplify]: Simplify 0 into 0
7.784 * [backup-simplify]: Simplify 0 into 0
7.785 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.786 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.789 * [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
7.789 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.790 * [backup-simplify]: Simplify (- 0) into 0
7.790 * [backup-simplify]: Simplify (+ 0 0) into 0
7.791 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
7.793 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.795 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
7.797 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.797 * [taylor]: Taking taylor expansion of 0 in k
7.797 * [backup-simplify]: Simplify 0 into 0
7.797 * [backup-simplify]: Simplify 0 into 0
7.797 * [backup-simplify]: Simplify 0 into 0
7.797 * [backup-simplify]: Simplify 0 into 0
7.799 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.800 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.804 * [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
7.804 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.804 * [backup-simplify]: Simplify (- 0) into 0
7.805 * [backup-simplify]: Simplify (+ 0 0) into 0
7.806 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
7.807 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.808 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
7.809 * [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
7.809 * [taylor]: Taking taylor expansion of 0 in k
7.809 * [backup-simplify]: Simplify 0 into 0
7.809 * [backup-simplify]: Simplify 0 into 0
7.810 * [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))))))
7.811 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
7.811 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
7.811 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
7.811 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
7.811 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
7.811 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
7.811 * [taylor]: Taking taylor expansion of 1/2 in k
7.811 * [backup-simplify]: Simplify 1/2 into 1/2
7.811 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
7.811 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.811 * [taylor]: Taking taylor expansion of k in k
7.811 * [backup-simplify]: Simplify 0 into 0
7.811 * [backup-simplify]: Simplify 1 into 1
7.811 * [backup-simplify]: Simplify (/ 1 1) into 1
7.811 * [taylor]: Taking taylor expansion of 1 in k
7.811 * [backup-simplify]: Simplify 1 into 1
7.811 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
7.811 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
7.811 * [taylor]: Taking taylor expansion of -2 in k
7.811 * [backup-simplify]: Simplify -2 into -2
7.811 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.811 * [taylor]: Taking taylor expansion of PI in k
7.811 * [backup-simplify]: Simplify PI into PI
7.811 * [taylor]: Taking taylor expansion of n in k
7.811 * [backup-simplify]: Simplify n into n
7.811 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.811 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
7.811 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
7.812 * [backup-simplify]: Simplify (+ 1 0) into 1
7.812 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.812 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
7.812 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
7.812 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
7.812 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
7.812 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
7.812 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
7.812 * [taylor]: Taking taylor expansion of 1/2 in n
7.812 * [backup-simplify]: Simplify 1/2 into 1/2
7.812 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
7.812 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.812 * [taylor]: Taking taylor expansion of k in n
7.812 * [backup-simplify]: Simplify k into k
7.812 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.812 * [taylor]: Taking taylor expansion of 1 in n
7.812 * [backup-simplify]: Simplify 1 into 1
7.812 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.812 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.812 * [taylor]: Taking taylor expansion of -2 in n
7.812 * [backup-simplify]: Simplify -2 into -2
7.812 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.813 * [taylor]: Taking taylor expansion of PI in n
7.813 * [backup-simplify]: Simplify PI into PI
7.813 * [taylor]: Taking taylor expansion of n in n
7.813 * [backup-simplify]: Simplify 0 into 0
7.813 * [backup-simplify]: Simplify 1 into 1
7.813 * [backup-simplify]: Simplify (/ PI 1) into PI
7.813 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.814 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.814 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
7.814 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
7.815 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.816 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
7.817 * [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)))))
7.817 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
7.817 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
7.817 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
7.817 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
7.817 * [taylor]: Taking taylor expansion of 1/2 in n
7.817 * [backup-simplify]: Simplify 1/2 into 1/2
7.817 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
7.817 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.817 * [taylor]: Taking taylor expansion of k in n
7.817 * [backup-simplify]: Simplify k into k
7.817 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.817 * [taylor]: Taking taylor expansion of 1 in n
7.817 * [backup-simplify]: Simplify 1 into 1
7.817 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.817 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.817 * [taylor]: Taking taylor expansion of -2 in n
7.817 * [backup-simplify]: Simplify -2 into -2
7.817 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.817 * [taylor]: Taking taylor expansion of PI in n
7.817 * [backup-simplify]: Simplify PI into PI
7.817 * [taylor]: Taking taylor expansion of n in n
7.817 * [backup-simplify]: Simplify 0 into 0
7.817 * [backup-simplify]: Simplify 1 into 1
7.817 * [backup-simplify]: Simplify (/ PI 1) into PI
7.818 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.818 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.818 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
7.818 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
7.819 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.820 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
7.821 * [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)))))
7.821 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
7.821 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
7.821 * [taylor]: Taking taylor expansion of 1/2 in k
7.821 * [backup-simplify]: Simplify 1/2 into 1/2
7.821 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
7.821 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
7.821 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.821 * [taylor]: Taking taylor expansion of k in k
7.821 * [backup-simplify]: Simplify 0 into 0
7.821 * [backup-simplify]: Simplify 1 into 1
7.821 * [backup-simplify]: Simplify (/ 1 1) into 1
7.821 * [taylor]: Taking taylor expansion of 1 in k
7.821 * [backup-simplify]: Simplify 1 into 1
7.821 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
7.821 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
7.821 * [taylor]: Taking taylor expansion of (* -2 PI) in k
7.821 * [taylor]: Taking taylor expansion of -2 in k
7.821 * [backup-simplify]: Simplify -2 into -2
7.821 * [taylor]: Taking taylor expansion of PI in k
7.821 * [backup-simplify]: Simplify PI into PI
7.822 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.822 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.822 * [taylor]: Taking taylor expansion of (log n) in k
7.822 * [taylor]: Taking taylor expansion of n in k
7.822 * [backup-simplify]: Simplify n into n
7.822 * [backup-simplify]: Simplify (log n) into (log n)
7.823 * [backup-simplify]: Simplify (+ 1 0) into 1
7.823 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.823 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
7.824 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
7.825 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
7.826 * [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)))))
7.826 * [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)))))
7.827 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.827 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
7.828 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
7.829 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.829 * [backup-simplify]: Simplify (+ 0 0) into 0
7.829 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
7.834 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.835 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
7.836 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.837 * [taylor]: Taking taylor expansion of 0 in k
7.837 * [backup-simplify]: Simplify 0 into 0
7.837 * [backup-simplify]: Simplify 0 into 0
7.837 * [backup-simplify]: Simplify 0 into 0
7.837 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.838 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
7.840 * [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
7.840 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.840 * [backup-simplify]: Simplify (+ 0 0) into 0
7.841 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
7.842 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.843 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
7.844 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.844 * [taylor]: Taking taylor expansion of 0 in k
7.844 * [backup-simplify]: Simplify 0 into 0
7.844 * [backup-simplify]: Simplify 0 into 0
7.844 * [backup-simplify]: Simplify 0 into 0
7.844 * [backup-simplify]: Simplify 0 into 0
7.845 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.846 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.849 * [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
7.849 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.850 * [backup-simplify]: Simplify (+ 0 0) into 0
7.850 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
7.851 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.853 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
7.855 * [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
7.856 * [taylor]: Taking taylor expansion of 0 in k
7.856 * [backup-simplify]: Simplify 0 into 0
7.856 * [backup-simplify]: Simplify 0 into 0
7.857 * [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))))))
7.857 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
7.857 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
7.857 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
7.857 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.857 * [taylor]: Taking taylor expansion of k in k
7.857 * [backup-simplify]: Simplify 0 into 0
7.857 * [backup-simplify]: Simplify 1 into 1
7.858 * [backup-simplify]: Simplify (/ 1 1) into 1
7.858 * [backup-simplify]: Simplify (sqrt 0) into 0
7.860 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.860 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.860 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.860 * [taylor]: Taking taylor expansion of k in k
7.860 * [backup-simplify]: Simplify 0 into 0
7.860 * [backup-simplify]: Simplify 1 into 1
7.860 * [backup-simplify]: Simplify (/ 1 1) into 1
7.860 * [backup-simplify]: Simplify (sqrt 0) into 0
7.862 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.862 * [backup-simplify]: Simplify 0 into 0
7.862 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.863 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
7.866 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.866 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.867 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.871 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.871 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.871 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
7.871 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
7.871 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
7.871 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.871 * [taylor]: Taking taylor expansion of k in k
7.871 * [backup-simplify]: Simplify 0 into 0
7.871 * [backup-simplify]: Simplify 1 into 1
7.871 * [backup-simplify]: Simplify (sqrt 0) into 0
7.873 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.873 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.873 * [taylor]: Taking taylor expansion of k in k
7.873 * [backup-simplify]: Simplify 0 into 0
7.873 * [backup-simplify]: Simplify 1 into 1
7.873 * [backup-simplify]: Simplify (sqrt 0) into 0
7.875 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.875 * [backup-simplify]: Simplify 0 into 0
7.875 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.878 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.878 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.882 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.882 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.882 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 k) 3)) (+ (* +nan.0 (pow (/ 1 k) 2)) (* +nan.0 (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
7.882 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
7.882 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
7.882 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
7.882 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.882 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.883 * [taylor]: Taking taylor expansion of -1 in k
7.883 * [backup-simplify]: Simplify -1 into -1
7.883 * [taylor]: Taking taylor expansion of k in k
7.883 * [backup-simplify]: Simplify 0 into 0
7.883 * [backup-simplify]: Simplify 1 into 1
7.883 * [backup-simplify]: Simplify (/ -1 1) into -1
7.883 * [backup-simplify]: Simplify (sqrt 0) into 0
7.885 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.885 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
7.885 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
7.885 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.886 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.886 * [taylor]: Taking taylor expansion of -1 in k
7.886 * [backup-simplify]: Simplify -1 into -1
7.886 * [taylor]: Taking taylor expansion of k in k
7.886 * [backup-simplify]: Simplify 0 into 0
7.886 * [backup-simplify]: Simplify 1 into 1
7.886 * [backup-simplify]: Simplify (/ -1 1) into -1
7.887 * [backup-simplify]: Simplify (sqrt 0) into 0
7.888 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.889 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
7.889 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.890 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
7.893 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.895 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
7.895 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
7.896 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.900 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.905 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
7.905 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
7.906 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
7.906 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1)
7.907 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
7.907 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
7.907 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.907 * [taylor]: Taking taylor expansion of 2 in n
7.907 * [backup-simplify]: Simplify 2 into 2
7.907 * [taylor]: Taking taylor expansion of (* n PI) in n
7.907 * [taylor]: Taking taylor expansion of n in n
7.907 * [backup-simplify]: Simplify 0 into 0
7.907 * [backup-simplify]: Simplify 1 into 1
7.907 * [taylor]: Taking taylor expansion of PI in n
7.907 * [backup-simplify]: Simplify PI into PI
7.907 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.907 * [taylor]: Taking taylor expansion of 2 in n
7.907 * [backup-simplify]: Simplify 2 into 2
7.907 * [taylor]: Taking taylor expansion of (* n PI) in n
7.907 * [taylor]: Taking taylor expansion of n in n
7.907 * [backup-simplify]: Simplify 0 into 0
7.907 * [backup-simplify]: Simplify 1 into 1
7.907 * [taylor]: Taking taylor expansion of PI in n
7.907 * [backup-simplify]: Simplify PI into PI
7.908 * [backup-simplify]: Simplify (* 0 PI) into 0
7.908 * [backup-simplify]: Simplify (* 2 0) into 0
7.908 * [backup-simplify]: Simplify 0 into 0
7.910 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.911 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.912 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.913 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.914 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
7.914 * [backup-simplify]: Simplify 0 into 0
7.915 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.917 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.917 * [backup-simplify]: Simplify 0 into 0
7.918 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.920 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
7.920 * [backup-simplify]: Simplify 0 into 0
7.921 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.923 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
7.923 * [backup-simplify]: Simplify 0 into 0
7.925 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.927 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
7.927 * [backup-simplify]: Simplify 0 into 0
7.929 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
7.931 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
7.931 * [backup-simplify]: Simplify 0 into 0
7.932 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
7.933 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
7.933 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
7.933 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.933 * [taylor]: Taking taylor expansion of 2 in n
7.933 * [backup-simplify]: Simplify 2 into 2
7.933 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.933 * [taylor]: Taking taylor expansion of PI in n
7.933 * [backup-simplify]: Simplify PI into PI
7.933 * [taylor]: Taking taylor expansion of n in n
7.933 * [backup-simplify]: Simplify 0 into 0
7.933 * [backup-simplify]: Simplify 1 into 1
7.933 * [backup-simplify]: Simplify (/ PI 1) into PI
7.933 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.933 * [taylor]: Taking taylor expansion of 2 in n
7.933 * [backup-simplify]: Simplify 2 into 2
7.934 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.934 * [taylor]: Taking taylor expansion of PI in n
7.934 * [backup-simplify]: Simplify PI into PI
7.934 * [taylor]: Taking taylor expansion of n in n
7.934 * [backup-simplify]: Simplify 0 into 0
7.934 * [backup-simplify]: Simplify 1 into 1
7.934 * [backup-simplify]: Simplify (/ PI 1) into PI
7.935 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.935 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.936 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.937 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.937 * [backup-simplify]: Simplify 0 into 0
7.938 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.939 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.939 * [backup-simplify]: Simplify 0 into 0
7.941 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.942 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.942 * [backup-simplify]: Simplify 0 into 0
7.943 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.944 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.945 * [backup-simplify]: Simplify 0 into 0
7.946 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.947 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.947 * [backup-simplify]: Simplify 0 into 0
7.949 * [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
7.950 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.950 * [backup-simplify]: Simplify 0 into 0
7.951 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
7.952 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
7.952 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
7.952 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.952 * [taylor]: Taking taylor expansion of -2 in n
7.952 * [backup-simplify]: Simplify -2 into -2
7.952 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.952 * [taylor]: Taking taylor expansion of PI in n
7.952 * [backup-simplify]: Simplify PI into PI
7.952 * [taylor]: Taking taylor expansion of n in n
7.952 * [backup-simplify]: Simplify 0 into 0
7.952 * [backup-simplify]: Simplify 1 into 1
7.952 * [backup-simplify]: Simplify (/ PI 1) into PI
7.952 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.952 * [taylor]: Taking taylor expansion of -2 in n
7.952 * [backup-simplify]: Simplify -2 into -2
7.952 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.952 * [taylor]: Taking taylor expansion of PI in n
7.953 * [backup-simplify]: Simplify PI into PI
7.953 * [taylor]: Taking taylor expansion of n in n
7.953 * [backup-simplify]: Simplify 0 into 0
7.953 * [backup-simplify]: Simplify 1 into 1
7.953 * [backup-simplify]: Simplify (/ PI 1) into PI
7.954 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.954 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.955 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.956 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
7.956 * [backup-simplify]: Simplify 0 into 0
7.957 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.958 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
7.958 * [backup-simplify]: Simplify 0 into 0
7.960 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.961 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.961 * [backup-simplify]: Simplify 0 into 0
7.962 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.963 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.963 * [backup-simplify]: Simplify 0 into 0
7.965 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.966 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.966 * [backup-simplify]: Simplify 0 into 0
7.967 * [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
7.969 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.969 * [backup-simplify]: Simplify 0 into 0
7.970 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
7.970 * * * * [progress]: [ 4 / 4 ] generating series at (2)
7.977 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
7.977 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
7.977 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
7.977 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
7.977 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
7.977 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
7.977 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
7.977 * [taylor]: Taking taylor expansion of 1/2 in n
7.977 * [backup-simplify]: Simplify 1/2 into 1/2
7.977 * [taylor]: Taking taylor expansion of (- 1 k) in n
7.977 * [taylor]: Taking taylor expansion of 1 in n
7.977 * [backup-simplify]: Simplify 1 into 1
7.977 * [taylor]: Taking taylor expansion of k in n
7.977 * [backup-simplify]: Simplify k into k
7.977 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.977 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.978 * [taylor]: Taking taylor expansion of 2 in n
7.978 * [backup-simplify]: Simplify 2 into 2
7.978 * [taylor]: Taking taylor expansion of (* n PI) in n
7.978 * [taylor]: Taking taylor expansion of n in n
7.978 * [backup-simplify]: Simplify 0 into 0
7.978 * [backup-simplify]: Simplify 1 into 1
7.978 * [taylor]: Taking taylor expansion of PI in n
7.978 * [backup-simplify]: Simplify PI into PI
7.979 * [backup-simplify]: Simplify (* 0 PI) into 0
7.979 * [backup-simplify]: Simplify (* 2 0) into 0
7.980 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.982 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.983 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.983 * [backup-simplify]: Simplify (- k) into (- k)
7.983 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
7.983 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
7.985 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.986 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
7.987 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
7.987 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
7.987 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.987 * [taylor]: Taking taylor expansion of k in n
7.987 * [backup-simplify]: Simplify k into k
7.987 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.988 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
7.988 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.988 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
7.988 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
7.988 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
7.988 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
7.988 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
7.988 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
7.988 * [taylor]: Taking taylor expansion of 1/2 in k
7.988 * [backup-simplify]: Simplify 1/2 into 1/2
7.988 * [taylor]: Taking taylor expansion of (- 1 k) in k
7.988 * [taylor]: Taking taylor expansion of 1 in k
7.988 * [backup-simplify]: Simplify 1 into 1
7.988 * [taylor]: Taking taylor expansion of k in k
7.988 * [backup-simplify]: Simplify 0 into 0
7.988 * [backup-simplify]: Simplify 1 into 1
7.988 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
7.988 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
7.988 * [taylor]: Taking taylor expansion of 2 in k
7.988 * [backup-simplify]: Simplify 2 into 2
7.988 * [taylor]: Taking taylor expansion of (* n PI) in k
7.988 * [taylor]: Taking taylor expansion of n in k
7.988 * [backup-simplify]: Simplify n into n
7.988 * [taylor]: Taking taylor expansion of PI in k
7.988 * [backup-simplify]: Simplify PI into PI
7.988 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.989 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
7.989 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
7.989 * [backup-simplify]: Simplify (- 0) into 0
7.990 * [backup-simplify]: Simplify (+ 1 0) into 1
7.990 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.990 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
7.990 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
7.990 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.990 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.990 * [taylor]: Taking taylor expansion of k in k
7.990 * [backup-simplify]: Simplify 0 into 0
7.990 * [backup-simplify]: Simplify 1 into 1
7.991 * [backup-simplify]: Simplify (/ 1 1) into 1
7.991 * [backup-simplify]: Simplify (sqrt 0) into 0
7.993 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.993 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
7.993 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
7.993 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
7.993 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
7.993 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
7.993 * [taylor]: Taking taylor expansion of 1/2 in k
7.993 * [backup-simplify]: Simplify 1/2 into 1/2
7.993 * [taylor]: Taking taylor expansion of (- 1 k) in k
7.993 * [taylor]: Taking taylor expansion of 1 in k
7.993 * [backup-simplify]: Simplify 1 into 1
7.993 * [taylor]: Taking taylor expansion of k in k
7.993 * [backup-simplify]: Simplify 0 into 0
7.993 * [backup-simplify]: Simplify 1 into 1
7.993 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
7.993 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
7.993 * [taylor]: Taking taylor expansion of 2 in k
7.993 * [backup-simplify]: Simplify 2 into 2
7.993 * [taylor]: Taking taylor expansion of (* n PI) in k
7.993 * [taylor]: Taking taylor expansion of n in k
7.993 * [backup-simplify]: Simplify n into n
7.993 * [taylor]: Taking taylor expansion of PI in k
7.993 * [backup-simplify]: Simplify PI into PI
7.993 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.993 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
7.993 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
7.993 * [backup-simplify]: Simplify (- 0) into 0
7.994 * [backup-simplify]: Simplify (+ 1 0) into 1
7.994 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.994 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
7.994 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
7.994 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.994 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.994 * [taylor]: Taking taylor expansion of k in k
7.994 * [backup-simplify]: Simplify 0 into 0
7.994 * [backup-simplify]: Simplify 1 into 1
7.994 * [backup-simplify]: Simplify (/ 1 1) into 1
7.995 * [backup-simplify]: Simplify (sqrt 0) into 0
7.996 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.996 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
7.996 * [taylor]: Taking taylor expansion of 0 in n
7.996 * [backup-simplify]: Simplify 0 into 0
7.996 * [backup-simplify]: Simplify 0 into 0
7.996 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
7.996 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
7.997 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
7.997 * [backup-simplify]: Simplify (- 1) into -1
7.997 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.998 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
7.998 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
7.998 * [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)))))
7.999 * [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)))))
7.999 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
7.999 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
7.999 * [taylor]: Taking taylor expansion of +nan.0 in n
7.999 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.999 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
7.999 * [taylor]: Taking taylor expansion of (sqrt 2) in n
7.999 * [taylor]: Taking taylor expansion of 2 in n
7.999 * [backup-simplify]: Simplify 2 into 2
7.999 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
7.999 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.000 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.000 * [taylor]: Taking taylor expansion of (* n PI) in n
8.000 * [taylor]: Taking taylor expansion of n in n
8.000 * [backup-simplify]: Simplify 0 into 0
8.000 * [backup-simplify]: Simplify 1 into 1
8.000 * [taylor]: Taking taylor expansion of PI in n
8.000 * [backup-simplify]: Simplify PI into PI
8.000 * [backup-simplify]: Simplify (* 0 PI) into 0
8.001 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.001 * [backup-simplify]: Simplify (sqrt 0) into 0
8.002 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.002 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
8.003 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.003 * [backup-simplify]: Simplify (- 0) into 0
8.003 * [backup-simplify]: Simplify 0 into 0
8.003 * [backup-simplify]: Simplify 0 into 0
8.004 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
8.006 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
8.006 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
8.007 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
8.008 * [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
8.008 * [backup-simplify]: Simplify (- 0) into 0
8.008 * [backup-simplify]: Simplify (+ 0 0) into 0
8.009 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
8.009 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
8.010 * [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)))
8.010 * [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)))))))
8.010 * [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
8.010 * [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
8.010 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
8.010 * [taylor]: Taking taylor expansion of +nan.0 in n
8.011 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.011 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
8.011 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
8.011 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.011 * [taylor]: Taking taylor expansion of 2 in n
8.011 * [backup-simplify]: Simplify 2 into 2
8.011 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.011 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.011 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
8.011 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.011 * [taylor]: Taking taylor expansion of 2 in n
8.011 * [backup-simplify]: Simplify 2 into 2
8.011 * [taylor]: Taking taylor expansion of (* n PI) in n
8.011 * [taylor]: Taking taylor expansion of n in n
8.011 * [backup-simplify]: Simplify 0 into 0
8.011 * [backup-simplify]: Simplify 1 into 1
8.011 * [taylor]: Taking taylor expansion of PI in n
8.011 * [backup-simplify]: Simplify PI into PI
8.012 * [backup-simplify]: Simplify (* 0 PI) into 0
8.012 * [backup-simplify]: Simplify (* 2 0) into 0
8.013 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.014 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.015 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.015 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.015 * [taylor]: Taking taylor expansion of (* n PI) in n
8.015 * [taylor]: Taking taylor expansion of n in n
8.015 * [backup-simplify]: Simplify 0 into 0
8.015 * [backup-simplify]: Simplify 1 into 1
8.015 * [taylor]: Taking taylor expansion of PI in n
8.015 * [backup-simplify]: Simplify PI into PI
8.015 * [backup-simplify]: Simplify (* 0 PI) into 0
8.016 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.016 * [backup-simplify]: Simplify (sqrt 0) into 0
8.017 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.017 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
8.017 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
8.017 * [taylor]: Taking taylor expansion of +nan.0 in n
8.017 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.017 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
8.017 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.017 * [taylor]: Taking taylor expansion of 2 in n
8.017 * [backup-simplify]: Simplify 2 into 2
8.018 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.018 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.018 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.018 * [taylor]: Taking taylor expansion of (* n PI) in n
8.018 * [taylor]: Taking taylor expansion of n in n
8.018 * [backup-simplify]: Simplify 0 into 0
8.018 * [backup-simplify]: Simplify 1 into 1
8.018 * [taylor]: Taking taylor expansion of PI in n
8.018 * [backup-simplify]: Simplify PI into PI
8.018 * [backup-simplify]: Simplify (* 0 PI) into 0
8.019 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.020 * [backup-simplify]: Simplify (sqrt 0) into 0
8.021 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.022 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.023 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
8.024 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
8.024 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.024 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
8.025 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.025 * [backup-simplify]: Simplify (- 0) into 0
8.025 * [backup-simplify]: Simplify (+ 0 0) into 0
8.025 * [backup-simplify]: Simplify (- 0) into 0
8.025 * [backup-simplify]: Simplify 0 into 0
8.027 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
8.032 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
8.036 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
8.039 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
8.039 * [backup-simplify]: Simplify 0 into 0
8.040 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.044 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
8.046 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.047 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
8.050 * [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
8.050 * [backup-simplify]: Simplify (- 0) into 0
8.051 * [backup-simplify]: Simplify (+ 0 0) into 0
8.052 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
8.054 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
8.056 * [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)))
8.057 * [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)))))))))
8.057 * [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
8.057 * [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
8.057 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
8.057 * [taylor]: Taking taylor expansion of +nan.0 in n
8.057 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.057 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
8.057 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
8.058 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.058 * [taylor]: Taking taylor expansion of 2 in n
8.058 * [backup-simplify]: Simplify 2 into 2
8.058 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.059 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.059 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
8.059 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.059 * [taylor]: Taking taylor expansion of 2 in n
8.059 * [backup-simplify]: Simplify 2 into 2
8.059 * [taylor]: Taking taylor expansion of (* n PI) in n
8.059 * [taylor]: Taking taylor expansion of n in n
8.059 * [backup-simplify]: Simplify 0 into 0
8.059 * [backup-simplify]: Simplify 1 into 1
8.059 * [taylor]: Taking taylor expansion of PI in n
8.059 * [backup-simplify]: Simplify PI into PI
8.060 * [backup-simplify]: Simplify (* 0 PI) into 0
8.060 * [backup-simplify]: Simplify (* 2 0) into 0
8.062 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.063 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.064 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.064 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.064 * [taylor]: Taking taylor expansion of (* n PI) in n
8.064 * [taylor]: Taking taylor expansion of n in n
8.064 * [backup-simplify]: Simplify 0 into 0
8.064 * [backup-simplify]: Simplify 1 into 1
8.064 * [taylor]: Taking taylor expansion of PI in n
8.064 * [backup-simplify]: Simplify PI into PI
8.065 * [backup-simplify]: Simplify (* 0 PI) into 0
8.066 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.066 * [backup-simplify]: Simplify (sqrt 0) into 0
8.067 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.067 * [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
8.067 * [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
8.067 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
8.067 * [taylor]: Taking taylor expansion of +nan.0 in n
8.067 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.067 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
8.067 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.067 * [taylor]: Taking taylor expansion of 2 in n
8.067 * [backup-simplify]: Simplify 2 into 2
8.067 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.068 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.068 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.068 * [taylor]: Taking taylor expansion of (* n PI) in n
8.068 * [taylor]: Taking taylor expansion of n in n
8.068 * [backup-simplify]: Simplify 0 into 0
8.068 * [backup-simplify]: Simplify 1 into 1
8.068 * [taylor]: Taking taylor expansion of PI in n
8.068 * [backup-simplify]: Simplify PI into PI
8.068 * [backup-simplify]: Simplify (* 0 PI) into 0
8.069 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.069 * [backup-simplify]: Simplify (sqrt 0) into 0
8.070 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.070 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
8.070 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
8.070 * [taylor]: Taking taylor expansion of +nan.0 in n
8.070 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.070 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
