0.001 * [progress]: [Phase 1 of 3] Setting up.
0.001 * * * [progress]: [1/2] Preparing points
0.201 * * * [progress]: [2/2] Setting up program.
0.207 * [progress]: [Phase 2 of 3] Improving.
0.207 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.208 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.208 * * [simplify]: iteration 1: (13 enodes)
0.217 * * [simplify]: iteration 2: (57 enodes)
0.235 * * [simplify]: iteration 3: (96 enodes)
0.292 * * [simplify]: iteration 4: (174 enodes)
0.353 * * [simplify]: iteration 5: (354 enodes)
0.524 * * [simplify]: iteration 6: (812 enodes)
1.148 * * [simplify]: Extracting #0: cost 1 inf + 0
1.148 * * [simplify]: Extracting #1: cost 59 inf + 0
1.154 * * [simplify]: Extracting #2: cost 223 inf + 1
1.156 * * [simplify]: Extracting #3: cost 295 inf + 210
1.158 * * [simplify]: Extracting #4: cost 270 inf + 8826
1.174 * * [simplify]: Extracting #5: cost 112 inf + 91732
1.234 * * [simplify]: Extracting #6: cost 3 inf + 174781
1.305 * * [simplify]: Extracting #7: cost 0 inf + 175756
1.355 * [simplify]: Simplified to:
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
1.362 * * [progress]: iteration 1 / 4
1.362 * * * [progress]: picking best candidate
1.372 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))>
1.372 * * * [progress]: localizing error
1.415 * * * [progress]: generating rewritten candidates
1.415 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
1.439 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
1.452 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
1.466 * * * [progress]: generating series expansions
1.466 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
1.467 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
1.467 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
1.467 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
1.467 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
1.467 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
1.467 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
1.467 * [taylor]: Taking taylor expansion of 1/2 in k
1.467 * [backup-simplify]: Simplify 1/2 into 1/2
1.467 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.467 * [taylor]: Taking taylor expansion of 1 in k
1.467 * [backup-simplify]: Simplify 1 into 1
1.467 * [taylor]: Taking taylor expansion of k in k
1.467 * [backup-simplify]: Simplify 0 into 0
1.467 * [backup-simplify]: Simplify 1 into 1
1.467 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.467 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.467 * [taylor]: Taking taylor expansion of 2 in k
1.467 * [backup-simplify]: Simplify 2 into 2
1.467 * [taylor]: Taking taylor expansion of (* n PI) in k
1.467 * [taylor]: Taking taylor expansion of n in k
1.467 * [backup-simplify]: Simplify n into n
1.467 * [taylor]: Taking taylor expansion of PI in k
1.467 * [backup-simplify]: Simplify PI into PI
1.468 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.468 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.468 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.468 * [backup-simplify]: Simplify (- 0) into 0
1.469 * [backup-simplify]: Simplify (+ 1 0) into 1
1.469 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.469 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.469 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.469 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.469 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.469 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.469 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.469 * [taylor]: Taking taylor expansion of 1/2 in n
1.469 * [backup-simplify]: Simplify 1/2 into 1/2
1.470 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.470 * [taylor]: Taking taylor expansion of 1 in n
1.470 * [backup-simplify]: Simplify 1 into 1
1.470 * [taylor]: Taking taylor expansion of k in n
1.470 * [backup-simplify]: Simplify k into k
1.470 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.470 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.470 * [taylor]: Taking taylor expansion of 2 in n
1.470 * [backup-simplify]: Simplify 2 into 2
1.470 * [taylor]: Taking taylor expansion of (* n PI) in n
1.470 * [taylor]: Taking taylor expansion of n in n
1.470 * [backup-