8.070 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
8.070 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.070 * [taylor]: Taking taylor expansion of 2 in n
8.070 * [backup-simplify]: Simplify 2 into 2
8.071 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.071 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.071 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
8.071 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
8.071 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.071 * [taylor]: Taking taylor expansion of 2 in n
8.071 * [backup-simplify]: Simplify 2 into 2
8.071 * [taylor]: Taking taylor expansion of (* n PI) in n
8.071 * [taylor]: Taking taylor expansion of n in n
8.071 * [backup-simplify]: Simplify 0 into 0
8.071 * [backup-simplify]: Simplify 1 into 1
8.071 * [taylor]: Taking taylor expansion of PI in n
8.071 * [backup-simplify]: Simplify PI into PI
8.072 * [backup-simplify]: Simplify (* 0 PI) into 0
8.072 * [backup-simplify]: Simplify (* 2 0) into 0
8.073 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.074 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.074 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.075 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.075 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.075 * [taylor]: Taking taylor expansion of (* n PI) in n
8.075 * [taylor]: Taking taylor expansion of n in n
8.075 * [backup-simplify]: Simplify 0 into 0
8.075 * [backup-simplify]: Simplify 1 into 1
8.075 * [taylor]: Taking taylor expansion of PI in n
8.075 * [backup-simplify]: Simplify PI into PI
8.076 * [backup-simplify]: Simplify (* 0 PI) into 0
8.077 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.077 * [backup-simplify]: Simplify (sqrt 0) into 0
8.078 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.079 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.080 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
8.081 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
8.081 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.081 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
8.081 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.082 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.083 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.084 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
8.085 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
8.086 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
8.091 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.092 * [backup-simplify]: Simplify (- 0) into 0
8.092 * [backup-simplify]: Simplify (+ 0 0) into 0
8.092 * [backup-simplify]: Simplify (- 0) into 0
8.092 * [backup-simplify]: Simplify (+ 0 0) into 0
8.093 * [backup-simplify]: Simplify (- 0) into 0
8.093 * [backup-simplify]: Simplify 0 into 0
8.093 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.094 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
8.095 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
8.096 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.097 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
8.098 * [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))))))))
8.102 * [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))))))))
8.104 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
8.108 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
8.111 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
8.121 * [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))))))))))
8.129 * [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)))))))
8.137 * [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)))))))
8.138 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.143 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
8.144 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
8.149 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
8.158 * [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))))
8.163 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
8.166 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
8.182 * [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)))))))))))))
8.183 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
8.183 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
8.183 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
8.183 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
8.183 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
8.183 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
8.183 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
8.184 * [taylor]: Taking taylor expansion of 1/2 in n
8.184 * [backup-simplify]: Simplify 1/2 into 1/2
8.184 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.184 * [taylor]: Taking taylor expansion of 1 in n
8.184 * [backup-simplify]: Simplify 1 into 1
8.184 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.184 * [taylor]: Taking taylor expansion of k in n
8.184 * [backup-simplify]: Simplify k into k
8.184 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.184 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.184 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.184 * [taylor]: Taking taylor expansion of 2 in n
8.184 * [backup-simplify]: Simplify 2 into 2
8.184 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.184 * [taylor]: Taking taylor expansion of PI in n
8.184 * [backup-simplify]: Simplify PI into PI
8.184 * [taylor]: Taking taylor expansion of n in n
8.184 * [backup-simplify]: Simplify 0 into 0
8.184 * [backup-simplify]: Simplify 1 into 1
8.185 * [backup-simplify]: Simplify (/ PI 1) into PI
8.185 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.187 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.187 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.187 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.187 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
8.188 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.190 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.191 * [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)))))
8.191 * [taylor]: Taking taylor expansion of (sqrt k) in n
8.191 * [taylor]: Taking taylor expansion of k in n
8.191 * [backup-simplify]: Simplify k into k
8.191 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
8.191 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
8.191 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
8.191 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
8.192 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
8.192 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
8.192 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
8.192 * [taylor]: Taking taylor expansion of 1/2 in k
8.192 * [backup-simplify]: Simplify 1/2 into 1/2
8.192 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
8.192 * [taylor]: Taking taylor expansion of 1 in k
8.192 * [backup-simplify]: Simplify 1 into 1
8.192 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.192 * [taylor]: Taking taylor expansion of k in k
8.192 * [backup-simplify]: Simplify 0 into 0
8.192 * [backup-simplify]: Simplify 1 into 1
8.192 * [backup-simplify]: Simplify (/ 1 1) into 1
8.192 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
8.192 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
8.192 * [taylor]: Taking taylor expansion of 2 in k
8.192 * [backup-simplify]: Simplify 2 into 2
8.192 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.192 * [taylor]: Taking taylor expansion of PI in k
8.192 * [backup-simplify]: Simplify PI into PI
8.192 * [taylor]: Taking taylor expansion of n in k
8.193 * [backup-simplify]: Simplify n into n
8.193 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.193 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
8.193 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
8.193 * [backup-simplify]: Simplify (- 1) into -1
8.194 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.194 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
8.194 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
8.194 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
8.195 * [taylor]: Taking taylor expansion of (sqrt k) in k
8.195 * [taylor]: Taking taylor expansion of k in k
8.195 * [backup-simplify]: Simplify 0 into 0
8.195 * [backup-simplify]: Simplify 1 into 1
8.195 * [backup-simplify]: Simplify (sqrt 0) into 0
8.197 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
8.197 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
8.197 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
8.197 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
8.197 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
8.197 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
8.197 * [taylor]: Taking taylor expansion of 1/2 in k
8.197 * [backup-simplify]: Simplify 1/2 into 1/2
8.197 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
8.197 * [taylor]: Taking taylor expansion of 1 in k
8.197 * [backup-simplify]: Simplify 1 into 1
8.197 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.197 * [taylor]: Taking taylor expansion of k in k
8.197 * [backup-simplify]: Simplify 0 into 0
8.197 * [backup-simplify]: Simplify 1 into 1
8.197 * [backup-simplify]: Simplify (/ 1 1) into 1
8.198 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
8.198 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
8.198 * [taylor]: Taking taylor expansion of 2 in k
8.198 * [backup-simplify]: Simplify 2 into 2
8.198 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.198 * [taylor]: Taking taylor expansion of PI in k
8.198 * [backup-simplify]: Simplify PI into PI
8.198 * [taylor]: Taking taylor expansion of n in k
8.198 * [backup-simplify]: Simplify n into n
8.198 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.198 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
8.198 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
8.198 * [backup-simplify]: Simplify (- 1) into -1
8.199 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.199 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
8.199 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
8.200 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
8.200 * [taylor]: Taking taylor expansion of (sqrt k) in k
8.200 * [taylor]: Taking taylor expansion of k in k
8.200 * [backup-simplify]: Simplify 0 into 0
8.200 * [backup-simplify]: Simplify 1 into 1
8.200 * [backup-simplify]: Simplify (sqrt 0) into 0
8.202 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
8.202 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
8.202 * [taylor]: Taking taylor expansion of 0 in n
8.202 * [backup-simplify]: Simplify 0 into 0
8.202 * [backup-simplify]: Simplify 0 into 0
8.203 * [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))))))))
8.203 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
8.203 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
8.203 * [taylor]: Taking taylor expansion of +nan.0 in n
8.203 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.203 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
8.203 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
8.203 * [taylor]: Taking taylor expansion of 1/2 in n
8.203 * [backup-simplify]: Simplify 1/2 into 1/2
8.203 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
8.203 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.203 * [taylor]: Taking taylor expansion of 1 in n
8.203 * [backup-simplify]: Simplify 1 into 1
8.203 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.203 * [taylor]: Taking taylor expansion of k in n
8.203 * [backup-simplify]: Simplify k into k
8.203 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.203 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.203 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.203 * [taylor]: Taking taylor expansion of 2 in n
8.204 * [backup-simplify]: Simplify 2 into 2
8.204 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.204 * [taylor]: Taking taylor expansion of PI in n
8.204 * [backup-simplify]: Simplify PI into PI
8.204 * [taylor]: Taking taylor expansion of n in n
8.204 * [backup-simplify]: Simplify 0 into 0
8.204 * [backup-simplify]: Simplify 1 into 1
8.204 * [backup-simplify]: Simplify (/ PI 1) into PI
8.205 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.206 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.206 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.206 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.208 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.209 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
8.211 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.212 * [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)))))
8.213 * [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))))))
8.215 * [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)))))))
8.216 * [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)))))))
8.216 * [backup-simplify]: Simplify 0 into 0
8.219 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
8.220 * [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))))))))
8.220 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
8.221 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
8.221 * [taylor]: Taking taylor expansion of +nan.0 in n
8.221 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.221 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
8.221 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
8.221 * [taylor]: Taking taylor expansion of 1/2 in n
8.221 * [backup-simplify]: Simplify 1/2 into 1/2
8.221 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
8.221 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.221 * [taylor]: Taking taylor expansion of 1 in n
8.221 * [backup-simplify]: Simplify 1 into 1
8.221 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.221 * [taylor]: Taking taylor expansion of k in n
8.221 * [backup-simplify]: Simplify k into k
8.221 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.221 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.221 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.221 * [taylor]: Taking taylor expansion of 2 in n
8.221 * [backup-simplify]: Simplify 2 into 2
8.221 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.221 * [taylor]: Taking taylor expansion of PI in n
8.221 * [backup-simplify]: Simplify PI into PI
8.221 * [taylor]: Taking taylor expansion of n in n
8.221 * [backup-simplify]: Simplify 0 into 0
8.221 * [backup-simplify]: Simplify 1 into 1
8.222 * [backup-simplify]: Simplify (/ PI 1) into PI
8.222 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.223 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.224 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.224 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.232 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.233 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
8.234 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.235 * [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)))))
8.237 * [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))))))
8.238 * [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)))))))
8.239 * [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)))))))
8.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.241 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
8.245 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
8.245 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.246 * [backup-simplify]: Simplify (- 0) into 0
8.246 * [backup-simplify]: Simplify (+ 0 0) into 0
8.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.249 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
8.251 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
8.253 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.256 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
8.256 * [backup-simplify]: Simplify (- 0) into 0
8.256 * [backup-simplify]: Simplify 0 into 0
8.256 * [backup-simplify]: Simplify 0 into 0
8.261 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
8.262 * [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))))))))
8.262 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
8.262 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
8.262 * [taylor]: Taking taylor expansion of +nan.0 in n
8.262 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.262 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
8.262 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
8.262 * [taylor]: Taking taylor expansion of 1/2 in n
8.262 * [backup-simplify]: Simplify 1/2 into 1/2
8.262 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
8.262 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.262 * [taylor]: Taking taylor expansion of 1 in n
8.263 * [backup-simplify]: Simplify 1 into 1
8.263 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.263 * [taylor]: Taking taylor expansion of k in n
8.263 * [backup-simplify]: Simplify k into k
8.263 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.263 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.263 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.263 * [taylor]: Taking taylor expansion of 2 in n
8.263 * [backup-simplify]: Simplify 2 into 2
8.263 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.263 * [taylor]: Taking taylor expansion of PI in n
8.263 * [backup-simplify]: Simplify PI into PI
8.263 * [taylor]: Taking taylor expansion of n in n
8.263 * [backup-simplify]: Simplify 0 into 0
8.263 * [backup-simplify]: Simplify 1 into 1
8.264 * [backup-simplify]: Simplify (/ PI 1) into PI
8.264 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.265 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.266 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.266 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.267 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.269 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
8.270 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.271 * [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)))))
8.273 * [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))))))
8.274 * [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)))))))
8.276 * [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)))))))
8.280 * [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))))))))
8.281 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
8.281 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
8.281 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
8.282 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
8.282 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
8.282 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
8.282 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
8.282 * [taylor]: Taking taylor expansion of 1/2 in n
8.282 * [backup-simplify]: Simplify 1/2 into 1/2
8.282 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
8.282 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.282 * [taylor]: Taking taylor expansion of k in n
8.282 * [backup-simplify]: Simplify k into k
8.282 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.282 * [taylor]: Taking taylor expansion of 1 in n
8.282 * [backup-simplify]: Simplify 1 into 1
8.282 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.282 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.282 * [taylor]: Taking taylor expansion of -2 in n
8.282 * [backup-simplify]: Simplify -2 into -2
8.282 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.282 * [taylor]: Taking taylor expansion of PI in n
8.282 * [backup-simplify]: Simplify PI into PI
8.282 * [taylor]: Taking taylor expansion of n in n
8.282 * [backup-simplify]: Simplify 0 into 0
8.282 * [backup-simplify]: Simplify 1 into 1
8.283 * [backup-simplify]: Simplify (/ PI 1) into PI
8.283 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.284 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.285 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
8.285 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
8.286 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.288 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
8.289 * [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)))))
8.289 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
8.289 * [taylor]: Taking taylor expansion of (/ -1 k) in n
8.289 * [taylor]: Taking taylor expansion of -1 in n
8.289 * [backup-simplify]: Simplify -1 into -1
8.289 * [taylor]: Taking taylor expansion of k in n
8.289 * [backup-simplify]: Simplify k into k
8.289 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
8.289 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
8.289 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
8.290 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
8.291 * [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)))
8.291 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
8.291 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
8.291 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
8.291 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
8.291 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
8.291 * [taylor]: Taking taylor expansion of 1/2 in k
8.291 * [backup-simplify]: Simplify 1/2 into 1/2
8.291 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
8.291 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.291 * [taylor]: Taking taylor expansion of k in k
8.291 * [backup-simplify]: Simplify 0 into 0
8.291 * [backup-simplify]: Simplify 1 into 1
8.292 * [backup-simplify]: Simplify (/ 1 1) into 1
8.292 * [taylor]: Taking taylor expansion of 1 in k
8.292 * [backup-simplify]: Simplify 1 into 1
8.292 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
8.292 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
8.292 * [taylor]: Taking taylor expansion of -2 in k
8.292 * [backup-simplify]: Simplify -2 into -2
8.292 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.292 * [taylor]: Taking taylor expansion of PI in k
8.292 * [backup-simplify]: Simplify PI into PI
8.292 * [taylor]: Taking taylor expansion of n in k
8.292 * [backup-simplify]: Simplify n into n
8.292 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.292 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
8.292 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
8.293 * [backup-simplify]: Simplify (+ 1 0) into 1
8.293 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.293 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
8.294 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
8.294 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
8.294 * [taylor]: Taking taylor expansion of (/ -1 k) in k
8.294 * [taylor]: Taking taylor expansion of -1 in k
8.294 * [backup-simplify]: Simplify -1 into -1
8.294 * [taylor]: Taking taylor expansion of k in k
8.294 * [backup-simplify]: Simplify 0 into 0
8.294 * [backup-simplify]: Simplify 1 into 1
8.294 * [backup-simplify]: Simplify (/ -1 1) into -1
8.295 * [backup-simplify]: Simplify (sqrt 0) into 0
8.296 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
8.297 * [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)))))
8.297 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
8.297 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
8.297 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
8.297 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
8.297 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
8.297 * [taylor]: Taking taylor expansion of 1/2 in k
8.297 * [backup-simplify]: Simplify 1/2 into 1/2
8.297 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
8.297 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.297 * [taylor]: Taking taylor expansion of k in k
8.297 * [backup-simplify]: Simplify 0 into 0
8.297 * [backup-simplify]: Simplify 1 into 1
8.297 * [backup-simplify]: Simplify (/ 1 1) into 1
8.297 * [taylor]: Taking taylor expansion of 1 in k
8.297 * [backup-simplify]: Simplify 1 into 1
8.297 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
8.297 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
8.297 * [taylor]: Taking taylor expansion of -2 in k
8.298 * [backup-simplify]: Simplify -2 into -2
8.298 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.298 * [taylor]: Taking taylor expansion of PI in k
8.298 * [backup-simplify]: Simplify PI into PI
8.298 * [taylor]: Taking taylor expansion of n in k
8.298 * [backup-simplify]: Simplify n into n
8.298 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.298 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
8.298 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
8.298 * [backup-simplify]: Simplify (+ 1 0) into 1
8.299 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.299 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
8.299 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
8.299 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
8.299 * [taylor]: Taking taylor expansion of (/ -1 k) in k
8.299 * [taylor]: Taking taylor expansion of -1 in k
8.299 * [backup-simplify]: Simplify -1 into -1
8.299 * [taylor]: Taking taylor expansion of k in k
8.299 * [backup-simplify]: Simplify 0 into 0
8.299 * [backup-simplify]: Simplify 1 into 1
8.300 * [backup-simplify]: Simplify (/ -1 1) into -1
8.300 * [backup-simplify]: Simplify (sqrt 0) into 0
8.302 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
8.302 * [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)))))
8.302 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
8.302 * [taylor]: Taking taylor expansion of +nan.0 in n
8.302 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.302 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
8.302 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
8.302 * [taylor]: Taking taylor expansion of 1/2 in n
8.302 * [backup-simplify]: Simplify 1/2 into 1/2
8.302 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
8.302 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.302 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.303 * [taylor]: Taking taylor expansion of -2 in n
8.303 * [backup-simplify]: Simplify -2 into -2
8.303 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.303 * [taylor]: Taking taylor expansion of PI in n
8.303 * [backup-simplify]: Simplify PI into PI
8.303 * [taylor]: Taking taylor expansion of n in n
8.303 * [backup-simplify]: Simplify 0 into 0
8.303 * [backup-simplify]: Simplify 1 into 1
8.303 * [backup-simplify]: Simplify (/ PI 1) into PI
8.304 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.305 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.305 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
8.305 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.305 * [taylor]: Taking taylor expansion of k in n
8.305 * [backup-simplify]: Simplify k into k
8.305 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.305 * [taylor]: Taking taylor expansion of 1 in n
8.305 * [backup-simplify]: Simplify 1 into 1
8.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.307 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
8.308 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
8.310 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
8.311 * [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)))))
8.312 * [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))))))
8.314 * [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))))))
8.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
8.318 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
8.319 * [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))))))
8.319 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
8.320 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
8.320 * [taylor]: Taking taylor expansion of +nan.0 in n
8.320 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.320 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
8.320 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
8.320 * [taylor]: Taking taylor expansion of 1/2 in n
8.320 * [backup-simplify]: Simplify 1/2 into 1/2
8.320 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
8.320 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.320 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.320 * [taylor]: Taking taylor expansion of -2 in n
8.320 * [backup-simplify]: Simplify -2 into -2
8.320 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.320 * [taylor]: Taking taylor expansion of PI in n
8.320 * [backup-simplify]: Simplify PI into PI
8.320 * [taylor]: Taking taylor expansion of n in n
8.320 * [backup-simplify]: Simplify 0 into 0
8.320 * [backup-simplify]: Simplify 1 into 1
8.321 * [backup-simplify]: Simplify (/ PI 1) into PI
8.321 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.322 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.322 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
8.322 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.322 * [taylor]: Taking taylor expansion of k in n
8.322 * [backup-simplify]: Simplify k into k
8.322 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.322 * [taylor]: Taking taylor expansion of 1 in n
8.322 * [backup-simplify]: Simplify 1 into 1
8.324 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.324 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
8.325 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
8.326 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
8.328 * [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)))))
8.329 * [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))))))
8.330 * [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)))))))
8.332 * [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)))))))
8.333 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.333 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.333 * [backup-simplify]: Simplify (+ 0 0) into 0
8.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.335 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
8.336 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
8.337 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
8.338 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
8.339 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.340 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
8.340 * [backup-simplify]: Simplify 0 into 0
8.341 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.343 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
8.345 * [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))))))
8.345 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
8.345 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
8.345 * [taylor]: Taking taylor expansion of +nan.0 in n
8.345 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.345 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
8.345 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
8.345 * [taylor]: Taking taylor expansion of 1/2 in n
8.345 * [backup-simplify]: Simplify 1/2 into 1/2
8.345 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
8.345 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.345 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.345 * [taylor]: Taking taylor expansion of -2 in n
8.345 * [backup-simplify]: Simplify -2 into -2
8.345 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.345 * [taylor]: Taking taylor expansion of PI in n
8.345 * [backup-simplify]: Simplify PI into PI
8.345 * [taylor]: Taking taylor expansion of n in n
8.345 * [backup-simplify]: Simplify 0 into 0
8.345 * [backup-simplify]: Simplify 1 into 1
8.346 * [backup-simplify]: Simplify (/ PI 1) into PI
8.346 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.347 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.347 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
8.347 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.347 * [taylor]: Taking taylor expansion of k in n
8.347 * [backup-simplify]: Simplify k into k
8.347 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.347 * [taylor]: Taking taylor expansion of 1 in n
8.347 * [backup-simplify]: Simplify 1 into 1
8.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.348 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
8.349 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
8.349 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
8.350 * [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)))))
8.351 * [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))))))
8.352 * [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)))))))
8.353 * [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)))))))
8.355 * [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))))))))))))
8.355 * * * [progress]: simplifying candidates
8.355 * * * * [progress]: [ 1 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
8.355 * * * * [progress]: [ 2 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
8.356 * * * * [progress]: [ 3 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
8.356 * * * * [progress]: [ 4 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
8.356 * * * * [progress]: [ 5 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
8.356 * * * * [progress]: [ 6 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
8.356 * * * * [progress]: [ 7 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
8.356 * * * * [progress]: [ 8 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
8.356 * * * * [progress]: [ 9 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
8.356 * * * * [progress]: [ 10 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
8.356 * * * * [progress]: [ 11 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2)))))>
8.356 * * * * [progress]: [ 12 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2)))))>
8.356 * * * * [progress]: [ 13 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2))))>
8.356 * * * * [progress]: [ 14 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2)))))>
8.356 * * * * [progress]: [ 15 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2)))))>
8.356 * * * * [progress]: [ 16 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2))))>
8.356 * * * * [progress]: [ 17 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
8.356 * * * * [progress]: [ 18 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
8.356 * * * * [progress]: [ 19 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
8.356 * * * * [progress]: [ 20 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2)))))>
8.356 * * * * [progress]: [ 21 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2)))))>
8.356 * * * * [progress]: [ 22 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2))))>
8.356 * * * * [progress]: [ 23 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2)))))>
8.357 * * * * [progress]: [ 24 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2)))))>
8.357 * * * * [progress]: [ 25 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))>
8.357 * * * * [progress]: [ 26 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
8.357 * * * * [progress]: [ 27 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
8.357 * * * * [progress]: [ 28 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
8.357 * * * * [progress]: [ 29 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
8.357 * * * * [progress]: [ 30 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
8.357 * * * * [progress]: [ 31 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
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8.357 * * * * [progress]: [ 33 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
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8.357 * * * * [progress]: [ 35 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.357 * * * * [progress]: [ 36 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.357 * * * * [progress]: [ 37 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.357 * * * * [progress]: [ 38 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.357 * * * * [progress]: [ 39 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
8.357 * * * * [progress]: [ 40 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (posit16->real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.357 * * * * [progress]: [ 41 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.357 * * * * [progress]: [ 46 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.358 * * * * [progress]: [ 49 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.358 * * * * [progress]: [ 51 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.358 * * * * [progress]: [ 53 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.358 * * * * [progress]: [ 54 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.358 * * * * [progress]: [ 55 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.358 * * * * [progress]: [ 56 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.358 * * * * [progress]: [ 57 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.358 * * * * [progress]: [ 58 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.358 * * * * [progress]: [ 61 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.358 * * * * [progress]: [ 63 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.358 * * * * [progress]: [ 64 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.358 * * * * [progress]: [ 67 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.358 * * * * [progress]: [ 68 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.358 * * * * [progress]: [ 69 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.359 * * * * [progress]: [ 78 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.359 * * * * [progress]: [ 86 / 188 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.359 * * * * [progress]: [ 90 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (+ (log 2) (log PI)) (log n))) (/ (- 1 k) 2))))>
8.359 * * * * [progress]: [ 91 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (log (* 2 PI)) (log n))) (/ (- 1 k) 2))))>
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8.359 * * * * [progress]: [ 93 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
8.359 * * * * [progress]: [ 94 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
8.360 * * * * [progress]: [ 95 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
8.360 * * * * [progress]: [ 96 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
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8.360 * * * * [progress]: [ 98 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
8.360 * * * * [progress]: [ 99 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
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8.360 * * * * [progress]: [ 103 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
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8.361 * * * * [progress]: [ 129 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
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8.361 * * * * [progress]: [ 131 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
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8.361 * * * * [progress]: [ 133 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.361 * * * * [progress]: [ 134 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
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8.362 * * * * [progress]: [ 145 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
8.362 * * * * [progress]: [ 146 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
8.362 * * * * [progress]: [ 147 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 148 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 149 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.362 * * * * [progress]: [ 150 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))>
8.362 * * * * [progress]: [ 151 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 152 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 153 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 154 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 155 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 156 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 157 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 158 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 159 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 160 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.362 * * * * [progress]: [ 161 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 162 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt 1)) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 163 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 164 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 165 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 166 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 167 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 168 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 169 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 170 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 171 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 172 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.363 * * * * [progress]: [ 173 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
8.363 * * * * [progress]: [ 174 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
8.363 * * * * [progress]: [ 175 / 188 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.363 * * * * [progress]: [ 176 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
8.363 * * * * [progress]: [ 177 / 188 ] 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)))))))>
8.363 * * * * [progress]: [ 178 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
8.363 * * * * [progress]: [ 179 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
8.363 * * * * [progress]: [ 180 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.363 * * * * [progress]: [ 181 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.363 * * * * [progress]: [ 182 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.363 * * * * [progress]: [ 183 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
8.364 * * * * [progress]: [ 184 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
8.364 * * * * [progress]: [ 185 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
8.364 * * * * [progress]: [ 186 / 188 ] 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))))))))))))))>
8.364 * * * * [progress]: [ 187 / 188 ] 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)))))))))>
8.364 * * * * [progress]: [ 188 / 188 ] 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)))))))))))))>
8.366 * [simplify]: Simplifying:
  (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))
  (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* (* 2 PI) n) (/ 1 2))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) 1)
  (pow (* (* 2 PI) n) (- 1 k))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (- 1/2)
  (- 1)
  (- (/ 1 2))
  (- (log (sqrt k)))
  (- 0 (log (sqrt k)))
  (- (log 1) (log (sqrt k)))
  (log (/ 1 (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (/ (sqrt k) 1)
  (real->posit16 (/ 1 (sqrt k)))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (+ (+ (log 2) (log PI)) (log n))
  (+ (log (* 2 PI)) (log n))
  (log (* (* 2 PI) n))
  (exp (* (* 2 PI) n))
  (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* 2 PI) (* (cbrt n) (cbrt n)))
  (* (* 2 PI) (sqrt n))
  (* (* 2 PI) 1)
  (* PI n)
  (real->posit16 (* (* 2 PI) n))
  (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* 1 (pow (* (* 2 PI) n) (/ 1 2)))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt k)) 1)
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))
  (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 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))))))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +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))))))))))))
8.369 * * [simplify]: iteration 0: 345 enodes
8.510 * * [simplify]: iteration 1: 931 enodes
9.021 * * [simplify]: iteration 2: 2858 enodes
9.917 * * [simplify]: iteration complete: 5001 enodes
9.917 * * [simplify]: Extracting #0: cost 91 inf + 0
9.918 * * [simplify]: Extracting #1: cost 535 inf + 3
9.921 * * [simplify]: Extracting #2: cost 1080 inf + 1670
9.930 * * [simplify]: Extracting #3: cost 1353 inf + 44765
9.969 * * [simplify]: Extracting #4: cost 777 inf + 222222
10.053 * * [simplify]: Extracting #5: cost 211 inf + 406683
10.166 * * [simplify]: Extracting #6: cost 18 inf + 491631
10.274 * * [simplify]: Extracting #7: cost 1 inf + 499114
10.370 * * [simplify]: Extracting #8: cost 0 inf + 499609
10.513 * * [simplify]: Extracting #9: cost 0 inf + 499209
10.673 * [simplify]: Simplified to:
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* (* n 2) PI))
  (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 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* n 2) PI) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (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)))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (* (* n 2) PI)
  (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)))
  (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)))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (pow (* (* n 2) PI) (- 1 k))
  (pow (* PI 2) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (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 (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
  (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
  (pow (* (* n 2) PI) (/ (- 1 k) 4))
  (pow (* (* n 2) PI) (/ (- 1 k) 4))
  (real->posit16 (pow (* (* n 2) PI) (/ (- 1 k) 2)))
  -1/2
  -1
  -1/2
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (/ 1 k) (sqrt k))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (/ (/ 1 k) (sqrt k))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  -1
  (- (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (sqrt k)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt (sqrt k)))
  1
  (sqrt k)
  (sqrt k)
  (sqrt k)
  (real->posit16 (/ 1 (sqrt k)))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (exp (+ (* PI n) (* PI n)))
  (* n (* 8 (* (* PI (* PI PI)) (* n n))))
  (* (* (* n 2) PI) (* (* (* n 2) PI) (* (* n 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))
  (* PI (* 2 (* (cbrt n) (cbrt n))))
  (* 2 (* PI (sqrt n)))
  (* PI 2)
  (* PI n)
  (real->posit16 (* (* n 2) PI))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (exp (/ (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)))
  (* (* (/ (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)))
  (* (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)))
  (sqrt (* (* n 2) PI))
  (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
  (* (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (* (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt k))
  (* (cbrt (/ 1 (sqrt k))) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
  (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (cbrt 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)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (cbrt 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)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (cbrt 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)) (sqrt (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 (* (* n 2) PI)) (sqrt k))
  (pow (* (* n 2) PI) (/ (- 1 k) 2))
  (real->posit16 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))
  (- (+ (+ (sqrt (* (* n 2) PI)) (* (* (* 1/8 (sqrt (* (* n 2) PI))) (* (log n) (log n))) (* k k))) (+ (* 1/8 (* (* (log (* PI 2)) (log (* PI 2))) (* (sqrt (* (* n 2) PI)) (* k k)))) (* (* 1/4 (log (* PI 2))) (* (* (sqrt (* (* n 2) PI)) (* k k)) (log n))))) (/ (* k (+ (* (sqrt (* (* n 2) PI)) (log n)) (* (log (* PI 2)) (sqrt (* (* n 2) PI))))) 2))
  (exp (* (/ (log (* (* n 2) PI)) 2) (- 1 k)))
  (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n))))))
  (+ (* (- (* k k)) +nan.0) (- +nan.0 (* k +nan.0)))
  (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k)))))
  (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (* k k))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (+ (- (* (* +nan.0 (sqrt 2)) (* PI n)) (* (* (* (log (* PI 2)) (sqrt 2)) (* (* PI n) k)) +nan.0)) (* (* +nan.0 (sqrt 2)) (- (* n (* (log n) (* k PI))) (* (* PI n) (* PI n))))) (- (* (* (* (* PI n) k) (sqrt 2)) +nan.0)))
  (- (* (- +nan.0) (/ (exp (* (/ (log (* (* n 2) PI)) 2) (- 1 k))) k)) (+ (* (/ (exp (* (/ (log (* (* n 2) PI)) 2) (- 1 k))) (* k k)) (/ +nan.0 k)) (* (/ (exp (* (/ (log (* (* n 2) PI)) 2) (- 1 k))) (* k k)) (- +nan.0))))
  (+ (- (/ (* (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))) +nan.0) (* k k)) (* +nan.0 (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))))) (- (/ (* +nan.0 (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n))))))) k)))
10.696 * * * [progress]: adding candidates to table
11.527 * * [progress]: iteration 3 / 4
11.527 * * * [progress]: picking best candidate
11.574 * * * * [pick]: Picked  #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
11.574 * * * [progress]: localizing error
11.607 * * * [progress]: generating rewritten candidates
11.607 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1)
11.632 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1)
11.652 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
11.692 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1)
11.717 * * * [progress]: generating series expansions
11.718 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1)
11.718 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
11.718 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
11.718 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
11.718 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
11.718 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
11.718 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.718 * [taylor]: Taking taylor expansion of 1/2 in k
11.718 * [backup-simplify]: Simplify 1/2 into 1/2
11.718 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.718 * [taylor]: Taking taylor expansion of 1/2 in k
11.718 * [backup-simplify]: Simplify 1/2 into 1/2
11.718 * [taylor]: Taking taylor expansion of k in k
11.718 * [backup-simplify]: Simplify 0 into 0
11.718 * [backup-simplify]: Simplify 1 into 1
11.718 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
11.718 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
11.718 * [taylor]: Taking taylor expansion of 2 in k
11.718 * [backup-simplify]: Simplify 2 into 2
11.718 * [taylor]: Taking taylor expansion of (* n PI) in k
11.718 * [taylor]: Taking taylor expansion of n in k
11.718 * [backup-simplify]: Simplify n into n
11.718 * [taylor]: Taking taylor expansion of PI in k
11.718 * [backup-simplify]: Simplify PI into PI
11.718 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.718 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
11.718 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
11.719 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.719 * [backup-simplify]: Simplify (- 0) into 0
11.719 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.719 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
11.720 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
11.720 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
11.720 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
11.720 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
11.720 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.720 * [taylor]: Taking taylor expansion of 1/2 in n
11.720 * [backup-simplify]: Simplify 1/2 into 1/2
11.720 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.720 * [taylor]: Taking taylor expansion of 1/2 in n
11.720 * [backup-simplify]: Simplify 1/2 into 1/2
11.720 * [taylor]: Taking taylor expansion of k in n
11.720 * [backup-simplify]: Simplify k into k
11.720 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.720 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.720 * [taylor]: Taking taylor expansion of 2 in n
11.720 * [backup-simplify]: Simplify 2 into 2
11.720 * [taylor]: Taking taylor expansion of (* n PI) in n
11.720 * [taylor]: Taking taylor expansion of n in n
11.720 * [backup-simplify]: Simplify 0 into 0
11.720 * [backup-simplify]: Simplify 1 into 1
11.720 * [taylor]: Taking taylor expansion of PI in n
11.720 * [backup-simplify]: Simplify PI into PI
11.720 * [backup-simplify]: Simplify (* 0 PI) into 0
11.721 * [backup-simplify]: Simplify (* 2 0) into 0
11.722 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.723 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.724 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.724 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.724 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.724 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.725 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.725 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
11.726 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
11.726 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
11.726 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
11.726 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
11.726 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.726 * [taylor]: Taking taylor expansion of 1/2 in n
11.726 * [backup-simplify]: Simplify 1/2 into 1/2
11.726 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.726 * [taylor]: Taking taylor expansion of 1/2 in n
11.726 * [backup-simplify]: Simplify 1/2 into 1/2
11.726 * [taylor]: Taking taylor expansion of k in n
11.726 * [backup-simplify]: Simplify k into k
11.726 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.726 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.726 * [taylor]: Taking taylor expansion of 2 in n
11.726 * [backup-simplify]: Simplify 2 into 2
11.726 * [taylor]: Taking taylor expansion of (* n PI) in n
11.726 * [taylor]: Taking taylor expansion of n in n
11.726 * [backup-simplify]: Simplify 0 into 0
11.726 * [backup-simplify]: Simplify 1 into 1
11.726 * [taylor]: Taking taylor expansion of PI in n
11.726 * [backup-simplify]: Simplify PI into PI
11.727 * [backup-simplify]: Simplify (* 0 PI) into 0
11.727 * [backup-simplify]: Simplify (* 2 0) into 0
11.728 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.729 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.730 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.730 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.730 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.730 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.731 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.731 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
11.732 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
11.732 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
11.732 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
11.732 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.732 * [taylor]: Taking taylor expansion of 1/2 in k
11.732 * [backup-simplify]: Simplify 1/2 into 1/2
11.732 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.732 * [taylor]: Taking taylor expansion of 1/2 in k
11.732 * [backup-simplify]: Simplify 1/2 into 1/2
11.732 * [taylor]: Taking taylor expansion of k in k
11.732 * [backup-simplify]: Simplify 0 into 0
11.732 * [backup-simplify]: Simplify 1 into 1
11.732 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
11.732 * [taylor]: Taking taylor expansion of (log n) in k
11.732 * [taylor]: Taking taylor expansion of n in k
11.732 * [backup-simplify]: Simplify n into n
11.732 * [backup-simplify]: Simplify (log n) into (log n)
11.733 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.733 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.733 * [taylor]: Taking taylor expansion of 2 in k
11.733 * [backup-simplify]: Simplify 2 into 2
11.733 * [taylor]: Taking taylor expansion of PI in k
11.733 * [backup-simplify]: Simplify PI into PI
11.733 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.734 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.734 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.734 * [backup-simplify]: Simplify (- 0) into 0
11.735 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.735 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.736 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
11.737 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
11.738 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
11.738 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.739 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
11.740 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.740 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
11.741 * [backup-simplify]: Simplify (- 0) into 0
11.741 * [backup-simplify]: Simplify (+ 0 0) into 0
11.742 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.742 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
11.744 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.744 * [taylor]: Taking taylor expansion of 0 in k
11.744 * [backup-simplify]: Simplify 0 into 0
11.744 * [backup-simplify]: Simplify 0 into 0
11.744 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.745 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.746 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.746 * [backup-simplify]: Simplify (+ 0 0) into 0
11.747 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
11.747 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.747 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.748 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
11.750 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
11.752 * [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)))))))
11.753 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.753 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.755 * [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
11.756 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
11.756 * [backup-simplify]: Simplify (- 0) into 0
11.756 * [backup-simplify]: Simplify (+ 0 0) into 0
11.757 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.759 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.761 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.762 * [taylor]: Taking taylor expansion of 0 in k
11.762 * [backup-simplify]: Simplify 0 into 0
11.762 * [backup-simplify]: Simplify 0 into 0
11.762 * [backup-simplify]: Simplify 0 into 0
11.763 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.764 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.768 * [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
11.768 * [backup-simplify]: Simplify (+ 0 0) into 0
11.769 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
11.770 * [backup-simplify]: Simplify (- 0) into 0
11.770 * [backup-simplify]: Simplify (+ 0 0) into 0
11.772 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.777 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 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)))))
11.782 * [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)))))
11.792 * [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)))))
11.792 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
11.792 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
11.792 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
11.792 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
11.792 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
11.792 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.792 * [taylor]: Taking taylor expansion of 1/2 in k
11.792 * [backup-simplify]: Simplify 1/2 into 1/2
11.792 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.792 * [taylor]: Taking taylor expansion of 1/2 in k
11.792 * [backup-simplify]: Simplify 1/2 into 1/2
11.793 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.793 * [taylor]: Taking taylor expansion of k in k
11.793 * [backup-simplify]: Simplify 0 into 0
11.793 * [backup-simplify]: Simplify 1 into 1
11.793 * [backup-simplify]: Simplify (/ 1 1) into 1
11.793 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
11.793 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
11.793 * [taylor]: Taking taylor expansion of 2 in k
11.793 * [backup-simplify]: Simplify 2 into 2
11.793 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.793 * [taylor]: Taking taylor expansion of PI in k
11.793 * [backup-simplify]: Simplify PI into PI
11.793 * [taylor]: Taking taylor expansion of n in k
11.793 * [backup-simplify]: Simplify n into n
11.793 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.793 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
11.793 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
11.794 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.794 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.795 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.795 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
11.795 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
11.795 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.795 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
11.795 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
11.795 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.795 * [taylor]: Taking taylor expansion of 1/2 in n
11.795 * [backup-simplify]: Simplify 1/2 into 1/2
11.795 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.795 * [taylor]: Taking taylor expansion of 1/2 in n
11.795 * [backup-simplify]: Simplify 1/2 into 1/2
11.795 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.795 * [taylor]: Taking taylor expansion of k in n
11.795 * [backup-simplify]: Simplify k into k
11.795 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.795 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.795 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.796 * [taylor]: Taking taylor expansion of 2 in n
11.796 * [backup-simplify]: Simplify 2 into 2
11.796 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.796 * [taylor]: Taking taylor expansion of PI in n
11.796 * [backup-simplify]: Simplify PI into PI
11.796 * [taylor]: Taking taylor expansion of n in n
11.796 * [backup-simplify]: Simplify 0 into 0
11.796 * [backup-simplify]: Simplify 1 into 1
11.796 * [backup-simplify]: Simplify (/ PI 1) into PI
11.797 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.798 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.798 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.798 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.798 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.800 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.801 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
11.802 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
11.802 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
11.802 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
11.802 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
11.802 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.802 * [taylor]: Taking taylor expansion of 1/2 in n
11.802 * [backup-simplify]: Simplify 1/2 into 1/2
11.802 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.802 * [taylor]: Taking taylor expansion of 1/2 in n
11.802 * [backup-simplify]: Simplify 1/2 into 1/2
11.802 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.802 * [taylor]: Taking taylor expansion of k in n
11.802 * [backup-simplify]: Simplify k into k
11.802 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.802 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.802 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.802 * [taylor]: Taking taylor expansion of 2 in n
11.802 * [backup-simplify]: Simplify 2 into 2
11.802 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.803 * [taylor]: Taking taylor expansion of PI in n
11.803 * [backup-simplify]: Simplify PI into PI
11.803 * [taylor]: Taking taylor expansion of n in n
11.803 * [backup-simplify]: Simplify 0 into 0
11.803 * [backup-simplify]: Simplify 1 into 1
11.803 * [backup-simplify]: Simplify (/ PI 1) into PI
11.804 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.805 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.805 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.805 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.805 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.807 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.808 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
11.809 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
11.809 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
11.809 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
11.809 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.809 * [taylor]: Taking taylor expansion of 1/2 in k
11.809 * [backup-simplify]: Simplify 1/2 into 1/2
11.809 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.809 * [taylor]: Taking taylor expansion of 1/2 in k
11.809 * [backup-simplify]: Simplify 1/2 into 1/2
11.809 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.809 * [taylor]: Taking taylor expansion of k in k
11.809 * [backup-simplify]: Simplify 0 into 0
11.809 * [backup-simplify]: Simplify 1 into 1
11.810 * [backup-simplify]: Simplify (/ 1 1) into 1
11.810 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
11.810 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.810 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.810 * [taylor]: Taking taylor expansion of 2 in k
11.810 * [backup-simplify]: Simplify 2 into 2
11.810 * [taylor]: Taking taylor expansion of PI in k
11.810 * [backup-simplify]: Simplify PI into PI
11.810 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.811 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.812 * [taylor]: Taking taylor expansion of (log n) in k
11.812 * [taylor]: Taking taylor expansion of n in k
11.812 * [backup-simplify]: Simplify n into n
11.812 * [backup-simplify]: Simplify (log n) into (log n)
11.812 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.812 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.813 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.813 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.814 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
11.815 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
11.817 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
11.818 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
11.819 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.819 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.821 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.821 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.822 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.822 * [backup-simplify]: Simplify (- 0) into 0
11.823 * [backup-simplify]: Simplify (+ 0 0) into 0
11.824 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.833 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
11.835 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
11.835 * [taylor]: Taking taylor expansion of 0 in k
11.835 * [backup-simplify]: Simplify 0 into 0
11.835 * [backup-simplify]: Simplify 0 into 0
11.835 * [backup-simplify]: Simplify 0 into 0
11.836 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.838 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.841 * [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
11.842 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.843 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.843 * [backup-simplify]: Simplify (- 0) into 0
11.843 * [backup-simplify]: Simplify (+ 0 0) into 0
11.845 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.846 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
11.849 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.849 * [taylor]: Taking taylor expansion of 0 in k
11.849 * [backup-simplify]: Simplify 0 into 0
11.849 * [backup-simplify]: Simplify 0 into 0
11.849 * [backup-simplify]: Simplify 0 into 0
11.849 * [backup-simplify]: Simplify 0 into 0
11.850 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.851 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.857 * [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
11.857 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.858 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
11.859 * [backup-simplify]: Simplify (- 0) into 0
11.859 * [backup-simplify]: Simplify (+ 0 0) into 0
11.860 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.862 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
11.865 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 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
11.866 * [taylor]: Taking taylor expansion of 0 in k
11.866 * [backup-simplify]: Simplify 0 into 0
11.866 * [backup-simplify]: Simplify 0 into 0
11.867 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
11.867 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
11.867 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
11.867 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.867 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
11.867 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
11.867 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.867 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.867 * [taylor]: Taking taylor expansion of 1/2 in k
11.867 * [backup-simplify]: Simplify 1/2 into 1/2
11.867 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.867 * [taylor]: Taking taylor expansion of k in k
11.867 * [backup-simplify]: Simplify 0 into 0
11.867 * [backup-simplify]: Simplify 1 into 1
11.868 * [backup-simplify]: Simplify (/ 1 1) into 1
11.868 * [taylor]: Taking taylor expansion of 1/2 in k
11.868 * [backup-simplify]: Simplify 1/2 into 1/2
11.868 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
11.868 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
11.868 * [taylor]: Taking taylor expansion of -2 in k
11.868 * [backup-simplify]: Simplify -2 into -2
11.868 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.868 * [taylor]: Taking taylor expansion of PI in k
11.868 * [backup-simplify]: Simplify PI into PI
11.868 * [taylor]: Taking taylor expansion of n in k
11.868 * [backup-simplify]: Simplify n into n
11.868 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.868 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
11.868 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
11.869 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.869 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.869 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
11.869 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
11.870 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.870 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
11.870 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
11.870 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.870 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.870 * [taylor]: Taking taylor expansion of 1/2 in n
11.870 * [backup-simplify]: Simplify 1/2 into 1/2
11.870 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.870 * [taylor]: Taking taylor expansion of k in n
11.870 * [backup-simplify]: Simplify k into k
11.870 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.870 * [taylor]: Taking taylor expansion of 1/2 in n
11.870 * [backup-simplify]: Simplify 1/2 into 1/2
11.870 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.870 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.870 * [taylor]: Taking taylor expansion of -2 in n
11.870 * [backup-simplify]: Simplify -2 into -2
11.870 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.870 * [taylor]: Taking taylor expansion of PI in n
11.870 * [backup-simplify]: Simplify PI into PI
11.870 * [taylor]: Taking taylor expansion of n in n
11.870 * [backup-simplify]: Simplify 0 into 0
11.870 * [backup-simplify]: Simplify 1 into 1
11.871 * [backup-simplify]: Simplify (/ PI 1) into PI
11.871 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.872 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.872 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.872 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.874 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.875 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
11.876 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
11.876 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.876 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
11.876 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
11.876 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.876 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.876 * [taylor]: Taking taylor expansion of 1/2 in n
11.876 * [backup-simplify]: Simplify 1/2 into 1/2
11.876 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.876 * [taylor]: Taking taylor expansion of k in n
11.876 * [backup-simplify]: Simplify k into k
11.876 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.876 * [taylor]: Taking taylor expansion of 1/2 in n
11.876 * [backup-simplify]: Simplify 1/2 into 1/2
11.876 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.876 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.876 * [taylor]: Taking taylor expansion of -2 in n
11.877 * [backup-simplify]: Simplify -2 into -2
11.877 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.877 * [taylor]: Taking taylor expansion of PI in n
11.877 * [backup-simplify]: Simplify PI into PI
11.877 * [taylor]: Taking taylor expansion of n in n
11.877 * [backup-simplify]: Simplify 0 into 0
11.877 * [backup-simplify]: Simplify 1 into 1
11.877 * [backup-simplify]: Simplify (/ PI 1) into PI
11.878 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.879 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.879 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.879 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.880 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.881 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
11.883 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
11.883 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
11.883 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
11.883 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.883 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.883 * [taylor]: Taking taylor expansion of 1/2 in k
11.883 * [backup-simplify]: Simplify 1/2 into 1/2
11.883 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.883 * [taylor]: Taking taylor expansion of k in k
11.883 * [backup-simplify]: Simplify 0 into 0
11.883 * [backup-simplify]: Simplify 1 into 1
11.883 * [backup-simplify]: Simplify (/ 1 1) into 1
11.883 * [taylor]: Taking taylor expansion of 1/2 in k
11.883 * [backup-simplify]: Simplify 1/2 into 1/2
11.883 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
11.883 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
11.883 * [taylor]: Taking taylor expansion of (* -2 PI) in k
11.883 * [taylor]: Taking taylor expansion of -2 in k
11.883 * [backup-simplify]: Simplify -2 into -2
11.883 * [taylor]: Taking taylor expansion of PI in k
11.883 * [backup-simplify]: Simplify PI into PI
11.884 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.885 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.885 * [taylor]: Taking taylor expansion of (log n) in k
11.885 * [taylor]: Taking taylor expansion of n in k
11.885 * [backup-simplify]: Simplify n into n
11.885 * [backup-simplify]: Simplify (log n) into (log n)
11.886 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.886 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.886 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.887 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
11.888 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
11.889 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
11.891 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
11.892 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.892 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
11.894 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
11.894 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.895 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.895 * [backup-simplify]: Simplify (+ 0 0) into 0
11.897 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.898 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
11.900 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
11.900 * [taylor]: Taking taylor expansion of 0 in k
11.900 * [backup-simplify]: Simplify 0 into 0
11.900 * [backup-simplify]: Simplify 0 into 0
11.901 * [backup-simplify]: Simplify 0 into 0
11.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.903 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
11.907 * [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
11.907 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.908 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.909 * [backup-simplify]: Simplify (+ 0 0) into 0
11.910 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.912 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
11.914 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.914 * [taylor]: Taking taylor expansion of 0 in k
11.914 * [backup-simplify]: Simplify 0 into 0
11.914 * [backup-simplify]: Simplify 0 into 0
11.914 * [backup-simplify]: Simplify 0 into 0
11.914 * [backup-simplify]: Simplify 0 into 0
11.916 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.917 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.922 * [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
11.923 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.924 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
11.924 * [backup-simplify]: Simplify (+ 0 0) into 0
11.926 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.928 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
11.931 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.931 * [taylor]: Taking taylor expansion of 0 in k
11.931 * [backup-simplify]: Simplify 0 into 0
11.931 * [backup-simplify]: Simplify 0 into 0
11.932 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
11.932 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1)
11.932 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
11.932 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
11.933 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
11.933 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
11.933 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
11.933 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.933 * [taylor]: Taking taylor expansion of 1/2 in k
11.933 * [backup-simplify]: Simplify 1/2 into 1/2
11.933 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.933 * [taylor]: Taking taylor expansion of 1/2 in k
11.933 * [backup-simplify]: Simplify 1/2 into 1/2
11.933 * [taylor]: Taking taylor expansion of k in k
11.933 * [backup-simplify]: Simplify 0 into 0
11.933 * [backup-simplify]: Simplify 1 into 1
11.933 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
11.933 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
11.933 * [taylor]: Taking taylor expansion of 2 in k
11.933 * [backup-simplify]: Simplify 2 into 2
11.933 * [taylor]: Taking taylor expansion of (* n PI) in k
11.933 * [taylor]: Taking taylor expansion of n in k
11.933 * [backup-simplify]: Simplify n into n
11.933 * [taylor]: Taking taylor expansion of PI in k
11.933 * [backup-simplify]: Simplify PI into PI
11.933 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.933 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
11.933 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
11.934 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.934 * [backup-simplify]: Simplify (- 0) into 0
11.935 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.935 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
11.935 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
11.935 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
11.935 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
11.935 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
11.935 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.935 * [taylor]: Taking taylor expansion of 1/2 in n
11.935 * [backup-simplify]: Simplify 1/2 into 1/2
11.935 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.935 * [taylor]: Taking taylor expansion of 1/2 in n
11.935 * [backup-simplify]: Simplify 1/2 into 1/2
11.935 * [taylor]: Taking taylor expansion of k in n
11.935 * [backup-simplify]: Simplify k into k
11.935 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.935 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.935 * [taylor]: Taking taylor expansion of 2 in n
11.935 * [backup-simplify]: Simplify 2 into 2
11.935 * [taylor]: Taking taylor expansion of (* n PI) in n
11.935 * [taylor]: Taking taylor expansion of n in n
11.935 * [backup-simplify]: Simplify 0 into 0
11.935 * [backup-simplify]: Simplify 1 into 1
11.935 * [taylor]: Taking taylor expansion of PI in n
11.936 * [backup-simplify]: Simplify PI into PI
11.936 * [backup-simplify]: Simplify (* 0 PI) into 0
11.936 * [backup-simplify]: Simplify (* 2 0) into 0
11.938 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.940 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.941 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.941 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.941 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.941 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.943 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.944 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
11.945 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
11.945 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
11.945 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
11.945 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
11.945 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.945 * [taylor]: Taking taylor expansion of 1/2 in n
11.946 * [backup-simplify]: Simplify 1/2 into 1/2
11.946 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.946 * [taylor]: Taking taylor expansion of 1/2 in n
11.946 * [backup-simplify]: Simplify 1/2 into 1/2
11.946 * [taylor]: Taking taylor expansion of k in n
11.946 * [backup-simplify]: Simplify k into k
11.946 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.946 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.946 * [taylor]: Taking taylor expansion of 2 in n
11.946 * [backup-simplify]: Simplify 2 into 2
11.946 * [taylor]: Taking taylor expansion of (* n PI) in n
11.946 * [taylor]: Taking taylor expansion of n in n
11.946 * [backup-simplify]: Simplify 0 into 0
11.946 * [backup-simplify]: Simplify 1 into 1
11.946 * [taylor]: Taking taylor expansion of PI in n
11.946 * [backup-simplify]: Simplify PI into PI
11.946 * [backup-simplify]: Simplify (* 0 PI) into 0
11.947 * [backup-simplify]: Simplify (* 2 0) into 0
11.949 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.950 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.952 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.952 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.952 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.952 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.953 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.955 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
11.956 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
11.956 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
11.956 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
11.956 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.956 * [taylor]: Taking taylor expansion of 1/2 in k
11.956 * [backup-simplify]: Simplify 1/2 into 1/2
11.956 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.956 * [taylor]: Taking taylor expansion of 1/2 in k
11.956 * [backup-simplify]: Simplify 1/2 into 1/2
11.956 * [taylor]: Taking taylor expansion of k in k
11.956 * [backup-simplify]: Simplify 0 into 0
11.956 * [backup-simplify]: Simplify 1 into 1
11.956 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
11.956 * [taylor]: Taking taylor expansion of (log n) in k
11.956 * [taylor]: Taking taylor expansion of n in k
11.956 * [backup-simplify]: Simplify n into n
11.956 * [backup-simplify]: Simplify (log n) into (log n)
11.956 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.956 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.956 * [taylor]: Taking taylor expansion of 2 in k
11.956 * [backup-simplify]: Simplify 2 into 2
11.956 * [taylor]: Taking taylor expansion of PI in k
11.956 * [backup-simplify]: Simplify PI into PI
11.957 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.958 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.958 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.959 * [backup-simplify]: Simplify (- 0) into 0
11.959 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.960 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.961 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
11.963 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
11.964 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
11.965 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.966 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
11.967 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.967 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
11.967 * [backup-simplify]: Simplify (- 0) into 0
11.967 * [backup-simplify]: Simplify (+ 0 0) into 0
11.968 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.969 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
11.970 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.970 * [taylor]: Taking taylor expansion of 0 in k
11.970 * [backup-simplify]: Simplify 0 into 0
11.970 * [backup-simplify]: Simplify 0 into 0
11.971 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.971 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.977 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.978 * [backup-simplify]: Simplify (+ 0 0) into 0
11.978 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
11.979 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.979 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.980 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
11.982 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
11.984 * [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)))))))
11.985 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.985 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.987 * [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
11.988 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
11.988 * [backup-simplify]: Simplify (- 0) into 0
11.988 * [backup-simplify]: Simplify (+ 0 0) into 0
11.989 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.990 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.993 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.993 * [taylor]: Taking taylor expansion of 0 in k
11.993 * [backup-simplify]: Simplify 0 into 0
11.993 * [backup-simplify]: Simplify 0 into 0
11.993 * [backup-simplify]: Simplify 0 into 0
11.994 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.994 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.996 * [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
11.997 * [backup-simplify]: Simplify (+ 0 0) into 0
11.997 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
11.998 * [backup-simplify]: Simplify (- 0) into 0
11.998 * [backup-simplify]: Simplify (+ 0 0) into 0
11.999 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.002 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 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)))))
12.005 * [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)))))
12.010 * [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)))))
12.011 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
12.011 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
12.011 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
12.011 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.011 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.011 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.011 * [taylor]: Taking taylor expansion of 1/2 in k
12.011 * [backup-simplify]: Simplify 1/2 into 1/2
12.011 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.011 * [taylor]: Taking taylor expansion of 1/2 in k
12.011 * [backup-simplify]: Simplify 1/2 into 1/2
12.011 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.011 * [taylor]: Taking taylor expansion of k in k
12.011 * [backup-simplify]: Simplify 0 into 0
12.011 * [backup-simplify]: Simplify 1 into 1
12.011 * [backup-simplify]: Simplify (/ 1 1) into 1
12.011 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.011 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.011 * [taylor]: Taking taylor expansion of 2 in k
12.011 * [backup-simplify]: Simplify 2 into 2
12.011 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.011 * [taylor]: Taking taylor expansion of PI in k
12.011 * [backup-simplify]: Simplify PI into PI
12.011 * [taylor]: Taking taylor expansion of n in k
12.011 * [backup-simplify]: Simplify n into n
12.011 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.011 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.011 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.012 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.012 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.012 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.012 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.012 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
12.012 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.012 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.013 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.013 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.013 * [taylor]: Taking taylor expansion of 1/2 in n
12.013 * [backup-simplify]: Simplify 1/2 into 1/2
12.013 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.013 * [taylor]: Taking taylor expansion of 1/2 in n
12.013 * [backup-simplify]: Simplify 1/2 into 1/2
12.013 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.013 * [taylor]: Taking taylor expansion of k in n
12.013 * [backup-simplify]: Simplify k into k
12.013 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.013 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.013 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.013 * [taylor]: Taking taylor expansion of 2 in n
12.013 * [backup-simplify]: Simplify 2 into 2
12.013 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.013 * [taylor]: Taking taylor expansion of PI in n
12.013 * [backup-simplify]: Simplify PI into PI
12.013 * [taylor]: Taking taylor expansion of n in n
12.013 * [backup-simplify]: Simplify 0 into 0
12.013 * [backup-simplify]: Simplify 1 into 1
12.013 * [backup-simplify]: Simplify (/ PI 1) into PI
12.014 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.014 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.014 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.014 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.014 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.015 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.017 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.017 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.017 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.017 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.017 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.017 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.017 * [taylor]: Taking taylor expansion of 1/2 in n
12.018 * [backup-simplify]: Simplify 1/2 into 1/2
12.018 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.018 * [taylor]: Taking taylor expansion of 1/2 in n
12.018 * [backup-simplify]: Simplify 1/2 into 1/2
12.018 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.018 * [taylor]: Taking taylor expansion of k in n
12.018 * [backup-simplify]: Simplify k into k
12.018 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.018 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.018 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.018 * [taylor]: Taking taylor expansion of 2 in n
12.018 * [backup-simplify]: Simplify 2 into 2
12.018 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.018 * [taylor]: Taking taylor expansion of PI in n
12.018 * [backup-simplify]: Simplify PI into PI
12.018 * [taylor]: Taking taylor expansion of n in n
12.018 * [backup-simplify]: Simplify 0 into 0
12.018 * [backup-simplify]: Simplify 1 into 1
12.018 * [backup-simplify]: Simplify (/ PI 1) into PI
12.018 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.019 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.019 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.019 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.019 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.020 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.021 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.022 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.022 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
12.022 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
12.022 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.022 * [taylor]: Taking taylor expansion of 1/2 in k
12.022 * [backup-simplify]: Simplify 1/2 into 1/2
12.022 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.022 * [taylor]: Taking taylor expansion of 1/2 in k
12.022 * [backup-simplify]: Simplify 1/2 into 1/2
12.022 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.022 * [taylor]: Taking taylor expansion of k in k
12.022 * [backup-simplify]: Simplify 0 into 0
12.022 * [backup-simplify]: Simplify 1 into 1
12.022 * [backup-simplify]: Simplify (/ 1 1) into 1
12.022 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.022 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.022 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.022 * [taylor]: Taking taylor expansion of 2 in k
12.022 * [backup-simplify]: Simplify 2 into 2
12.022 * [taylor]: Taking taylor expansion of PI in k
12.022 * [backup-simplify]: Simplify PI into PI
12.023 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.023 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.023 * [taylor]: Taking taylor expansion of (log n) in k
12.023 * [taylor]: Taking taylor expansion of n in k
12.023 * [backup-simplify]: Simplify n into n
12.023 * [backup-simplify]: Simplify (log n) into (log n)
12.024 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.024 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.024 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.024 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.025 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.026 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.026 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.027 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.028 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.028 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.029 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.029 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.030 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.030 * [backup-simplify]: Simplify (- 0) into 0
12.030 * [backup-simplify]: Simplify (+ 0 0) into 0
12.031 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.032 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.033 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.033 * [taylor]: Taking taylor expansion of 0 in k
12.033 * [backup-simplify]: Simplify 0 into 0
12.033 * [backup-simplify]: Simplify 0 into 0
12.033 * [backup-simplify]: Simplify 0 into 0
12.034 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.034 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.036 * [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
12.036 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.037 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.037 * [backup-simplify]: Simplify (- 0) into 0
12.037 * [backup-simplify]: Simplify (+ 0 0) into 0
12.038 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.039 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.041 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.041 * [taylor]: Taking taylor expansion of 0 in k
12.041 * [backup-simplify]: Simplify 0 into 0
12.041 * [backup-simplify]: Simplify 0 into 0
12.041 * [backup-simplify]: Simplify 0 into 0
12.041 * [backup-simplify]: Simplify 0 into 0
12.042 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.042 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.046 * [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
12.046 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.047 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.047 * [backup-simplify]: Simplify (- 0) into 0
12.047 * [backup-simplify]: Simplify (+ 0 0) into 0
12.048 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.049 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.051 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 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
12.051 * [taylor]: Taking taylor expansion of 0 in k
12.051 * [backup-simplify]: Simplify 0 into 0
12.051 * [backup-simplify]: Simplify 0 into 0
12.052 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
12.052 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
12.052 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
12.052 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
12.052 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
12.052 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
12.052 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.052 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.052 * [taylor]: Taking taylor expansion of 1/2 in k
12.052 * [backup-simplify]: Simplify 1/2 into 1/2
12.052 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.052 * [taylor]: Taking taylor expansion of k in k
12.052 * [backup-simplify]: Simplify 0 into 0
12.052 * [backup-simplify]: Simplify 1 into 1
12.053 * [backup-simplify]: Simplify (/ 1 1) into 1
12.053 * [taylor]: Taking taylor expansion of 1/2 in k
12.053 * [backup-simplify]: Simplify 1/2 into 1/2
12.053 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.053 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.053 * [taylor]: Taking taylor expansion of -2 in k
12.053 * [backup-simplify]: Simplify -2 into -2
12.053 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.053 * [taylor]: Taking taylor expansion of PI in k
12.053 * [backup-simplify]: Simplify PI into PI
12.053 * [taylor]: Taking taylor expansion of n in k
12.053 * [backup-simplify]: Simplify n into n
12.053 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.053 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.053 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.053 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.053 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.053 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.054 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
12.054 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.054 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.054 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.054 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.054 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.054 * [taylor]: Taking taylor expansion of 1/2 in n
12.054 * [backup-simplify]: Simplify 1/2 into 1/2
12.054 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.054 * [taylor]: Taking taylor expansion of k in n
12.054 * [backup-simplify]: Simplify k into k
12.054 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.054 * [taylor]: Taking taylor expansion of 1/2 in n
12.054 * [backup-simplify]: Simplify 1/2 into 1/2
12.054 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.054 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.054 * [taylor]: Taking taylor expansion of -2 in n
12.054 * [backup-simplify]: Simplify -2 into -2
12.054 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.054 * [taylor]: Taking taylor expansion of PI in n
12.054 * [backup-simplify]: Simplify PI into PI
12.054 * [taylor]: Taking taylor expansion of n in n
12.054 * [backup-simplify]: Simplify 0 into 0
12.054 * [backup-simplify]: Simplify 1 into 1
12.054 * [backup-simplify]: Simplify (/ PI 1) into PI
12.055 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.055 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.055 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.055 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.057 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.058 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.058 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.058 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.058 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.058 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.058 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.058 * [taylor]: Taking taylor expansion of 1/2 in n
12.058 * [backup-simplify]: Simplify 1/2 into 1/2
12.058 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.058 * [taylor]: Taking taylor expansion of k in n
12.058 * [backup-simplify]: Simplify k into k
12.058 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.058 * [taylor]: Taking taylor expansion of 1/2 in n
12.058 * [backup-simplify]: Simplify 1/2 into 1/2
12.058 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.058 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.058 * [taylor]: Taking taylor expansion of -2 in n
12.058 * [backup-simplify]: Simplify -2 into -2
12.058 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.058 * [taylor]: Taking taylor expansion of PI in n
12.058 * [backup-simplify]: Simplify PI into PI
12.058 * [taylor]: Taking taylor expansion of n in n
12.058 * [backup-simplify]: Simplify 0 into 0
12.058 * [backup-simplify]: Simplify 1 into 1
12.058 * [backup-simplify]: Simplify (/ PI 1) into PI
12.059 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.060 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.060 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.060 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.061 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.061 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.062 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.062 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
12.062 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
12.062 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.062 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.062 * [taylor]: Taking taylor expansion of 1/2 in k
12.062 * [backup-simplify]: Simplify 1/2 into 1/2
12.062 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.062 * [taylor]: Taking taylor expansion of k in k
12.062 * [backup-simplify]: Simplify 0 into 0
12.062 * [backup-simplify]: Simplify 1 into 1
12.063 * [backup-simplify]: Simplify (/ 1 1) into 1
12.063 * [taylor]: Taking taylor expansion of 1/2 in k
12.063 * [backup-simplify]: Simplify 1/2 into 1/2
12.063 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.063 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.063 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.063 * [taylor]: Taking taylor expansion of -2 in k
12.063 * [backup-simplify]: Simplify -2 into -2
12.063 * [taylor]: Taking taylor expansion of PI in k
12.063 * [backup-simplify]: Simplify PI into PI
12.063 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.064 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.064 * [taylor]: Taking taylor expansion of (log n) in k
12.064 * [taylor]: Taking taylor expansion of n in k
12.064 * [backup-simplify]: Simplify n into n
12.064 * [backup-simplify]: Simplify (log n) into (log n)
12.064 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.064 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.064 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.065 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.071 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
12.072 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.074 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.075 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.075 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.077 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.077 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.078 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.078 * [backup-simplify]: Simplify (+ 0 0) into 0
12.080 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.081 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.083 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.083 * [taylor]: Taking taylor expansion of 0 in k
12.083 * [backup-simplify]: Simplify 0 into 0
12.083 * [backup-simplify]: Simplify 0 into 0
12.083 * [backup-simplify]: Simplify 0 into 0
12.084 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.085 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.089 * [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
12.089 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.090 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.091 * [backup-simplify]: Simplify (+ 0 0) into 0
12.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.095 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.097 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.097 * [taylor]: Taking taylor expansion of 0 in k
12.097 * [backup-simplify]: Simplify 0 into 0
12.097 * [backup-simplify]: Simplify 0 into 0
12.097 * [backup-simplify]: Simplify 0 into 0
12.097 * [backup-simplify]: Simplify 0 into 0
12.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.100 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.106 * [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
12.107 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.108 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.108 * [backup-simplify]: Simplify (+ 0 0) into 0
12.109 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.111 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
12.112 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.112 * [taylor]: Taking taylor expansion of 0 in k
12.112 * [backup-simplify]: Simplify 0 into 0
12.112 * [backup-simplify]: Simplify 0 into 0
12.113 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
12.113 * * * * [progress]: [ 3 / 4 ] generating series at (2)
12.113 * [backup-simplify]: Simplify (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
12.113 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
12.113 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
12.114 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.114 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.114 * [taylor]: Taking taylor expansion of k in k
12.114 * [backup-simplify]: Simplify 0 into 0
12.114 * [backup-simplify]: Simplify 1 into 1
12.114 * [backup-simplify]: Simplify (/ 1 1) into 1
12.114 * [backup-simplify]: Simplify (sqrt 0) into 0
12.115 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.115 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
12.115 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
12.115 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
12.115 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.115 * [taylor]: Taking taylor expansion of 1/2 in k
12.115 * [backup-simplify]: Simplify 1/2 into 1/2
12.115 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.115 * [taylor]: Taking taylor expansion of 1/2 in k
12.115 * [backup-simplify]: Simplify 1/2 into 1/2
12.115 * [taylor]: Taking taylor expansion of k in k
12.115 * [backup-simplify]: Simplify 0 into 0
12.115 * [backup-simplify]: Simplify 1 into 1
12.115 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.115 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.115 * [taylor]: Taking taylor expansion of 2 in k
12.115 * [backup-simplify]: Simplify 2 into 2
12.115 * [taylor]: Taking taylor expansion of (* n PI) in k
12.115 * [taylor]: Taking taylor expansion of n in k
12.115 * [backup-simplify]: Simplify n into n
12.115 * [taylor]: Taking taylor expansion of PI in k
12.115 * [backup-simplify]: Simplify PI into PI
12.115 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.115 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.115 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.116 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.116 * [backup-simplify]: Simplify (- 0) into 0
12.116 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.116 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.116 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.116 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
12.116 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.116 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.116 * [taylor]: Taking taylor expansion of k in n
12.116 * [backup-simplify]: Simplify k into k
12.116 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.117 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.117 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.117 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.117 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.117 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.117 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.117 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.117 * [taylor]: Taking taylor expansion of 1/2 in n
12.117 * [backup-simplify]: Simplify 1/2 into 1/2
12.117 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.117 * [taylor]: Taking taylor expansion of 1/2 in n
12.117 * [backup-simplify]: Simplify 1/2 into 1/2
12.117 * [taylor]: Taking taylor expansion of k in n
12.117 * [backup-simplify]: Simplify k into k
12.117 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.117 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.117 * [taylor]: Taking taylor expansion of 2 in n
12.117 * [backup-simplify]: Simplify 2 into 2
12.117 * [taylor]: Taking taylor expansion of (* n PI) in n
12.117 * [taylor]: Taking taylor expansion of n in n
12.117 * [backup-simplify]: Simplify 0 into 0
12.117 * [backup-simplify]: Simplify 1 into 1
12.117 * [taylor]: Taking taylor expansion of PI in n
12.117 * [backup-simplify]: Simplify PI into PI
12.117 * [backup-simplify]: Simplify (* 0 PI) into 0
12.118 * [backup-simplify]: Simplify (* 2 0) into 0
12.119 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.119 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.120 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.120 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.120 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.120 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.121 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.122 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.123 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
12.123 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
12.123 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.123 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.123 * [taylor]: Taking taylor expansion of k in n
12.123 * [backup-simplify]: Simplify k into k
12.123 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.123 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.123 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.123 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.123 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.123 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.123 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.123 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.123 * [taylor]: Taking taylor expansion of 1/2 in n
12.123 * [backup-simplify]: Simplify 1/2 into 1/2
12.123 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.123 * [taylor]: Taking taylor expansion of 1/2 in n
12.123 * [backup-simplify]: Simplify 1/2 into 1/2
12.123 * [taylor]: Taking taylor expansion of k in n
12.123 * [backup-simplify]: Simplify k into k
12.123 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.123 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.123 * [taylor]: Taking taylor expansion of 2 in n
12.123 * [backup-simplify]: Simplify 2 into 2
12.123 * [taylor]: Taking taylor expansion of (* n PI) in n
12.123 * [taylor]: Taking taylor expansion of n in n
12.123 * [backup-simplify]: Simplify 0 into 0
12.123 * [backup-simplify]: Simplify 1 into 1
12.123 * [taylor]: Taking taylor expansion of PI in n
12.123 * [backup-simplify]: Simplify PI into PI
12.124 * [backup-simplify]: Simplify (* 0 PI) into 0
12.124 * [backup-simplify]: Simplify (* 2 0) into 0
12.125 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.126 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.126 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.126 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.126 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.127 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.127 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.128 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.129 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
12.130 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k)))
12.130 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
12.130 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
12.130 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
12.130 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.130 * [taylor]: Taking taylor expansion of 1/2 in k
12.130 * [backup-simplify]: Simplify 1/2 into 1/2
12.130 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.130 * [taylor]: Taking taylor expansion of 1/2 in k
12.130 * [backup-simplify]: Simplify 1/2 into 1/2
12.130 * [taylor]: Taking taylor expansion of k in k
12.130 * [backup-simplify]: Simplify 0 into 0
12.130 * [backup-simplify]: Simplify 1 into 1
12.130 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
12.130 * [taylor]: Taking taylor expansion of (log n) in k
12.130 * [taylor]: Taking taylor expansion of n in k
12.130 * [backup-simplify]: Simplify n into n
12.130 * [backup-simplify]: Simplify (log n) into (log n)
12.130 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.130 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.130 * [taylor]: Taking taylor expansion of 2 in k
12.130 * [backup-simplify]: Simplify 2 into 2
12.130 * [taylor]: Taking taylor expansion of PI in k
12.130 * [backup-simplify]: Simplify PI into PI
12.131 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.131 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.132 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.132 * [backup-simplify]: Simplify (- 0) into 0
12.132 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.133 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.134 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
12.134 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.134 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.134 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.134 * [taylor]: Taking taylor expansion of k in k
12.134 * [backup-simplify]: Simplify 0 into 0
12.134 * [backup-simplify]: Simplify 1 into 1
12.135 * [backup-simplify]: Simplify (/ 1 1) into 1
12.135 * [backup-simplify]: Simplify (sqrt 0) into 0
12.136 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.137 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
12.137 * [backup-simplify]: Simplify 0 into 0
12.137 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.138 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.139 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.139 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
12.140 * [backup-simplify]: Simplify (- 0) into 0
12.140 * [backup-simplify]: Simplify (+ 0 0) into 0
12.141 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.141 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.143 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.143 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
12.143 * [taylor]: Taking taylor expansion of 0 in k
12.143 * [backup-simplify]: Simplify 0 into 0
12.144 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.144 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.145 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.146 * [backup-simplify]: Simplify (+ 0 0) into 0
12.146 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
12.146 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.147 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.148 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
12.149 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
12.152 * [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)))))))
12.153 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
12.153 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.154 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.156 * [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
12.156 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
12.157 * [backup-simplify]: Simplify (- 0) into 0
12.157 * [backup-simplify]: Simplify (+ 0 0) into 0
12.158 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.159 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.160 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.161 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.161 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
12.163 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
12.163 * [taylor]: Taking taylor expansion of 0 in k
12.163 * [backup-simplify]: Simplify 0 into 0
12.163 * [backup-simplify]: Simplify 0 into 0
12.164 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.167 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.168 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.170 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.173 * [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
12.173 * [backup-simplify]: Simplify (+ 0 0) into 0
12.174 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
12.175 * [backup-simplify]: Simplify (- 0) into 0
12.175 * [backup-simplify]: Simplify (+ 0 0) into 0
12.177 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.188 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 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)))))
12.197 * [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))))))))
12.202 * [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))))))))
12.203 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.205 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.208 * [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
12.209 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
12.209 * [backup-simplify]: Simplify (- 0) into 0
12.209 * [backup-simplify]: Simplify (+ 0 0) into 0
12.210 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.211 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
12.213 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.213 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.214 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
12.215 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
12.215 * [taylor]: Taking taylor expansion of 0 in k
12.215 * [backup-simplify]: Simplify 0 into 0
12.215 * [backup-simplify]: Simplify 0 into 0
12.215 * [backup-simplify]: Simplify 0 into 0
12.215 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.218 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.219 * [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
12.220 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.223 * [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
12.223 * [backup-simplify]: Simplify (+ 0 0) into 0
12.224 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
12.224 * [backup-simplify]: Simplify (- 0) into 0
12.225 * [backup-simplify]: Simplify (+ 0 0) into 0
12.226 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
12.230 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 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)))))))
12.245 * [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))))))))))))))
12.256 * [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))))))))))))))
12.274 * [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))))))))))))))))))))))
12.275 * [backup-simplify]: Simplify (* (sqrt (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
12.275 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
12.275 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
12.275 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.275 * [taylor]: Taking taylor expansion of k in k
12.275 * [backup-simplify]: Simplify 0 into 0
12.275 * [backup-simplify]: Simplify 1 into 1
12.275 * [backup-simplify]: Simplify (sqrt 0) into 0
12.277 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.277 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
12.277 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.277 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.277 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.277 * [taylor]: Taking taylor expansion of 1/2 in k
12.277 * [backup-simplify]: Simplify 1/2 into 1/2
12.277 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.277 * [taylor]: Taking taylor expansion of 1/2 in k
12.277 * [backup-simplify]: Simplify 1/2 into 1/2
12.277 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.277 * [taylor]: Taking taylor expansion of k in k
12.277 * [backup-simplify]: Simplify 0 into 0
12.277 * [backup-simplify]: Simplify 1 into 1
12.278 * [backup-simplify]: Simplify (/ 1 1) into 1
12.278 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.278 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.278 * [taylor]: Taking taylor expansion of 2 in k
12.278 * [backup-simplify]: Simplify 2 into 2
12.278 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.278 * [taylor]: Taking taylor expansion of PI in k
12.278 * [backup-simplify]: Simplify PI into PI
12.278 * [taylor]: Taking taylor expansion of n in k
12.278 * [backup-simplify]: Simplify n into n
12.278 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.278 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.278 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.278 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.279 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.279 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.279 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.280 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
12.280 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
12.280 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.280 * [taylor]: Taking taylor expansion of k in n
12.280 * [backup-simplify]: Simplify k into k
12.280 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.280 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.280 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.280 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.280 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.280 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.280 * [taylor]: Taking taylor expansion of 1/2 in n
12.280 * [backup-simplify]: Simplify 1/2 into 1/2
12.280 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.280 * [taylor]: Taking taylor expansion of 1/2 in n
12.280 * [backup-simplify]: Simplify 1/2 into 1/2
12.280 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.280 * [taylor]: Taking taylor expansion of k in n
12.280 * [backup-simplify]: Simplify k into k
12.280 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.280 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.280 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.280 * [taylor]: Taking taylor expansion of 2 in n
12.280 * [backup-simplify]: Simplify 2 into 2
12.280 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.280 * [taylor]: Taking taylor expansion of PI in n
12.280 * [backup-simplify]: Simplify PI into PI
12.280 * [taylor]: Taking taylor expansion of n in n
12.280 * [backup-simplify]: Simplify 0 into 0
12.280 * [backup-simplify]: Simplify 1 into 1
12.281 * [backup-simplify]: Simplify (/ PI 1) into PI
12.281 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.282 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.282 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.282 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.282 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.283 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.284 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.284 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.284 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
12.284 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.284 * [taylor]: Taking taylor expansion of k in n
12.284 * [backup-simplify]: Simplify k into k
12.285 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.285 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.285 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.285 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.285 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.285 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.285 * [taylor]: Taking taylor expansion of 1/2 in n
12.285 * [backup-simplify]: Simplify 1/2 into 1/2
12.285 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.285 * [taylor]: Taking taylor expansion of 1/2 in n
12.285 * [backup-simplify]: Simplify 1/2 into 1/2
12.285 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.285 * [taylor]: Taking taylor expansion of k in n
12.285 * [backup-simplify]: Simplify k into k
12.285 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.285 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.285 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.285 * [taylor]: Taking taylor expansion of 2 in n
12.285 * [backup-simplify]: Simplify 2 into 2
12.285 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.285 * [taylor]: Taking taylor expansion of PI in n
12.285 * [backup-simplify]: Simplify PI into PI
12.285 * [taylor]: Taking taylor expansion of n in n
12.285 * [backup-simplify]: Simplify 0 into 0
12.285 * [backup-simplify]: Simplify 1 into 1
12.285 * [backup-simplify]: Simplify (/ PI 1) into PI
12.286 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.286 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.286 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.286 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.286 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.288 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.289 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.289 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
12.290 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
12.290 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
12.290 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
12.290 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.290 * [taylor]: Taking taylor expansion of 1/2 in k
12.290 * [backup-simplify]: Simplify 1/2 into 1/2
12.290 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.290 * [taylor]: Taking taylor expansion of 1/2 in k
12.290 * [backup-simplify]: Simplify 1/2 into 1/2
12.290 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.290 * [taylor]: Taking taylor expansion of k in k
12.290 * [backup-simplify]: Simplify 0 into 0
12.290 * [backup-simplify]: Simplify 1 into 1
12.290 * [backup-simplify]: Simplify (/ 1 1) into 1
12.290 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.290 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.290 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.290 * [taylor]: Taking taylor expansion of 2 in k
12.290 * [backup-simplify]: Simplify 2 into 2
12.290 * [taylor]: Taking taylor expansion of PI in k
12.290 * [backup-simplify]: Simplify PI into PI
12.290 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.291 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.291 * [taylor]: Taking taylor expansion of (log n) in k
12.291 * [taylor]: Taking taylor expansion of n in k
12.291 * [backup-simplify]: Simplify n into n
12.291 * [backup-simplify]: Simplify (log n) into (log n)
12.296 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.296 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.296 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.296 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.297 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.298 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.299 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.299 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.299 * [taylor]: Taking taylor expansion of k in k
12.299 * [backup-simplify]: Simplify 0 into 0
12.299 * [backup-simplify]: Simplify 1 into 1
12.299 * [backup-simplify]: Simplify (sqrt 0) into 0
12.300 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.301 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
12.301 * [backup-simplify]: Simplify 0 into 0
12.302 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.302 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.303 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.303 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.303 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.304 * [backup-simplify]: Simplify (- 0) into 0
12.304 * [backup-simplify]: Simplify (+ 0 0) into 0
12.305 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.306 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.310 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.311 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
12.311 * [taylor]: Taking taylor expansion of 0 in k
12.311 * [backup-simplify]: Simplify 0 into 0
12.312 * [backup-simplify]: Simplify 0 into 0
12.313 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.315 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.317 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.320 * [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
12.320 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.322 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.322 * [backup-simplify]: Simplify (- 0) into 0
12.322 * [backup-simplify]: Simplify (+ 0 0) into 0
12.324 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.325 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.328 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.328 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
12.330 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
12.330 * [taylor]: Taking taylor expansion of 0 in k
12.330 * [backup-simplify]: Simplify 0 into 0
12.330 * [backup-simplify]: Simplify 0 into 0
12.330 * [backup-simplify]: Simplify 0 into 0
12.333 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.335 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.336 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.337 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.339 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.344 * [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
12.344 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.346 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.346 * [backup-simplify]: Simplify (- 0) into 0
12.346 * [backup-simplify]: Simplify (+ 0 0) into 0
12.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.350 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.353 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 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
12.353 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
12.355 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
12.355 * [taylor]: Taking taylor expansion of 0 in k
12.355 * [backup-simplify]: Simplify 0 into 0
12.355 * [backup-simplify]: Simplify 0 into 0
12.356 * [backup-simplify]: Simplify 0 into 0
12.356 * [backup-simplify]: Simplify 0 into 0
12.359 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.361 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.363 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.367 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
12.368 * [backup-simplify]: Simplify (* (sqrt (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
12.368 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
12.368 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
12.368 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
12.368 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
12.368 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
12.368 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.368 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.368 * [taylor]: Taking taylor expansion of 1/2 in k
12.368 * [backup-simplify]: Simplify 1/2 into 1/2
12.368 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.368 * [taylor]: Taking taylor expansion of k in k
12.368 * [backup-simplify]: Simplify 0 into 0
12.368 * [backup-simplify]: Simplify 1 into 1
12.368 * [backup-simplify]: Simplify (/ 1 1) into 1
12.368 * [taylor]: Taking taylor expansion of 1/2 in k
12.368 * [backup-simplify]: Simplify 1/2 into 1/2
12.369 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.369 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.369 * [taylor]: Taking taylor expansion of -2 in k
12.369 * [backup-simplify]: Simplify -2 into -2
12.369 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.369 * [taylor]: Taking taylor expansion of PI in k
12.369 * [backup-simplify]: Simplify PI into PI
12.369 * [taylor]: Taking taylor expansion of n in k
12.369 * [backup-simplify]: Simplify n into n
12.369 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.369 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.369 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.369 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.370 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.370 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.370 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
12.371 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.371 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.371 * [taylor]: Taking taylor expansion of -1 in k
12.371 * [backup-simplify]: Simplify -1 into -1
12.371 * [taylor]: Taking taylor expansion of k in k
12.371 * [backup-simplify]: Simplify 0 into 0
12.371 * [backup-simplify]: Simplify 1 into 1
12.371 * [backup-simplify]: Simplify (/ -1 1) into -1
12.371 * [backup-simplify]: Simplify (sqrt 0) into 0
12.373 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.373 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
12.373 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
12.373 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.373 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.373 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.373 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.373 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.373 * [taylor]: Taking taylor expansion of 1/2 in n
12.373 * [backup-simplify]: Simplify 1/2 into 1/2
12.373 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.373 * [taylor]: Taking taylor expansion of k in n
12.374 * [backup-simplify]: Simplify k into k
12.374 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.374 * [taylor]: Taking taylor expansion of 1/2 in n
12.374 * [backup-simplify]: Simplify 1/2 into 1/2
12.374 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.374 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.374 * [taylor]: Taking taylor expansion of -2 in n
12.374 * [backup-simplify]: Simplify -2 into -2
12.374 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.374 * [taylor]: Taking taylor expansion of PI in n
12.374 * [backup-simplify]: Simplify PI into PI
12.374 * [taylor]: Taking taylor expansion of n in n
12.374 * [backup-simplify]: Simplify 0 into 0
12.374 * [backup-simplify]: Simplify 1 into 1
12.374 * [backup-simplify]: Simplify (/ PI 1) into PI
12.375 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.377 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.377 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.377 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.379 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.380 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.381 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.381 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.381 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.381 * [taylor]: Taking taylor expansion of -1 in n
12.381 * [backup-simplify]: Simplify -1 into -1
12.381 * [taylor]: Taking taylor expansion of k in n
12.381 * [backup-simplify]: Simplify k into k
12.381 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.381 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.382 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.382 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.383 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
12.383 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
12.383 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.383 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.383 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.383 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.383 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.383 * [taylor]: Taking taylor expansion of 1/2 in n
12.383 * [backup-simplify]: Simplify 1/2 into 1/2
12.383 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.383 * [taylor]: Taking taylor expansion of k in n
12.383 * [backup-simplify]: Simplify k into k
12.383 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.383 * [taylor]: Taking taylor expansion of 1/2 in n
12.384 * [backup-simplify]: Simplify 1/2 into 1/2
12.384 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.384 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.384 * [taylor]: Taking taylor expansion of -2 in n
12.384 * [backup-simplify]: Simplify -2 into -2
12.384 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.384 * [taylor]: Taking taylor expansion of PI in n
12.384 * [backup-simplify]: Simplify PI into PI
12.384 * [taylor]: Taking taylor expansion of n in n
12.384 * [backup-simplify]: Simplify 0 into 0
12.384 * [backup-simplify]: Simplify 1 into 1
12.384 * [backup-simplify]: Simplify (/ PI 1) into PI
12.385 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.386 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.386 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.386 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.387 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.389 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.390 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.390 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.390 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.390 * [taylor]: Taking taylor expansion of -1 in n
12.390 * [backup-simplify]: Simplify -1 into -1
12.390 * [taylor]: Taking taylor expansion of k in n
12.390 * [backup-simplify]: Simplify k into k
12.390 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.390 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.390 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.390 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.392 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
12.392 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
12.392 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
12.392 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
12.392 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.392 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.392 * [taylor]: Taking taylor expansion of 1/2 in k
12.392 * [backup-simplify]: Simplify 1/2 into 1/2
12.392 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.392 * [taylor]: Taking taylor expansion of k in k
12.392 * [backup-simplify]: Simplify 0 into 0
12.392 * [backup-simplify]: Simplify 1 into 1
12.392 * [backup-simplify]: Simplify (/ 1 1) into 1
12.392 * [taylor]: Taking taylor expansion of 1/2 in k
12.392 * [backup-simplify]: Simplify 1/2 into 1/2
12.392 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.392 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.392 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.393 * [taylor]: Taking taylor expansion of -2 in k
12.393 * [backup-simplify]: Simplify -2 into -2
12.393 * [taylor]: Taking taylor expansion of PI in k
12.393 * [backup-simplify]: Simplify PI into PI
12.393 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.394 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.394 * [taylor]: Taking taylor expansion of (log n) in k
12.394 * [taylor]: Taking taylor expansion of n in k
12.394 * [backup-simplify]: Simplify n into n
12.394 * [backup-simplify]: Simplify (log n) into (log n)
12.395 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.395 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.395 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.396 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.397 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
12.398 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.399 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.399 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.399 * [taylor]: Taking taylor expansion of -1 in k
12.399 * [backup-simplify]: Simplify -1 into -1
12.399 * [taylor]: Taking taylor expansion of k in k
12.399 * [backup-simplify]: Simplify 0 into 0
12.399 * [backup-simplify]: Simplify 1 into 1
12.399 * [backup-simplify]: Simplify (/ -1 1) into -1
12.400 * [backup-simplify]: Simplify (sqrt 0) into 0
12.401 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.402 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
12.404 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
12.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.405 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.407 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.407 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.408 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.408 * [backup-simplify]: Simplify (+ 0 0) into 0
12.410 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.411 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.413 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.414 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
12.414 * [taylor]: Taking taylor expansion of 0 in k
12.414 * [backup-simplify]: Simplify 0 into 0
12.414 * [backup-simplify]: Simplify 0 into 0
12.414 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.416 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.417 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
12.418 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
12.419 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.419 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.421 * [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
12.421 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.422 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.422 * [backup-simplify]: Simplify (+ 0 0) into 0
12.423 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.424 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.430 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.431 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.431 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
12.432 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
12.432 * [taylor]: Taking taylor expansion of 0 in k
12.432 * [backup-simplify]: Simplify 0 into 0
12.432 * [backup-simplify]: Simplify 0 into 0
12.432 * [backup-simplify]: Simplify 0 into 0
12.433 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.435 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.438 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
12.438 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
12.441 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
12.441 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1)
12.441 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
12.441 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
12.441 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.441 * [taylor]: Taking taylor expansion of 2 in n
12.442 * [backup-simplify]: Simplify 2 into 2
12.442 * [taylor]: Taking taylor expansion of (* n PI) in n
12.442 * [taylor]: Taking taylor expansion of n in n
12.442 * [backup-simplify]: Simplify 0 into 0
12.442 * [backup-simplify]: Simplify 1 into 1
12.442 * [taylor]: Taking taylor expansion of PI in n
12.442 * [backup-simplify]: Simplify PI into PI
12.442 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.442 * [taylor]: Taking taylor expansion of 2 in n
12.442 * [backup-simplify]: Simplify 2 into 2
12.442 * [taylor]: Taking taylor expansion of (* n PI) in n
12.442 * [taylor]: Taking taylor expansion of n in n
12.442 * [backup-simplify]: Simplify 0 into 0
12.442 * [backup-simplify]: Simplify 1 into 1
12.442 * [taylor]: Taking taylor expansion of PI in n
12.442 * [backup-simplify]: Simplify PI into PI
12.442 * [backup-simplify]: Simplify (* 0 PI) into 0
12.443 * [backup-simplify]: Simplify (* 2 0) into 0
12.443 * [backup-simplify]: Simplify 0 into 0
12.445 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.446 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.447 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.448 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.449 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.449 * [backup-simplify]: Simplify 0 into 0
12.450 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.451 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.451 * [backup-simplify]: Simplify 0 into 0
12.453 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.454 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.454 * [backup-simplify]: Simplify 0 into 0
12.456 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.457 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
12.457 * [backup-simplify]: Simplify 0 into 0
12.458 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.459 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
12.459 * [backup-simplify]: Simplify 0 into 0
12.460 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
12.461 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
12.461 * [backup-simplify]: Simplify 0 into 0
12.462 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
12.462 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
12.462 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
12.462 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.462 * [taylor]: Taking taylor expansion of 2 in n
12.462 * [backup-simplify]: Simplify 2 into 2
12.462 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.462 * [taylor]: Taking taylor expansion of PI in n
12.462 * [backup-simplify]: Simplify PI into PI
12.462 * [taylor]: Taking taylor expansion of n in n
12.462 * [backup-simplify]: Simplify 0 into 0
12.462 * [backup-simplify]: Simplify 1 into 1
12.462 * [backup-simplify]: Simplify (/ PI 1) into PI
12.462 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.462 * [taylor]: Taking taylor expansion of 2 in n
12.462 * [backup-simplify]: Simplify 2 into 2
12.462 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.462 * [taylor]: Taking taylor expansion of PI in n
12.462 * [backup-simplify]: Simplify PI into PI
12.462 * [taylor]: Taking taylor expansion of n in n
12.462 * [backup-simplify]: Simplify 0 into 0
12.462 * [backup-simplify]: Simplify 1 into 1
12.463 * [backup-simplify]: Simplify (/ PI 1) into PI
12.463 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.463 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.464 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.464 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.464 * [backup-simplify]: Simplify 0 into 0
12.465 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.465 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.465 * [backup-simplify]: Simplify 0 into 0
12.466 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.467 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.467 * [backup-simplify]: Simplify 0 into 0
12.468 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.468 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.468 * [backup-simplify]: Simplify 0 into 0
12.469 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.470 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.470 * [backup-simplify]: Simplify 0 into 0
12.471 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.472 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.472 * [backup-simplify]: Simplify 0 into 0
12.472 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
12.472 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
12.472 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
12.472 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.472 * [taylor]: Taking taylor expansion of -2 in n
12.472 * [backup-simplify]: Simplify -2 into -2
12.472 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.472 * [taylor]: Taking taylor expansion of PI in n
12.472 * [backup-simplify]: Simplify PI into PI
12.472 * [taylor]: Taking taylor expansion of n in n
12.472 * [backup-simplify]: Simplify 0 into 0
12.472 * [backup-simplify]: Simplify 1 into 1
12.473 * [backup-simplify]: Simplify (/ PI 1) into PI
12.473 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.473 * [taylor]: Taking taylor expansion of -2 in n
12.473 * [backup-simplify]: Simplify -2 into -2
12.473 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.473 * [taylor]: Taking taylor expansion of PI in n
12.473 * [backup-simplify]: Simplify PI into PI
12.473 * [taylor]: Taking taylor expansion of n in n
12.473 * [backup-simplify]: Simplify 0 into 0
12.473 * [backup-simplify]: Simplify 1 into 1
12.473 * [backup-simplify]: Simplify (/ PI 1) into PI
12.474 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.474 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.474 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.475 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.475 * [backup-simplify]: Simplify 0 into 0
12.475 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.476 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.476 * [backup-simplify]: Simplify 0 into 0
12.477 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.477 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.477 * [backup-simplify]: Simplify 0 into 0
12.478 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.479 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.479 * [backup-simplify]: Simplify 0 into 0
12.480 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.480 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.480 * [backup-simplify]: Simplify 0 into 0
12.481 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.482 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.482 * [backup-simplify]: Simplify 0 into 0
12.482 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
12.483 * * * [progress]: simplifying candidates
12.483 * * * * [progress]: [ 1 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 2 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 3 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 4 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 5 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 6 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 7 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 8 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))))>
12.483 * * * * [progress]: [ 9 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 10 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 11 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.483 * * * * [progress]: [ 12 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 13 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 14 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.483 * * * * [progress]: [ 15 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 16 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 17 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))>
12.483 * * * * [progress]: [ 18 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))))>
12.483 * * * * [progress]: [ 19 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.483 * * * * [progress]: [ 20 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.483 * * * * [progress]: [ 21 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.484 * * * * [progress]: [ 22 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.484 * * * * [progress]: [ 23 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.484 * * * * [progress]: [ 24 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.484 * * * * [progress]: [ 25 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 26 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.484 * * * * [progress]: [ 27 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 28 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 29 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 30 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 31 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 32 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 33 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 34 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 35 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 36 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 37 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 38 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 39 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 40 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 41 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 42 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 43 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.484 * * * * [progress]: [ 44 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.485 * * * * [progress]: [ 45 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.485 * * * * [progress]: [ 46 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.485 * * * * [progress]: [ 47 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.485 * * * * [progress]: [ 48 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.485 * * * * [progress]: [ 49 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.485 * * * * [progress]: [ 50 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.485 * * * * [progress]: [ 51 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.485 * * * * [progress]: [ 52 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.485 * * * * [progress]: [ 53 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (+ 1/2 1/2)))>
12.485 * * * * [progress]: [ 54 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (+ 1/2 (/ 1 2))))>
12.485 * * * * [progress]: [ 55 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (+ 1 1)))>
12.485 * * * * [progress]: [ 56 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (+ (/ 1 2) 1/2)))>
12.485 * * * * [progress]: [ 57 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (+ (/ 1 2) (/ 1 2))))>
12.485 * * * * [progress]: [ 58 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) 1/2))>
12.485 * * * * [progress]: [ 59 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1))>
12.485 * * * * [progress]: [ 60 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ 1 2)))>
12.485 * * * * [progress]: [ 61 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) 2))>
12.485 * * * * [progress]: [ 62 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (+ 1 1)))>
12.485 * * * * [progress]: [ 63 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1))>
12.485 * * * * [progress]: [ 64 / 327 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.485 * * * * [progress]: [ 65 / 327 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.485 * * * * [progress]: [ 66 / 327 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.485 * * * * [progress]: [ 67 / 327 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.485 * * * * [progress]: [ 68 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (cbrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.486 * * * * [progress]: [ 69 / 327 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.486 * * * * [progress]: [ 70 / 327 ] simplifiying candidate #<alt (λ (k n) (sqrt (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.486 * * * * [progress]: [ 71 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.486 * * * * [progress]: [ 72 / 327 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
12.486 * * * * [progress]: [ 73 / 327 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (sqrt (sqrt k)) (sqrt (sqrt k)))))>
12.486 * * * * [progress]: [ 74 / 327 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.486 * * * * [progress]: [ 75 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.486 * * * * [progress]: [ 76 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (* (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.486 * * * * [progress]: [ 77 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.486 * * * * [progress]: [ 78 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.486 * * * * [progress]: [ 79 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))))>
12.486 * * * * [progress]: [ 80 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))))>
12.486 * * * * [progress]: [ 81 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))))>
12.486 * * * * [progress]: [ 82 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))))>
12.486 * * * * [progress]: [ 83 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.486 * * * * [progress]: [ 84 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.486 * * * * [progress]: [ 85 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.486 * * * * [progress]: [ 86 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.486 * * * * [progress]: [ 87 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.486 * * * * [progress]: [ 88 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.487 * * * * [progress]: [ 89 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 90 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 91 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 92 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 93 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.487 * * * * [progress]: [ 94 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.487 * * * * [progress]: [ 95 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 96 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 97 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))))>
12.487 * * * * [progress]: [ 98 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))))>
12.487 * * * * [progress]: [ 99 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 100 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 101 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 102 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 103 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.487 * * * * [progress]: [ 104 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.487 * * * * [progress]: [ 105 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 106 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 107 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 108 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.487 * * * * [progress]: [ 109 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.487 * * * * [progress]: [ 110 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.488 * * * * [progress]: [ 111 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 112 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))))>
12.488 * * * * [progress]: [ 113 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 114 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 115 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1)))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
12.488 * * * * [progress]: [ 116 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 117 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 118 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) 1)) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) 1))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
12.488 * * * * [progress]: [ 119 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 120 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))))>
12.488 * * * * [progress]: [ 121 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 122 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 123 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1)))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))))>
12.488 * * * * [progress]: [ 124 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 125 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 126 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1)) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))))>
12.488 * * * * [progress]: [ 127 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))>
12.488 * * * * [progress]: [ 128 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))))>
12.488 * * * * [progress]: [ 129 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 130 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 131 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1)))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))))>
12.489 * * * * [progress]: [ 132 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 133 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 134 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1)) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))))>
12.489 * * * * [progress]: [ 135 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 136 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))))>
12.489 * * * * [progress]: [ 137 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 138 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 139 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt 1))) (sqrt (/ 1 (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.489 * * * * [progress]: [ 140 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 141 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 142 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 1)) (sqrt (/ 1 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.489 * * * * [progress]: [ 143 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))))>
12.489 * * * * [progress]: [ 144 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))))>
12.489 * * * * [progress]: [ 145 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.490 * * * * [progress]: [ 146 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.490 * * * * [progress]: [ 147 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
12.490 * * * * [progress]: [ 148 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.490 * * * * [progress]: [ 149 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.490 * * * * [progress]: [ 150 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
12.490 * * * * [progress]: [ 151 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt 1) (sqrt 1)) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.490 * * * * [progress]: [ 152 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))))))>
12.490 * * * * [progress]: [ 153 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.490 * * * * [progress]: [ 154 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.490 * * * * [progress]: [ 155 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* 1 1) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.491 * * * * [progress]: [ 156 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.491 * * * * [progress]: [ 157 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.491 * * * * [progress]: [ 158 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.491 * * * * [progress]: [ 159 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.491 * * * * [progress]: [ 160 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.491 * * * * [progress]: [ 161 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.491 * * * * [progress]: [ 162 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.491 * * * * [progress]: [ 163 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.491 * * * * [progress]: [ 164 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.491 * * * * [progress]: [ 165 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.491 * * * * [progress]: [ 166 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.491 * * * * [progress]: [ 167 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.492 * * * * [progress]: [ 168 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.492 * * * * [progress]: [ 169 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.492 * * * * [progress]: [ 170 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.492 * * * * [progress]: [ 171 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.492 * * * * [progress]: [ 172 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.492 * * * * [progress]: [ 173 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.492 * * * * [progress]: [ 174 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.492 * * * * [progress]: [ 175 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.492 * * * * [progress]: [ 176 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.493 * * * * [progress]: [ 177 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.493 * * * * [progress]: [ 178 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.493 * * * * [progress]: [ 179 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.493 * * * * [progress]: [ 180 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.493 * * * * [progress]: [ 181 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.493 * * * * [progress]: [ 182 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.493 * * * * [progress]: [ 183 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.493 * * * * [progress]: [ 184 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.494 * * * * [progress]: [ 185 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.494 * * * * [progress]: [ 186 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.494 * * * * [progress]: [ 187 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.494 * * * * [progress]: [ 188 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.494 * * * * [progress]: [ 189 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.494 * * * * [progress]: [ 190 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.494 * * * * [progress]: [ 191 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.494 * * * * [progress]: [ 192 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (* 2 1/2)))>
12.494 * * * * [progress]: [ 193 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (* 2 1)))>
12.494 * * * * [progress]: [ 194 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (* 2 (/ 1 2))))>
12.494 * * * * [progress]: [ 195 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.495 * * * * [progress]: [ 196 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.495 * * * * [progress]: [ 197 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.495 * * * * [progress]: [ 198 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k))))))>
12.495 * * * * [progress]: [ 199 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k))))))>
12.495 * * * * [progress]: [ 200 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k))))))>
12.495 * * * * [progress]: [ 201 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k)))))>
12.495 * * * * [progress]: [ 202 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k))))))>
12.495 * * * * [progress]: [ 203 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k)))))>
12.495 * * * * [progress]: [ 204 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k))))))>
12.495 * * * * [progress]: [ 205 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k))))))>
12.495 * * * * [progress]: [ 206 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k))))))>
12.495 * * * * [progress]: [ 207 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k)))))>
12.496 * * * * [progress]: [ 208 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k))))))>
12.496 * * * * [progress]: [ 209 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k)))))>
12.496 * * * * [progress]: [ 210 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))>
12.496 * * * * [progress]: [ 211 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k))))))>
12.496 * * * * [progress]: [ 212 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
12.496 * * * * [progress]: [ 213 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
12.496 * * * * [progress]: [ 214 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
12.496 * * * * [progress]: [ 215 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) 1))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
12.496 * * * * [progress]: [ 216 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
12.496 * * * * [progress]: [ 217 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k))))))>
12.496 * * * * [progress]: [ 218 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
12.496 * * * * [progress]: [ 219 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.497 * * * * [progress]: [ 220 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
12.497 * * * * [progress]: [ 221 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.497 * * * * [progress]: [ 222 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
12.497 * * * * [progress]: [ 223 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k))))))>
12.497 * * * * [progress]: [ 224 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
12.497 * * * * [progress]: [ 225 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.497 * * * * [progress]: [ 226 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
12.497 * * * * [progress]: [ 227 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.497 * * * * [progress]: [ 228 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))))>
12.497 * * * * [progress]: [ 229 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k))))))>
12.497 * * * * [progress]: [ 230 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
12.497 * * * * [progress]: [ 231 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt 1)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.498 * * * * [progress]: [ 232 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
12.498 * * * * [progress]: [ 233 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 1))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.498 * * * * [progress]: [ 234 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k))))))>
12.498 * * * * [progress]: [ 235 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k))))))>
12.498 * * * * [progress]: [ 236 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
12.498 * * * * [progress]: [ 237 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
12.498 * * * * [progress]: [ 238 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
12.498 * * * * [progress]: [ 239 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
12.498 * * * * [progress]: [ 240 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt 1)) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.498 * * * * [progress]: [ 241 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (/ 1 (sqrt k)))))>
12.498 * * * * [progress]: [ 242 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.498 * * * * [progress]: [ 243 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) 1) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.499 * * * * [progress]: [ 244 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 245 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 246 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 247 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 248 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 249 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 250 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 251 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 252 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 253 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 254 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.499 * * * * [progress]: [ 255 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 256 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 257 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 258 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 259 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 260 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 261 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 262 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 263 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 264 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) 1)) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 265 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 266 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.500 * * * * [progress]: [ 267 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 268 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 269 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 270 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1)) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 271 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 272 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 273 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 274 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 275 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 276 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1)) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 277 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 278 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 279 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 280 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 281 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 282 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 1)) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.501 * * * * [progress]: [ 283 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 284 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 285 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 286 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 287 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 288 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 289 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt 1) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 290 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 291 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 292 / 327 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.502 * * * * [progress]: [ 293 / 327 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))>
12.502 * * * * [progress]: [ 294 / 327 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt k))))>
12.502 * * * * [progress]: [ 295 / 327 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.502 * * * * [progress]: [ 296 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 297 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 298 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 299 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 300 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 301 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (exp (+ (log (* n 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 302 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (exp (log (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 303 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (log (exp (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 304 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 305 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.502 * * * * [progress]: [ 306 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 307 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 308 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 309 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 1 (* (* n 2) PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 310 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 311 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 312 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* (* n 2) 1) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 313 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 314 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 315 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 316 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (- (+ (* 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)))))>
12.503 * * * * [progress]: [ 317 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))))>
12.503 * * * * [progress]: [ 318 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))))>
12.503 * * * * [progress]: [ 319 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (- (+ (* 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))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 320 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.503 * * * * [progress]: [ 321 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.505 * * * * [progress]: [ 322 / 327 ] 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)))))))))))))))))))))))>
12.505 * * * * [progress]: [ 323 / 327 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
12.505 * * * * [progress]: [ 324 / 327 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
12.505 * * * * [progress]: [ 325 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.505 * * * * [progress]: [ 326 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.505 * * * * [progress]: [ 327 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.510 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (+ 1/2 1/2)
  (+ 1/2 (/ 1 2))
  (+ 1 1)
  (+ (/ 1 2) 1/2)
  (+ (/ 1 2) (/ 1 2))
  (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (+ 1 1)
  (+ (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))
  (log (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))
  (exp (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))
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  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1)))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt 1))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 1)))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt 1))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) 1)
  (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (real->posit16 (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (+ (log n) (log 2)) (log PI))
  (+ (log (* n 2)) (log PI))
  (log (* (* n 2) PI))
  (exp (* (* n 2) PI))
  (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))
  (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) 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 PI) (cbrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) 1)
  (* 2 PI)
  (real->posit16 (* (* n 2) PI))
  (- (+ (* 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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 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)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 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))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
12.519 * * [simplify]: iteration 0: 455 enodes
12.735 * * [simplify]: iteration 1: 946 enodes
13.129 * * [simplify]: iteration 2: 3062 enodes
14.033 * * [simplify]: iteration complete: 5001 enodes
14.033 * * [simplify]: Extracting #0: cost 144 inf + 0
14.036 * * [simplify]: Extracting #1: cost 716 inf + 2
14.043 * * [simplify]: Extracting #2: cost 1326 inf + 1040
14.058 * * [simplify]: Extracting #3: cost 1392 inf + 31738
14.107 * * [simplify]: Extracting #4: cost 929 inf + 189942
14.182 * * [simplify]: Extracting #5: cost 433 inf + 384292
14.296 * * [simplify]: Extracting #6: cost 213 inf + 522343
14.436 * * [simplify]: Extracting #7: cost 33 inf + 640088
14.554 * * [simplify]: Extracting #8: cost 0 inf + 661683
14.719 * * [simplify]: Extracting #9: cost 0 inf + 660563
14.857 * * [simplify]: Extracting #10: cost 0 inf + 660483
15.049 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ k 2))
  (pow (* PI (+ n n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* PI (+ n n)) (sqrt (- 1/2 (/ k 2))))
  (* PI (+ n n))
  (pow (* PI (+ n n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* PI (+ n n)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* PI (+ n n))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ (- k) 2))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ (- k) 2))
  (pow (+ n n) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (exp (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (* (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (pow (* PI (+ n n)) (- 1/4 (/ k 4)))
  (pow (* PI (+ n n)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ k 2))
  (pow (* PI (+ n n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* PI (+ n n)) (sqrt (- 1/2 (/ k 2))))
  (* PI (+ n n))
  (pow (* PI (+ n n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* PI (+ n n)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* PI (+ n n))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ (- k) 2))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ (- k) 2))
  (pow (+ n n) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (exp (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (* (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (pow (* PI (+ n n)) (- 1/4 (/ k 4)))
  (pow (* PI (+ n n)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  1
  1
  2
  1
  1
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  2
  (- (* (- 1/2 (/ k 2)) (log (* PI (+ n n)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* PI (+ n n)))) (log (sqrt k)))
  (exp (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (pow (* PI (+ n n)) (- 1/2 (/ k 2)))
  (sqrt k)
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (cbrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (sqrt (* PI (+ n n))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (cbrt (sqrt k)))
  (/ (sqrt (* PI (+ n n))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (cbrt (sqrt k)))
  (/ (sqrt (* PI (+ n n))) (fabs (cbrt k)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (cbrt k)))
  (/ (sqrt (* PI (+ n n))) (fabs (cbrt k)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (cbrt k)))
  (/ (sqrt (* PI (+ n n))) (sqrt (sqrt k)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))
  (/ (sqrt (* PI (+ n n))) (sqrt (sqrt k)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))
  (/ (sqrt (* PI (+ n n))) (sqrt (sqrt k)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))
  (/ (sqrt (* PI (+ n n))) (sqrt (sqrt k)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))
  (sqrt (* PI (+ n n)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))
  (sqrt (* PI (+ n n)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))
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  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (fabs (cbrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))))
  (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ 1 (fabs (cbrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (fabs (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (pow (* PI (+ n n)) (- 1/4 (/ k 4)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (pow (* PI (+ n n)) (- 1/4 (/ k 4)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (* (sqrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (sqrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (cbrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (cbrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))
  (* (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (cbrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt k))))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (real->posit16 (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* PI (+ n n))
  (* PI (+ n n))
  (log (* PI (+ n n)))
  (log (* PI (+ n n)))
  (log (* PI (+ n n)))
  (exp (* PI (+ n n)))
  (* (* (* n n) n) (* (* 8 PI) (* PI PI)))
  (* (* PI (+ n n)) (* (* PI (+ n n)) (* PI (+ n n))))
  (* (cbrt (* PI (+ n n))) (cbrt (* PI (+ n n))))
  (cbrt (* PI (+ n n)))
  (* (* PI (+ n n)) (* (* PI (+ n n)) (* PI (+ n n))))
  (sqrt (* PI (+ n n)))
  (sqrt (* PI (+ n n)))
  (* (+ n n) (* (cbrt PI) (cbrt PI)))
  (* (+ n n) (sqrt PI))
  (+ n n)
  (+ PI PI)
  (real->posit16 (* PI (+ n n)))
  (+ (+ (+ (* (* (sqrt (* PI (+ n n))) (* (log (+ PI PI)) (log (+ PI PI)))) (* (* k k) 1/8)) (sqrt (* PI (+ n n)))) (- (* (* 1/8 (* (* (log n) (log n)) (sqrt (* PI (+ n n))))) (* k k)) (* 1/2 (+ (* (log n) (* k (sqrt (* PI (+ n n))))) (* (* k (sqrt (* PI (+ n n)))) (log (+ PI PI))))))) (* (* (log (+ PI PI)) (sqrt (* PI (+ n n)))) (* (* (log n) (* k k)) 1/4)))
  (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n)))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2))))
  (+ (+ (+ (* (* (sqrt (* PI (+ n n))) (* (log (+ PI PI)) (log (+ PI PI)))) (* (* k k) 1/8)) (sqrt (* PI (+ n n)))) (- (* (* 1/8 (* (* (log n) (log n)) (sqrt (* PI (+ n n))))) (* k k)) (* 1/2 (+ (* (log n) (* k (sqrt (* PI (+ n n))))) (* (* k (sqrt (* PI (+ n n)))) (log (+ PI PI))))))) (* (* (log (+ PI PI)) (sqrt (* PI (+ n n)))) (* (* (log n) (* k k)) 1/4)))
  (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n)))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2))))
  (- (- (* (* +nan.0 (log (+ PI PI))) (* (sqrt (* PI (+ n n))) (* (log n) (* k k)))) (+ (- (* (* (log (+ PI PI)) (* (sqrt (* PI (+ n n))) (* k k))) +nan.0) (* (* (* (sqrt (* PI (+ n n))) +nan.0) (* (log n) (log n))) (* k k))) (- (* (* k (sqrt (* PI (+ n n)))) +nan.0) (+ (- (* (sqrt (* PI (+ n n))) +nan.0) (* +nan.0 (* (* (log (+ PI PI)) (log (+ PI PI))) (* (sqrt (* PI (+ n n))) (* k k))))) (+ (- (* +nan.0 (* (sqrt (* PI (+ n n))) (* (log n) (* k k)))) (* (* (sqrt (* PI (+ n n))) (* k k)) +nan.0)) (* +nan.0 (- (* (* k (sqrt (* PI (+ n n)))) (log (+ PI PI))) (* (log n) (* k (sqrt (* PI (+ n n)))))))))))))
  (- (- (* (/ (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))) (* k k)) (/ +nan.0 k)) (* +nan.0 (- (/ (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))) k) (/ (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))) (* k k))))))
  (+ (* +nan.0 (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2)))) k))) (* +nan.0 (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2)))) (* k k)) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2)))))))
  (* PI (+ n n))
  (* PI (+ n n))
  (* PI (+ n n))
15.122 * * * [progress]: adding candidates to table
16.693 * * [progress]: iteration 4 / 4
16.693 * * * [progress]: picking best candidate
16.727 * * * * [pick]: Picked  #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
16.727 * * * [progress]: localizing error
16.816 * * * [progress]: generating rewritten candidates
16.816 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1)
16.848 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 1)
16.882 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1)
16.894 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1)
16.920 * * * [progress]: generating series expansions
16.920 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1)
16.920 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
16.920 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
16.920 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
16.920 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
16.920 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
16.920 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
16.920 * [taylor]: Taking taylor expansion of 1/2 in k
16.920 * [backup-simplify]: Simplify 1/2 into 1/2
16.920 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
16.920 * [taylor]: Taking taylor expansion of 1/2 in k
16.920 * [backup-simplify]: Simplify 1/2 into 1/2
16.920 * [taylor]: Taking taylor expansion of k in k
16.920 * [backup-simplify]: Simplify 0 into 0
16.920 * [backup-simplify]: Simplify 1 into 1
16.920 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
16.920 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
16.920 * [taylor]: Taking taylor expansion of 2 in k
16.920 * [backup-simplify]: Simplify 2 into 2
16.920 * [taylor]: Taking taylor expansion of (* n PI) in k
16.920 * [taylor]: Taking taylor expansion of n in k
16.920 * [backup-simplify]: Simplify n into n
16.920 * [taylor]: Taking taylor expansion of PI in k
16.920 * [backup-simplify]: Simplify PI into PI
16.921 * [backup-simplify]: Simplify (* n PI) into (* n PI)
16.921 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
16.921 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
16.921 * [backup-simplify]: Simplify (* 1/2 0) into 0
16.921 * [backup-simplify]: Simplify (- 0) into 0
16.922 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.922 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
16.922 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
16.922 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
16.922 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
16.922 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
16.922 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
16.922 * [taylor]: Taking taylor expansion of 1/2 in n
16.922 * [backup-simplify]: Simplify 1/2 into 1/2
16.922 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
16.922 * [taylor]: Taking taylor expansion of 1/2 in n
16.922 * [backup-simplify]: Simplify 1/2 into 1/2
16.922 * [taylor]: Taking taylor expansion of k in n
16.922 * [backup-simplify]: Simplify k into k
16.922 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.922 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.922 * [taylor]: Taking taylor expansion of 2 in n
16.922 * [backup-simplify]: Simplify 2 into 2
16.922 * [taylor]: Taking taylor expansion of (* n PI) in n
16.922 * [taylor]: Taking taylor expansion of n in n
16.922 * [backup-simplify]: Simplify 0 into 0
16.922 * [backup-simplify]: Simplify 1 into 1
16.922 * [taylor]: Taking taylor expansion of PI in n
16.922 * [backup-simplify]: Simplify PI into PI
16.923 * [backup-simplify]: Simplify (* 0 PI) into 0
16.923 * [backup-simplify]: Simplify (* 2 0) into 0
16.924 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.925 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.926 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.926 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
16.926 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
16.926 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
16.927 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.927 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
16.928 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
16.928 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
16.928 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
16.928 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
16.928 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
16.928 * [taylor]: Taking taylor expansion of 1/2 in n
16.928 * [backup-simplify]: Simplify 1/2 into 1/2
16.928 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
16.928 * [taylor]: Taking taylor expansion of 1/2 in n
16.928 * [backup-simplify]: Simplify 1/2 into 1/2
16.928 * [taylor]: Taking taylor expansion of k in n
16.928 * [backup-simplify]: Simplify k into k
16.928 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.928 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.928 * [taylor]: Taking taylor expansion of 2 in n
16.928 * [backup-simplify]: Simplify 2 into 2
16.928 * [taylor]: Taking taylor expansion of (* n PI) in n
16.928 * [taylor]: Taking taylor expansion of n in n
16.928 * [backup-simplify]: Simplify 0 into 0
16.928 * [backup-simplify]: Simplify 1 into 1
16.928 * [taylor]: Taking taylor expansion of PI in n
16.928 * [backup-simplify]: Simplify PI into PI
16.929 * [backup-simplify]: Simplify (* 0 PI) into 0
16.929 * [backup-simplify]: Simplify (* 2 0) into 0
16.930 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.931 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.932 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.932 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
16.932 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
16.932 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
16.933 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.933 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
16.934 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
16.934 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
16.934 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
16.934 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
16.934 * [taylor]: Taking taylor expansion of 1/2 in k
16.934 * [backup-simplify]: Simplify 1/2 into 1/2
16.934 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
16.934 * [taylor]: Taking taylor expansion of 1/2 in k
16.934 * [backup-simplify]: Simplify 1/2 into 1/2
16.934 * [taylor]: Taking taylor expansion of k in k
16.934 * [backup-simplify]: Simplify 0 into 0
16.934 * [backup-simplify]: Simplify 1 into 1
16.934 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
16.934 * [taylor]: Taking taylor expansion of (log n) in k
16.934 * [taylor]: Taking taylor expansion of n in k
16.934 * [backup-simplify]: Simplify n into n
16.935 * [backup-simplify]: Simplify (log n) into (log n)
16.935 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
16.935 * [taylor]: Taking taylor expansion of (* 2 PI) in k
16.935 * [taylor]: Taking taylor expansion of 2 in k
16.935 * [backup-simplify]: Simplify 2 into 2
16.935 * [taylor]: Taking taylor expansion of PI in k
16.935 * [backup-simplify]: Simplify PI into PI
16.935 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.936 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.936 * [backup-simplify]: Simplify (* 1/2 0) into 0
16.936 * [backup-simplify]: Simplify (- 0) into 0
16.937 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
16.937 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.938 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
16.939 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
16.939 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
16.940 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.941 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
16.942 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.942 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
16.942 * [backup-simplify]: Simplify (- 0) into 0
16.943 * [backup-simplify]: Simplify (+ 0 0) into 0
16.944 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.945 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
16.946 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.946 * [taylor]: Taking taylor expansion of 0 in k
16.946 * [backup-simplify]: Simplify 0 into 0
16.946 * [backup-simplify]: Simplify 0 into 0
16.946 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
16.947 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.948 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.948 * [backup-simplify]: Simplify (+ 0 0) into 0
16.949 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
16.949 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.949 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.950 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
16.952 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
16.954 * [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)))))))
16.955 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.955 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.957 * [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
16.958 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
16.958 * [backup-simplify]: Simplify (- 0) into 0
16.958 * [backup-simplify]: Simplify (+ 0 0) into 0
16.959 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.960 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.962 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.962 * [taylor]: Taking taylor expansion of 0 in k
16.962 * [backup-simplify]: Simplify 0 into 0
16.962 * [backup-simplify]: Simplify 0 into 0
16.962 * [backup-simplify]: Simplify 0 into 0
16.964 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
16.965 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.969 * [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
16.970 * [backup-simplify]: Simplify (+ 0 0) into 0
16.971 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
16.971 * [backup-simplify]: Simplify (- 0) into 0
16.972 * [backup-simplify]: Simplify (+ 0 0) into 0
16.974 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.977 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 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)))))
16.983 * [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)))))
16.992 * [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)))))
16.993 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
16.993 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
16.993 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
16.993 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
16.993 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
16.993 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
16.993 * [taylor]: Taking taylor expansion of 1/2 in k
16.993 * [backup-simplify]: Simplify 1/2 into 1/2
16.993 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
16.993 * [taylor]: Taking taylor expansion of 1/2 in k
16.993 * [backup-simplify]: Simplify 1/2 into 1/2
16.993 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.993 * [taylor]: Taking taylor expansion of k in k
16.993 * [backup-simplify]: Simplify 0 into 0
16.993 * [backup-simplify]: Simplify 1 into 1
16.993 * [backup-simplify]: Simplify (/ 1 1) into 1
16.993 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
16.993 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
16.993 * [taylor]: Taking taylor expansion of 2 in k
16.993 * [backup-simplify]: Simplify 2 into 2
16.994 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.994 * [taylor]: Taking taylor expansion of PI in k
16.994 * [backup-simplify]: Simplify PI into PI
16.994 * [taylor]: Taking taylor expansion of n in k
16.994 * [backup-simplify]: Simplify n into n
16.994 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.994 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
16.994 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
16.994 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
16.995 * [backup-simplify]: Simplify (- 1/2) into -1/2
16.995 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
16.995 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
16.995 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
16.995 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
16.995 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
16.995 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
16.996 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
16.996 * [taylor]: Taking taylor expansion of 1/2 in n
16.996 * [backup-simplify]: Simplify 1/2 into 1/2
16.996 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
16.996 * [taylor]: Taking taylor expansion of 1/2 in n
16.996 * [backup-simplify]: Simplify 1/2 into 1/2
16.996 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.996 * [taylor]: Taking taylor expansion of k in n
16.996 * [backup-simplify]: Simplify k into k
16.996 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.996 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.996 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.996 * [taylor]: Taking taylor expansion of 2 in n
16.996 * [backup-simplify]: Simplify 2 into 2
16.996 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.996 * [taylor]: Taking taylor expansion of PI in n
16.996 * [backup-simplify]: Simplify PI into PI
16.996 * [taylor]: Taking taylor expansion of n in n
16.996 * [backup-simplify]: Simplify 0 into 0
16.996 * [backup-simplify]: Simplify 1 into 1
16.997 * [backup-simplify]: Simplify (/ PI 1) into PI
16.997 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.998 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.998 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
16.998 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
16.998 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
16.999 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.000 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
17.000 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.001 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
17.001 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
17.001 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
17.001 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
17.001 * [taylor]: Taking taylor expansion of 1/2 in n
17.001 * [backup-simplify]: Simplify 1/2 into 1/2
17.001 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.001 * [taylor]: Taking taylor expansion of 1/2 in n
17.001 * [backup-simplify]: Simplify 1/2 into 1/2
17.001 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.001 * [taylor]: Taking taylor expansion of k in n
17.001 * [backup-simplify]: Simplify k into k
17.001 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.001 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
17.001 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.001 * [taylor]: Taking taylor expansion of 2 in n
17.001 * [backup-simplify]: Simplify 2 into 2
17.001 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.001 * [taylor]: Taking taylor expansion of PI in n
17.001 * [backup-simplify]: Simplify PI into PI
17.001 * [taylor]: Taking taylor expansion of n in n
17.001 * [backup-simplify]: Simplify 0 into 0
17.001 * [backup-simplify]: Simplify 1 into 1
17.001 * [backup-simplify]: Simplify (/ PI 1) into PI
17.001 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.002 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.002 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.002 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
17.002 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
17.003 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.004 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
17.005 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.005 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
17.005 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
17.005 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
17.005 * [taylor]: Taking taylor expansion of 1/2 in k
17.005 * [backup-simplify]: Simplify 1/2 into 1/2
17.005 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.005 * [taylor]: Taking taylor expansion of 1/2 in k
17.005 * [backup-simplify]: Simplify 1/2 into 1/2
17.005 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.005 * [taylor]: Taking taylor expansion of k in k
17.005 * [backup-simplify]: Simplify 0 into 0
17.005 * [backup-simplify]: Simplify 1 into 1
17.005 * [backup-simplify]: Simplify (/ 1 1) into 1
17.005 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
17.005 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.005 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.005 * [taylor]: Taking taylor expansion of 2 in k
17.005 * [backup-simplify]: Simplify 2 into 2
17.005 * [taylor]: Taking taylor expansion of PI in k
17.005 * [backup-simplify]: Simplify PI into PI
17.006 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.006 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.006 * [taylor]: Taking taylor expansion of (log n) in k
17.006 * [taylor]: Taking taylor expansion of n in k
17.006 * [backup-simplify]: Simplify n into n
17.006 * [backup-simplify]: Simplify (log n) into (log n)
17.007 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.007 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.007 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.007 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.008 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
17.009 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
17.009 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.010 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.011 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.011 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.017 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.017 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.017 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.018 * [backup-simplify]: Simplify (- 0) into 0
17.018 * [backup-simplify]: Simplify (+ 0 0) into 0
17.019 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.019 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
17.021 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.021 * [taylor]: Taking taylor expansion of 0 in k
17.021 * [backup-simplify]: Simplify 0 into 0
17.021 * [backup-simplify]: Simplify 0 into 0
17.021 * [backup-simplify]: Simplify 0 into 0
17.021 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.022 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.024 * [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
17.024 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.025 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.025 * [backup-simplify]: Simplify (- 0) into 0
17.025 * [backup-simplify]: Simplify (+ 0 0) into 0
17.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.027 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
17.028 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.028 * [taylor]: Taking taylor expansion of 0 in k
17.028 * [backup-simplify]: Simplify 0 into 0
17.028 * [backup-simplify]: Simplify 0 into 0
17.029 * [backup-simplify]: Simplify 0 into 0
17.029 * [backup-simplify]: Simplify 0 into 0
17.030 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.030 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.034 * [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
17.034 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.035 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.035 * [backup-simplify]: Simplify (- 0) into 0
17.035 * [backup-simplify]: Simplify (+ 0 0) into 0
17.036 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.038 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
17.040 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 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
17.040 * [taylor]: Taking taylor expansion of 0 in k
17.040 * [backup-simplify]: Simplify 0 into 0
17.040 * [backup-simplify]: Simplify 0 into 0
17.042 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
17.042 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
17.042 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
17.042 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
17.042 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
17.042 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
17.042 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.042 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.042 * [taylor]: Taking taylor expansion of 1/2 in k
17.042 * [backup-simplify]: Simplify 1/2 into 1/2
17.042 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.042 * [taylor]: Taking taylor expansion of k in k
17.042 * [backup-simplify]: Simplify 0 into 0
17.042 * [backup-simplify]: Simplify 1 into 1
17.043 * [backup-simplify]: Simplify (/ 1 1) into 1
17.043 * [taylor]: Taking taylor expansion of 1/2 in k
17.043 * [backup-simplify]: Simplify 1/2 into 1/2
17.043 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
17.043 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
17.043 * [taylor]: Taking taylor expansion of -2 in k
17.043 * [backup-simplify]: Simplify -2 into -2
17.043 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.043 * [taylor]: Taking taylor expansion of PI in k
17.043 * [backup-simplify]: Simplify PI into PI
17.043 * [taylor]: Taking taylor expansion of n in k
17.043 * [backup-simplify]: Simplify n into n
17.043 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.043 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
17.043 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
17.044 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.044 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.044 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
17.044 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
17.044 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.045 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.045 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.045 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.045 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.045 * [taylor]: Taking taylor expansion of 1/2 in n
17.045 * [backup-simplify]: Simplify 1/2 into 1/2
17.045 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.045 * [taylor]: Taking taylor expansion of k in n
17.045 * [backup-simplify]: Simplify k into k
17.045 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.045 * [taylor]: Taking taylor expansion of 1/2 in n
17.045 * [backup-simplify]: Simplify 1/2 into 1/2
17.045 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.045 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.045 * [taylor]: Taking taylor expansion of -2 in n
17.045 * [backup-simplify]: Simplify -2 into -2
17.045 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.045 * [taylor]: Taking taylor expansion of PI in n
17.045 * [backup-simplify]: Simplify PI into PI
17.045 * [taylor]: Taking taylor expansion of n in n
17.045 * [backup-simplify]: Simplify 0 into 0
17.045 * [backup-simplify]: Simplify 1 into 1
17.046 * [backup-simplify]: Simplify (/ PI 1) into PI
17.046 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.047 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.047 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.048 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.050 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.051 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
17.052 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.052 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.052 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.052 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.052 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.053 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.053 * [taylor]: Taking taylor expansion of 1/2 in n
17.053 * [backup-simplify]: Simplify 1/2 into 1/2
17.053 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.053 * [taylor]: Taking taylor expansion of k in n
17.053 * [backup-simplify]: Simplify k into k
17.053 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.053 * [taylor]: Taking taylor expansion of 1/2 in n
17.053 * [backup-simplify]: Simplify 1/2 into 1/2
17.053 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.053 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.053 * [taylor]: Taking taylor expansion of -2 in n
17.053 * [backup-simplify]: Simplify -2 into -2
17.053 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.053 * [taylor]: Taking taylor expansion of PI in n
17.053 * [backup-simplify]: Simplify PI into PI
17.053 * [taylor]: Taking taylor expansion of n in n
17.053 * [backup-simplify]: Simplify 0 into 0
17.053 * [backup-simplify]: Simplify 1 into 1
17.054 * [backup-simplify]: Simplify (/ PI 1) into PI
17.054 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.055 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.055 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.056 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.057 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.058 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
17.059 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.060 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
17.060 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
17.060 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.060 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.060 * [taylor]: Taking taylor expansion of 1/2 in k
17.060 * [backup-simplify]: Simplify 1/2 into 1/2
17.060 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.060 * [taylor]: Taking taylor expansion of k in k
17.060 * [backup-simplify]: Simplify 0 into 0
17.060 * [backup-simplify]: Simplify 1 into 1
17.060 * [backup-simplify]: Simplify (/ 1 1) into 1
17.060 * [taylor]: Taking taylor expansion of 1/2 in k
17.060 * [backup-simplify]: Simplify 1/2 into 1/2
17.060 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
17.060 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
17.060 * [taylor]: Taking taylor expansion of (* -2 PI) in k
17.060 * [taylor]: Taking taylor expansion of -2 in k
17.060 * [backup-simplify]: Simplify -2 into -2
17.061 * [taylor]: Taking taylor expansion of PI in k
17.061 * [backup-simplify]: Simplify PI into PI
17.061 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.062 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.062 * [taylor]: Taking taylor expansion of (log n) in k
17.062 * [taylor]: Taking taylor expansion of n in k
17.062 * [backup-simplify]: Simplify n into n
17.062 * [backup-simplify]: Simplify (log n) into (log n)
17.063 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.063 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.063 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.064 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
17.066 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
17.067 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.068 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.069 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.070 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
17.071 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
17.071 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.071 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.071 * [backup-simplify]: Simplify (+ 0 0) into 0
17.072 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.073 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
17.074 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.074 * [taylor]: Taking taylor expansion of 0 in k
17.074 * [backup-simplify]: Simplify 0 into 0
17.074 * [backup-simplify]: Simplify 0 into 0
17.074 * [backup-simplify]: Simplify 0 into 0
17.075 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.075 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
17.077 * [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
17.077 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.078 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.078 * [backup-simplify]: Simplify (+ 0 0) into 0
17.079 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.080 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
17.082 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.082 * [taylor]: Taking taylor expansion of 0 in k
17.082 * [backup-simplify]: Simplify 0 into 0
17.082 * [backup-simplify]: Simplify 0 into 0
17.082 * [backup-simplify]: Simplify 0 into 0
17.082 * [backup-simplify]: Simplify 0 into 0
17.083 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.083 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.087 * [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
17.087 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.088 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.088 * [backup-simplify]: Simplify (+ 0 0) into 0
17.089 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.091 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
17.094 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.094 * [taylor]: Taking taylor expansion of 0 in k
17.094 * [backup-simplify]: Simplify 0 into 0
17.094 * [backup-simplify]: Simplify 0 into 0
17.096 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
17.096 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 1)
17.096 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
17.096 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
17.096 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
17.096 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
17.096 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
17.096 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.096 * [taylor]: Taking taylor expansion of 1/2 in k
17.096 * [backup-simplify]: Simplify 1/2 into 1/2
17.096 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.096 * [taylor]: Taking taylor expansion of 1/2 in k
17.096 * [backup-simplify]: Simplify 1/2 into 1/2
17.096 * [taylor]: Taking taylor expansion of k in k
17.096 * [backup-simplify]: Simplify 0 into 0
17.096 * [backup-simplify]: Simplify 1 into 1
17.096 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
17.096 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
17.096 * [taylor]: Taking taylor expansion of 2 in k
17.096 * [backup-simplify]: Simplify 2 into 2
17.096 * [taylor]: Taking taylor expansion of (* n PI) in k
17.096 * [taylor]: Taking taylor expansion of n in k
17.096 * [backup-simplify]: Simplify n into n
17.097 * [taylor]: Taking taylor expansion of PI in k
17.097 * [backup-simplify]: Simplify PI into PI
17.097 * [backup-simplify]: Simplify (* n PI) into (* n PI)
17.097 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
17.097 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
17.097 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.098 * [backup-simplify]: Simplify (- 0) into 0
17.098 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.098 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
17.098 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
17.098 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
17.098 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
17.098 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
17.098 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.098 * [taylor]: Taking taylor expansion of 1/2 in n
17.098 * [backup-simplify]: Simplify 1/2 into 1/2
17.098 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.098 * [taylor]: Taking taylor expansion of 1/2 in n
17.099 * [backup-simplify]: Simplify 1/2 into 1/2
17.099 * [taylor]: Taking taylor expansion of k in n
17.099 * [backup-simplify]: Simplify k into k
17.099 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.099 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.099 * [taylor]: Taking taylor expansion of 2 in n
17.099 * [backup-simplify]: Simplify 2 into 2
17.099 * [taylor]: Taking taylor expansion of (* n PI) in n
17.099 * [taylor]: Taking taylor expansion of n in n
17.099 * [backup-simplify]: Simplify 0 into 0
17.099 * [backup-simplify]: Simplify 1 into 1
17.099 * [taylor]: Taking taylor expansion of PI in n
17.099 * [backup-simplify]: Simplify PI into PI
17.099 * [backup-simplify]: Simplify (* 0 PI) into 0
17.100 * [backup-simplify]: Simplify (* 2 0) into 0
17.101 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.103 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.104 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.104 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.104 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.104 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.106 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.107 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
17.108 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
17.108 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
17.108 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
17.108 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
17.108 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.108 * [taylor]: Taking taylor expansion of 1/2 in n
17.108 * [backup-simplify]: Simplify 1/2 into 1/2
17.108 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.108 * [taylor]: Taking taylor expansion of 1/2 in n
17.108 * [backup-simplify]: Simplify 1/2 into 1/2
17.108 * [taylor]: Taking taylor expansion of k in n
17.108 * [backup-simplify]: Simplify k into k
17.108 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.108 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.108 * [taylor]: Taking taylor expansion of 2 in n
17.108 * [backup-simplify]: Simplify 2 into 2
17.108 * [taylor]: Taking taylor expansion of (* n PI) in n
17.108 * [taylor]: Taking taylor expansion of n in n
17.109 * [backup-simplify]: Simplify 0 into 0
17.109 * [backup-simplify]: Simplify 1 into 1
17.109 * [taylor]: Taking taylor expansion of PI in n
17.109 * [backup-simplify]: Simplify PI into PI
17.109 * [backup-simplify]: Simplify (* 0 PI) into 0
17.110 * [backup-simplify]: Simplify (* 2 0) into 0
17.111 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.113 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.114 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.114 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.114 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.114 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.115 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.117 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
17.118 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
17.118 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
17.118 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
17.118 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.118 * [taylor]: Taking taylor expansion of 1/2 in k
17.118 * [backup-simplify]: Simplify 1/2 into 1/2
17.118 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.118 * [taylor]: Taking taylor expansion of 1/2 in k
17.118 * [backup-simplify]: Simplify 1/2 into 1/2
17.118 * [taylor]: Taking taylor expansion of k in k
17.118 * [backup-simplify]: Simplify 0 into 0
17.118 * [backup-simplify]: Simplify 1 into 1
17.118 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
17.118 * [taylor]: Taking taylor expansion of (log n) in k
17.118 * [taylor]: Taking taylor expansion of n in k
17.118 * [backup-simplify]: Simplify n into n
17.118 * [backup-simplify]: Simplify (log n) into (log n)
17.118 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.118 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.118 * [taylor]: Taking taylor expansion of 2 in k
17.118 * [backup-simplify]: Simplify 2 into 2
17.118 * [taylor]: Taking taylor expansion of PI in k
17.118 * [backup-simplify]: Simplify PI into PI
17.119 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.120 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.120 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.121 * [backup-simplify]: Simplify (- 0) into 0
17.121 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.122 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.123 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
17.125 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
17.126 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
17.127 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.128 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
17.130 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.131 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
17.131 * [backup-simplify]: Simplify (- 0) into 0
17.131 * [backup-simplify]: Simplify (+ 0 0) into 0
17.133 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.141 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
17.143 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
17.143 * [taylor]: Taking taylor expansion of 0 in k
17.143 * [backup-simplify]: Simplify 0 into 0
17.143 * [backup-simplify]: Simplify 0 into 0
17.144 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
17.145 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.147 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.147 * [backup-simplify]: Simplify (+ 0 0) into 0
17.148 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
17.148 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.149 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.150 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
17.153 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
17.156 * [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)))))))
17.158 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.159 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.163 * [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
17.164 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
17.164 * [backup-simplify]: Simplify (- 0) into 0
17.165 * [backup-simplify]: Simplify (+ 0 0) into 0
17.166 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.168 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
17.170 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.170 * [taylor]: Taking taylor expansion of 0 in k
17.170 * [backup-simplify]: Simplify 0 into 0
17.171 * [backup-simplify]: Simplify 0 into 0
17.171 * [backup-simplify]: Simplify 0 into 0
17.173 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
17.174 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.178 * [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
17.178 * [backup-simplify]: Simplify (+ 0 0) into 0
17.179 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
17.180 * [backup-simplify]: Simplify (- 0) into 0
17.181 * [backup-simplify]: Simplify (+ 0 0) into 0
17.183 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
17.187 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 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)))))
17.192 * [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)))))
17.202 * [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)))))
17.202 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
17.202 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
17.202 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
17.202 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
17.202 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
17.203 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
17.203 * [taylor]: Taking taylor expansion of 1/2 in k
17.203 * [backup-simplify]: Simplify 1/2 into 1/2
17.203 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.203 * [taylor]: Taking taylor expansion of 1/2 in k
17.203 * [backup-simplify]: Simplify 1/2 into 1/2
17.203 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.203 * [taylor]: Taking taylor expansion of k in k
17.203 * [backup-simplify]: Simplify 0 into 0
17.203 * [backup-simplify]: Simplify 1 into 1
17.203 * [backup-simplify]: Simplify (/ 1 1) into 1
17.203 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
17.203 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
17.203 * [taylor]: Taking taylor expansion of 2 in k
17.203 * [backup-simplify]: Simplify 2 into 2
17.203 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.203 * [taylor]: Taking taylor expansion of PI in k
17.203 * [backup-simplify]: Simplify PI into PI
17.203 * [taylor]: Taking taylor expansion of n in k
17.203 * [backup-simplify]: Simplify n into n
17.203 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.204 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
17.204 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
17.204 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.204 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.205 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.205 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
17.205 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
17.205 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
17.205 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
17.205 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
17.205 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
17.205 * [taylor]: Taking taylor expansion of 1/2 in n
17.205 * [backup-simplify]: Simplify 1/2 into 1/2
17.205 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.205 * [taylor]: Taking taylor expansion of 1/2 in n
17.205 * [backup-simplify]: Simplify 1/2 into 1/2
17.205 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.205 * [taylor]: Taking taylor expansion of k in n
17.205 * [backup-simplify]: Simplify k into k
17.206 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.206 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
17.206 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.206 * [taylor]: Taking taylor expansion of 2 in n
17.206 * [backup-simplify]: Simplify 2 into 2
17.206 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.206 * [taylor]: Taking taylor expansion of PI in n
17.206 * [backup-simplify]: Simplify PI into PI
17.206 * [taylor]: Taking taylor expansion of n in n
17.206 * [backup-simplify]: Simplify 0 into 0
17.206 * [backup-simplify]: Simplify 1 into 1
17.206 * [backup-simplify]: Simplify (/ PI 1) into PI
17.207 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.208 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.208 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.208 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
17.208 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
17.210 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.211 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
17.212 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.212 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
17.212 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
17.212 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
17.212 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
17.212 * [taylor]: Taking taylor expansion of 1/2 in n
17.212 * [backup-simplify]: Simplify 1/2 into 1/2
17.212 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.212 * [taylor]: Taking taylor expansion of 1/2 in n
17.212 * [backup-simplify]: Simplify 1/2 into 1/2
17.212 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.212 * [taylor]: Taking taylor expansion of k in n
17.212 * [backup-simplify]: Simplify k into k
17.212 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.213 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
17.213 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.213 * [taylor]: Taking taylor expansion of 2 in n
17.213 * [backup-simplify]: Simplify 2 into 2
17.213 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.213 * [taylor]: Taking taylor expansion of PI in n
17.213 * [backup-simplify]: Simplify PI into PI
17.213 * [taylor]: Taking taylor expansion of n in n
17.213 * [backup-simplify]: Simplify 0 into 0
17.213 * [backup-simplify]: Simplify 1 into 1
17.213 * [backup-simplify]: Simplify (/ PI 1) into PI
17.214 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.215 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.215 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.215 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
17.215 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
17.217 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.218 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
17.219 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.219 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
17.219 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
17.219 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
17.219 * [taylor]: Taking taylor expansion of 1/2 in k
17.219 * [backup-simplify]: Simplify 1/2 into 1/2
17.219 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.219 * [taylor]: Taking taylor expansion of 1/2 in k
17.219 * [backup-simplify]: Simplify 1/2 into 1/2
17.219 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.220 * [taylor]: Taking taylor expansion of k in k
17.220 * [backup-simplify]: Simplify 0 into 0
17.220 * [backup-simplify]: Simplify 1 into 1
17.220 * [backup-simplify]: Simplify (/ 1 1) into 1
17.220 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
17.220 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.220 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.220 * [taylor]: Taking taylor expansion of 2 in k
17.220 * [backup-simplify]: Simplify 2 into 2
17.220 * [taylor]: Taking taylor expansion of PI in k
17.220 * [backup-simplify]: Simplify PI into PI
17.221 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.222 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.222 * [taylor]: Taking taylor expansion of (log n) in k
17.222 * [taylor]: Taking taylor expansion of n in k
17.222 * [backup-simplify]: Simplify n into n
17.222 * [backup-simplify]: Simplify (log n) into (log n)
17.222 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.223 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.223 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.223 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.224 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
17.225 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
17.227 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.228 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.229 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.230 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.232 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.232 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.232 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.233 * [backup-simplify]: Simplify (- 0) into 0
17.233 * [backup-simplify]: Simplify (+ 0 0) into 0
17.235 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.236 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
17.238 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.238 * [taylor]: Taking taylor expansion of 0 in k
17.238 * [backup-simplify]: Simplify 0 into 0
17.238 * [backup-simplify]: Simplify 0 into 0
17.238 * [backup-simplify]: Simplify 0 into 0
17.239 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.240 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.244 * [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
17.244 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.245 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.246 * [backup-simplify]: Simplify (- 0) into 0
17.246 * [backup-simplify]: Simplify (+ 0 0) into 0
17.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.249 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
17.252 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.252 * [taylor]: Taking taylor expansion of 0 in k
17.252 * [backup-simplify]: Simplify 0 into 0
17.252 * [backup-simplify]: Simplify 0 into 0
17.252 * [backup-simplify]: Simplify 0 into 0
17.252 * [backup-simplify]: Simplify 0 into 0
17.253 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.254 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.260 * [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
17.261 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.261 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.262 * [backup-simplify]: Simplify (- 0) into 0
17.262 * [backup-simplify]: Simplify (+ 0 0) into 0
17.263 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.264 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
17.266 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 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
17.266 * [taylor]: Taking taylor expansion of 0 in k
17.266 * [backup-simplify]: Simplify 0 into 0
17.266 * [backup-simplify]: Simplify 0 into 0
17.266 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
17.267 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
17.267 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
17.267 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
17.267 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
17.267 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
17.267 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.267 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.267 * [taylor]: Taking taylor expansion of 1/2 in k
17.267 * [backup-simplify]: Simplify 1/2 into 1/2
17.267 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.267 * [taylor]: Taking taylor expansion of k in k
17.267 * [backup-simplify]: Simplify 0 into 0
17.267 * [backup-simplify]: Simplify 1 into 1
17.267 * [backup-simplify]: Simplify (/ 1 1) into 1
17.267 * [taylor]: Taking taylor expansion of 1/2 in k
17.267 * [backup-simplify]: Simplify 1/2 into 1/2
17.267 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
17.267 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
17.267 * [taylor]: Taking taylor expansion of -2 in k
17.267 * [backup-simplify]: Simplify -2 into -2
17.267 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.267 * [taylor]: Taking taylor expansion of PI in k
17.267 * [backup-simplify]: Simplify PI into PI
17.267 * [taylor]: Taking taylor expansion of n in k
17.267 * [backup-simplify]: Simplify n into n
17.267 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.267 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
17.267 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
17.268 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.268 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.268 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
17.268 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
17.268 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.268 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.268 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.268 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.268 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.268 * [taylor]: Taking taylor expansion of 1/2 in n
17.268 * [backup-simplify]: Simplify 1/2 into 1/2
17.268 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.268 * [taylor]: Taking taylor expansion of k in n
17.268 * [backup-simplify]: Simplify k into k
17.268 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.268 * [taylor]: Taking taylor expansion of 1/2 in n
17.268 * [backup-simplify]: Simplify 1/2 into 1/2
17.268 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.268 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.268 * [taylor]: Taking taylor expansion of -2 in n
17.268 * [backup-simplify]: Simplify -2 into -2
17.268 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.269 * [taylor]: Taking taylor expansion of PI in n
17.269 * [backup-simplify]: Simplify PI into PI
17.269 * [taylor]: Taking taylor expansion of n in n
17.269 * [backup-simplify]: Simplify 0 into 0
17.269 * [backup-simplify]: Simplify 1 into 1
17.269 * [backup-simplify]: Simplify (/ PI 1) into PI
17.269 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.270 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.270 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.270 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.271 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.272 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
17.272 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.272 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.272 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.272 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.272 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.272 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.272 * [taylor]: Taking taylor expansion of 1/2 in n
17.272 * [backup-simplify]: Simplify 1/2 into 1/2
17.272 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.272 * [taylor]: Taking taylor expansion of k in n
17.273 * [backup-simplify]: Simplify k into k
17.273 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.273 * [taylor]: Taking taylor expansion of 1/2 in n
17.273 * [backup-simplify]: Simplify 1/2 into 1/2
17.273 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.273 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.273 * [taylor]: Taking taylor expansion of -2 in n
17.273 * [backup-simplify]: Simplify -2 into -2
17.273 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.273 * [taylor]: Taking taylor expansion of PI in n
17.273 * [backup-simplify]: Simplify PI into PI
17.273 * [taylor]: Taking taylor expansion of n in n
17.273 * [backup-simplify]: Simplify 0 into 0
17.273 * [backup-simplify]: Simplify 1 into 1
17.273 * [backup-simplify]: Simplify (/ PI 1) into PI
17.273 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.274 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.274 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.274 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.275 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.276 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
17.282 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.282 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
17.282 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
17.282 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.282 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.282 * [taylor]: Taking taylor expansion of 1/2 in k
17.282 * [backup-simplify]: Simplify 1/2 into 1/2
17.282 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.282 * [taylor]: Taking taylor expansion of k in k
17.282 * [backup-simplify]: Simplify 0 into 0
17.282 * [backup-simplify]: Simplify 1 into 1
17.282 * [backup-simplify]: Simplify (/ 1 1) into 1
17.282 * [taylor]: Taking taylor expansion of 1/2 in k
17.282 * [backup-simplify]: Simplify 1/2 into 1/2
17.282 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
17.282 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
17.282 * [taylor]: Taking taylor expansion of (* -2 PI) in k
17.282 * [taylor]: Taking taylor expansion of -2 in k
17.282 * [backup-simplify]: Simplify -2 into -2
17.282 * [taylor]: Taking taylor expansion of PI in k
17.282 * [backup-simplify]: Simplify PI into PI
17.283 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.283 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.283 * [taylor]: Taking taylor expansion of (log n) in k
17.283 * [taylor]: Taking taylor expansion of n in k
17.283 * [backup-simplify]: Simplify n into n
17.284 * [backup-simplify]: Simplify (log n) into (log n)
17.284 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.284 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.284 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.285 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
17.286 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
17.286 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.287 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.288 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.288 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
17.289 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
17.289 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.290 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.290 * [backup-simplify]: Simplify (+ 0 0) into 0
17.291 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.292 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
17.293 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.293 * [taylor]: Taking taylor expansion of 0 in k
17.293 * [backup-simplify]: Simplify 0 into 0
17.293 * [backup-simplify]: Simplify 0 into 0
17.293 * [backup-simplify]: Simplify 0 into 0
17.295 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.296 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
17.300 * [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
17.300 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.301 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.301 * [backup-simplify]: Simplify (+ 0 0) into 0
17.303 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.304 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
17.307 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.307 * [taylor]: Taking taylor expansion of 0 in k
17.307 * [backup-simplify]: Simplify 0 into 0
17.307 * [backup-simplify]: Simplify 0 into 0
17.307 * [backup-simplify]: Simplify 0 into 0
17.307 * [backup-simplify]: Simplify 0 into 0
17.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.310 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.316 * [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
17.316 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.318 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.318 * [backup-simplify]: Simplify (+ 0 0) into 0
17.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.322 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
17.324 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.325 * [taylor]: Taking taylor expansion of 0 in k
17.325 * [backup-simplify]: Simplify 0 into 0
17.325 * [backup-simplify]: Simplify 0 into 0
17.326 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
17.326 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1)
17.326 * [backup-simplify]: Simplify (/ 1 (sqrt (sqrt k))) into (pow (/ 1 k) 1/4)
17.326 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/4) in (k) around 0
17.326 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
17.326 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
17.326 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
17.326 * [taylor]: Taking taylor expansion of 1/4 in k
17.326 * [backup-simplify]: Simplify 1/4 into 1/4
17.326 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
17.326 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.326 * [taylor]: Taking taylor expansion of k in k
17.326 * [backup-simplify]: Simplify 0 into 0
17.326 * [backup-simplify]: Simplify 1 into 1
17.327 * [backup-simplify]: Simplify (/ 1 1) into 1
17.327 * [backup-simplify]: Simplify (log 1) into 0
17.328 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.328 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
17.328 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
17.328 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
17.328 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
17.328 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
17.328 * [taylor]: Taking taylor expansion of 1/4 in k
17.328 * [backup-simplify]: Simplify 1/4 into 1/4
17.328 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
17.328 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.328 * [taylor]: Taking taylor expansion of k in k
17.328 * [backup-simplify]: Simplify 0 into 0
17.328 * [backup-simplify]: Simplify 1 into 1
17.328 * [backup-simplify]: Simplify (/ 1 1) into 1
17.329 * [backup-simplify]: Simplify (log 1) into 0
17.329 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.329 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
17.329 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
17.330 * [backup-simplify]: Simplify (pow k -1/4) into (pow k -1/4)
17.330 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
17.332 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
17.332 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.333 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
17.334 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
17.334 * [backup-simplify]: Simplify 0 into 0
17.335 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.338 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
17.339 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.340 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
17.342 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.342 * [backup-simplify]: Simplify 0 into 0
17.343 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.349 * [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
17.349 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.351 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
17.352 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.352 * [backup-simplify]: Simplify 0 into 0
17.354 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.364 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
17.365 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.366 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
17.369 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.369 * [backup-simplify]: Simplify 0 into 0
17.371 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.388 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
17.389 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.391 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
17.396 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.396 * [backup-simplify]: Simplify 0 into 0
17.397 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.437 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
17.438 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.441 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
17.448 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.448 * [backup-simplify]: Simplify 0 into 0
17.448 * [backup-simplify]: Simplify (pow k -1/4) into (pow k -1/4)
17.448 * [backup-simplify]: Simplify (/ 1 (sqrt (sqrt (/ 1 k)))) into (pow k 1/4)
17.448 * [approximate]: Taking taylor expansion of (pow k 1/4) in (k) around 0
17.448 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
17.448 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
17.448 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
17.448 * [taylor]: Taking taylor expansion of 1/4 in k
17.448 * [backup-simplify]: Simplify 1/4 into 1/4
17.448 * [taylor]: Taking taylor expansion of (log k) in k
17.448 * [taylor]: Taking taylor expansion of k in k
17.448 * [backup-simplify]: Simplify 0 into 0
17.448 * [backup-simplify]: Simplify 1 into 1
17.449 * [backup-simplify]: Simplify (log 1) into 0
17.449 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.449 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
17.449 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
17.449 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
17.449 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
17.449 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
17.449 * [taylor]: Taking taylor expansion of 1/4 in k
17.450 * [backup-simplify]: Simplify 1/4 into 1/4
17.450 * [taylor]: Taking taylor expansion of (log k) in k
17.450 * [taylor]: Taking taylor expansion of k in k
17.450 * [backup-simplify]: Simplify 0 into 0
17.450 * [backup-simplify]: Simplify 1 into 1
17.450 * [backup-simplify]: Simplify (log 1) into 0
17.450 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.451 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
17.451 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
17.451 * [backup-simplify]: Simplify (pow k 1/4) into (pow k 1/4)
17.452 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
17.453 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.453 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
17.454 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
17.454 * [backup-simplify]: Simplify 0 into 0
17.455 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
17.456 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.456 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
17.457 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.457 * [backup-simplify]: Simplify 0 into 0
17.460 * [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
17.460 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.461 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
17.462 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.462 * [backup-simplify]: Simplify 0 into 0
17.468 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
17.468 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.469 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
17.471 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.471 * [backup-simplify]: Simplify 0 into 0
17.481 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
17.481 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.482 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
17.485 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.485 * [backup-simplify]: Simplify 0 into 0
17.515 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
17.516 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.519 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
17.525 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.525 * [backup-simplify]: Simplify 0 into 0
17.525 * [backup-simplify]: Simplify (pow (/ 1 k) 1/4) into (pow (/ 1 k) 1/4)
17.526 * [backup-simplify]: Simplify (/ 1 (sqrt (sqrt (/ 1 (- k))))) into (sqrt (/ 1 (sqrt (/ -1 k))))
17.526 * [approximate]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in (k) around 0
17.526 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
17.526 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
17.526 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.526 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.526 * [taylor]: Taking taylor expansion of -1 in k
17.526 * [backup-simplify]: Simplify -1 into -1
17.526 * [taylor]: Taking taylor expansion of k in k
17.526 * [backup-simplify]: Simplify 0 into 0
17.526 * [backup-simplify]: Simplify 1 into 1
17.527 * [backup-simplify]: Simplify (/ -1 1) into -1
17.527 * [backup-simplify]: Simplify (sqrt 0) into 0
17.529 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.529 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
17.530 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
17.531 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
17.534 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.536 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
17.538 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
17.538 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
17.538 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
17.538 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.538 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.538 * [taylor]: Taking taylor expansion of -1 in k
17.538 * [backup-simplify]: Simplify -1 into -1
17.538 * [taylor]: Taking taylor expansion of k in k
17.538 * [backup-simplify]: Simplify 0 into 0
17.538 * [backup-simplify]: Simplify 1 into 1
17.539 * [backup-simplify]: Simplify (/ -1 1) into -1
17.539 * [backup-simplify]: Simplify (sqrt 0) into 0
17.541 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.541 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
17.541 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
17.542 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
17.545 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.547 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
17.549 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
17.550 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
17.551 * [backup-simplify]: Simplify (/ +nan.0 (sqrt +nan.0)) into (/ +nan.0 (sqrt +nan.0))
17.552 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.556 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.560 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
17.573 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
17.580 * [backup-simplify]: Simplify (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) into (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
17.589 * [backup-simplify]: Simplify (+ (* (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow (/ 1 (- k)) 2)) (+ (* (/ +nan.0 (sqrt +nan.0)) (/ 1 (- k))) (sqrt +nan.0))) into (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
17.590 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1)
17.590 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
17.590 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
17.590 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.590 * [taylor]: Taking taylor expansion of 2 in n
17.590 * [backup-simplify]: Simplify 2 into 2
17.590 * [taylor]: Taking taylor expansion of (* n PI) in n
17.590 * [taylor]: Taking taylor expansion of n in n
17.590 * [backup-simplify]: Simplify 0 into 0
17.590 * [backup-simplify]: Simplify 1 into 1
17.590 * [taylor]: Taking taylor expansion of PI in n
17.590 * [backup-simplify]: Simplify PI into PI
17.590 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.590 * [taylor]: Taking taylor expansion of 2 in n
17.590 * [backup-simplify]: Simplify 2 into 2
17.590 * [taylor]: Taking taylor expansion of (* n PI) in n
17.590 * [taylor]: Taking taylor expansion of n in n
17.590 * [backup-simplify]: Simplify 0 into 0
17.590 * [backup-simplify]: Simplify 1 into 1
17.590 * [taylor]: Taking taylor expansion of PI in n
17.590 * [backup-simplify]: Simplify PI into PI
17.591 * [backup-simplify]: Simplify (* 0 PI) into 0
17.591 * [backup-simplify]: Simplify (* 2 0) into 0
17.591 * [backup-simplify]: Simplify 0 into 0
17.593 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.595 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.595 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.596 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.597 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
17.597 * [backup-simplify]: Simplify 0 into 0
17.599 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.600 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.600 * [backup-simplify]: Simplify 0 into 0
17.602 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.603 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
17.603 * [backup-simplify]: Simplify 0 into 0
17.605 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.607 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
17.607 * [backup-simplify]: Simplify 0 into 0
17.609 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.610 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
17.610 * [backup-simplify]: Simplify 0 into 0
17.613 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
17.615 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
17.615 * [backup-simplify]: Simplify 0 into 0
17.616 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
17.616 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
17.616 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
17.616 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.616 * [taylor]: Taking taylor expansion of 2 in n
17.616 * [backup-simplify]: Simplify 2 into 2
17.616 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.616 * [taylor]: Taking taylor expansion of PI in n
17.616 * [backup-simplify]: Simplify PI into PI
17.616 * [taylor]: Taking taylor expansion of n in n
17.616 * [backup-simplify]: Simplify 0 into 0
17.616 * [backup-simplify]: Simplify 1 into 1
17.617 * [backup-simplify]: Simplify (/ PI 1) into PI
17.617 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.617 * [taylor]: Taking taylor expansion of 2 in n
17.617 * [backup-simplify]: Simplify 2 into 2
17.617 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.617 * [taylor]: Taking taylor expansion of PI in n
17.617 * [backup-simplify]: Simplify PI into PI
17.617 * [taylor]: Taking taylor expansion of n in n
17.617 * [backup-simplify]: Simplify 0 into 0
17.617 * [backup-simplify]: Simplify 1 into 1
17.617 * [backup-simplify]: Simplify (/ PI 1) into PI
17.618 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.618 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.619 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.620 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.620 * [backup-simplify]: Simplify 0 into 0
17.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.623 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.623 * [backup-simplify]: Simplify 0 into 0
17.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.625 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.625 * [backup-simplify]: Simplify 0 into 0
17.627 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.628 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.628 * [backup-simplify]: Simplify 0 into 0
17.629 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.631 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.631 * [backup-simplify]: Simplify 0 into 0
17.632 * [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
17.634 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.634 * [backup-simplify]: Simplify 0 into 0
17.635 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
17.635 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
17.635 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
17.635 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.635 * [taylor]: Taking taylor expansion of -2 in n
17.635 * [backup-simplify]: Simplify -2 into -2
17.635 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.635 * [taylor]: Taking taylor expansion of PI in n
17.635 * [backup-simplify]: Simplify PI into PI
17.635 * [taylor]: Taking taylor expansion of n in n
17.635 * [backup-simplify]: Simplify 0 into 0
17.635 * [backup-simplify]: Simplify 1 into 1
17.636 * [backup-simplify]: Simplify (/ PI 1) into PI
17.636 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.636 * [taylor]: Taking taylor expansion of -2 in n
17.636 * [backup-simplify]: Simplify -2 into -2
17.636 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.636 * [taylor]: Taking taylor expansion of PI in n
17.636 * [backup-simplify]: Simplify PI into PI
17.636 * [taylor]: Taking taylor expansion of n in n
17.636 * [backup-simplify]: Simplify 0 into 0
17.636 * [backup-simplify]: Simplify 1 into 1
17.637 * [backup-simplify]: Simplify (/ PI 1) into PI
17.637 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.637 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.638 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.638 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
17.638 * [backup-simplify]: Simplify 0 into 0
17.639 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.640 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
17.640 * [backup-simplify]: Simplify 0 into 0
17.640 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.641 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.641 * [backup-simplify]: Simplify 0 into 0
17.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.643 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.643 * [backup-simplify]: Simplify 0 into 0
17.644 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.645 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.645 * [backup-simplify]: Simplify 0 into 0
17.646 * [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
17.647 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.647 * [backup-simplify]: Simplify 0 into 0
17.647 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
17.647 * * * [progress]: simplifying candidates
17.647 * * * * [progress]: [ 1 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 2 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 3 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 4 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 5 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 6 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 7 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 8 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 9 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 10 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 11 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 12 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 13 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 14 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 15 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 16 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 17 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 18 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 19 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 20 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.648 * * * * [progress]: [ 21 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 22 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 23 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 24 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 25 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 26 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 27 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 28 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 29 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 30 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 31 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 32 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 33 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 34 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 35 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 36 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 37 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 38 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 39 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 40 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.649 * * * * [progress]: [ 41 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 42 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 43 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 44 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 45 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 46 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 47 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 48 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 49 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 50 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 51 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 52 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 53 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (sqrt (sqrt k)) -1))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 54 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (sqrt k) (- 1/2)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 55 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (sqrt (sqrt k)) (- 1)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 56 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow k (- (/ 1/2 2))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 57 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (sqrt k) (- (/ 1 2))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 58 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow k (- (/ (/ 1 2) 2))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 59 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (/ 1 (sqrt (sqrt k))) 1))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 60 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (exp (- (log (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 61 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (exp (- 0 (log (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 62 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (exp (- (log 1) (log (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.650 * * * * [progress]: [ 63 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (exp (log (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 64 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (log (exp (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 65 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (cbrt (/ (* (* 1 1) 1) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 66 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (cbrt (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 67 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (cbrt (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 68 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 69 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (- 1) (- (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 70 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1) (cbrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 71 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1) (sqrt (cbrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 72 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1) (sqrt (sqrt (cbrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 73 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 74 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 1))) (/ (cbrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 75 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 76 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 77 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 78 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 79 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1) (cbrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 80 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1) (sqrt (cbrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 81 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1) (sqrt (sqrt (cbrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 82 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 83 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt 1))) (/ (sqrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.651 * * * * [progress]: [ 84 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 85 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 86 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 87 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 88 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1 (cbrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 89 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1 (sqrt (cbrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 90 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1 (sqrt (sqrt (cbrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 91 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 92 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt 1))) (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 93 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 94 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt 1)) (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 95 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 96 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 1) (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 97 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* 1 (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 98 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* 1 (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 99 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (/ (sqrt (sqrt k)) 1)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 100 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 101 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 102 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 103 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 104 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.652 * * * * [progress]: [ 105 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 106 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt 1)) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 107 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 108 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 1) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 109 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (cbrt 1))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 110 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt 1))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 111 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (/ (sqrt (sqrt k)) 1)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 112 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (posit16->real (real->posit16 (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 113 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 114 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 115 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 116 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 117 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (exp (+ (log (* n 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 118 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (exp (log (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 119 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (log (exp (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 120 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 121 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 122 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 123 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 124 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 125 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* 1 (* (* n 2) PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.653 * * * * [progress]: [ 126 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 127 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 128 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* (* n 2) 1) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 129 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 130 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 131 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 132 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (- (+ (* 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 (sqrt k))))))>
17.654 * * * * [progress]: [ 133 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 134 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 135 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (- (+ (* 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))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 136 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 137 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 138 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow k -1/4))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 139 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (/ 1 k) 1/4))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 140 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 141 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 142 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.654 * * * * [progress]: [ 143 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.656 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (- 1/2)
  (- 1)
  (- (/ 1/2 2))
  (- (/ 1 2))
  (- (/ (/ 1 2) 2))
  (- (log (sqrt (sqrt k))))
  (- 0 (log (sqrt (sqrt k))))
  (- (log 1) (log (sqrt (sqrt k))))
  (log (/ 1 (sqrt (sqrt k))))
  (exp (/ 1 (sqrt (sqrt k))))
  (/ (* (* 1 1) 1) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k)))))
  (cbrt (/ 1 (sqrt (sqrt k))))
  (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))))
  (sqrt (/ 1 (sqrt (sqrt k))))
  (sqrt (/ 1 (sqrt (sqrt k))))
  (- 1)
  (- (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt 1) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt 1) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt 1) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 1)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt 1) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt 1) (sqrt (cbrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt 1) (sqrt (sqrt (cbrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt 1)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) 1)
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ (sqrt (sqrt k)) (cbrt 1))
  (/ (sqrt (sqrt k)) (sqrt 1))
  (/ (sqrt (sqrt k)) 1)
  (real->posit16 (/ 1 (sqrt (sqrt k))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (+ (log n) (log 2)) (log PI))
  (+ (log (* n 2)) (log PI))
  (log (* (* n 2) PI))
  (exp (* (* n 2) PI))
  (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))
  (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) 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 PI) (cbrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) 1)
  (* 2 PI)
  (real->posit16 (* (* n 2) PI))
  (- (+ (* 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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 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)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (pow k -1/4)
  (pow (/ 1 k) 1/4)
  (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
17.658 * * [simplify]: iteration 0: 232 enodes
17.767 * * [simplify]: iteration 1: 540 enodes
17.984 * * [simplify]: iteration 2: 1700 enodes
18.504 * * [simplify]: iteration complete: 5004 enodes
18.504 * * [simplify]: Extracting #0: cost 58 inf + 0
18.505 * * [simplify]: Extracting #1: cost 551 inf + 4
18.512 * * [simplify]: Extracting #2: cost 1233 inf + 31351
18.540 * * [simplify]: Extracting #3: cost 1314 inf + 126857
18.598 * * [simplify]: Extracting #4: cost 642 inf + 295056
18.691 * * [simplify]: Extracting #5: cost 169 inf + 458876
18.844 * * [simplify]: Extracting #6: cost 17 inf + 509911
18.994 * * [simplify]: Extracting #7: cost 0 inf + 514256
19.094 * * [simplify]: Extracting #8: cost 0 inf + 513996
19.249 * [simplify]: Simplified to:
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (* (* n 2) PI)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* n 2) PI)
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (* (* n 2) PI)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* n 2) PI)
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  -1/2
  -1
  -1/4
  -1/2
  -1/4
  (- (log (sqrt (sqrt k))))
  (- (log (sqrt (sqrt k))))
  (- (log (sqrt (sqrt k))))
  (- (log (sqrt (sqrt k))))
  (exp (/ 1 (sqrt (sqrt k))))
  (/ (/ 1 (sqrt k)) (sqrt (sqrt k)))
  (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k)))))
  (cbrt (/ 1 (sqrt (sqrt k))))
  (/ (/ 1 (sqrt k)) (sqrt (sqrt k)))
  (sqrt (/ 1 (sqrt (sqrt k))))
  (sqrt (/ 1 (sqrt (sqrt k))))
  -1
  (- (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (sqrt (sqrt k))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (sqrt (sqrt k))
  (sqrt (sqrt k))
  (sqrt (sqrt k))
  (real->posit16 (/ 1 (sqrt (sqrt k))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (exp (+ (* PI n) (* PI n)))
  (* PI (* (* n (* n n)) (* (* 8 PI) PI)))
  (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 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 PI)) (cbrt PI))
  (* (sqrt PI) (* n 2))
  (* n 2)
  (* 2 PI)
  (real->posit16 (* (* n 2) PI))
  (+ (+ (* (sqrt (* (* n 2) PI)) (+ (* 1/8 (* (* (log n) k) (* (log n) k))) (* (* (log (* 2 PI)) 1/4) (* (* (log n) k) k)))) (* 1/8 (* (sqrt (* (* n 2) PI)) (* (* k (log (* 2 PI))) (* k (log (* 2 PI))))))) (- (sqrt (* (* n 2) PI)) (/ (* (* (sqrt (* (* n 2) PI)) k) (log (* (* n 2) PI))) 2)))
  (exp (* (log (* (* n 2) PI)) (+ 1/2 (* -1/2 k))))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (+ 1/2 (* -1/2 k))))
  (+ (+ (* (sqrt (* (* n 2) PI)) (+ (* 1/8 (* (* (log n) k) (* (log n) k))) (* (* (log (* 2 PI)) 1/4) (* (* (log n) k) k)))) (* 1/8 (* (sqrt (* (* n 2) PI)) (* (* k (log (* 2 PI))) (* k (log (* 2 PI))))))) (- (sqrt (* (* n 2) PI)) (/ (* (* (sqrt (* (* n 2) PI)) k) (log (* (* n 2) PI))) 2)))
  (exp (* (log (* (* n 2) PI)) (+ 1/2 (* -1/2 k))))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (+ 1/2 (* -1/2 k))))
  (pow k -1/4)
  (pow (/ 1 k) 1/4)
  (- (+ (- (sqrt +nan.0) (/ (/ +nan.0 k) (sqrt +nan.0))) (/ (/ +nan.0 (* k k)) (* +nan.0 (sqrt +nan.0)))) (/ (/ +nan.0 (* k k)) (sqrt +nan.0)))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (* (* n 2) PI)
19.279 * * * [progress]: adding candidates to table
20.156 * [progress]: [Phase 3 of 3] Extracting.
20.156 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>)
20.158 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2 PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) n k)
20.158 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>)
20.223 * * * * [regimes]: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (#<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>)
20.330 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>)
20.427 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>)
20.500 * * * [regime]: Found split indices: #<option (#s(si 1 255))>
20.501 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
20.501 * * [simplify]: iteration 0: 13 enodes
20.503 * * [simplify]: iteration 1: 18 enodes
20.506 * * [simplify]: iteration complete: 18 enodes
20.506 * * [simplify]: Extracting #0: cost 1 inf + 0
20.506 * * [simplify]: Extracting #1: cost 3 inf + 0
20.506 * * [simplify]: Extracting #2: cost 7 inf + 0
20.506 * * [simplify]: Extracting #3: cost 11 inf + 1
20.506 * * [simplify]: Extracting #4: cost 5 inf + 252
20.506 * * [simplify]: Extracting #5: cost 4 inf + 253
20.506 * * [simplify]: Extracting #6: cost 1 inf + 753
20.507 * * [simplify]: Extracting #7: cost 0 inf + 1248
20.507 * [simplify]: Simplified to:
  (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
27.402 * [regime-testing]: Baseline error score: 0.3901292900075434
27.405 * [regime-testing]: Oracle error score: 0.09343127695810291
27.409 * [regime-testing]: End program error score: 0.3901292900075434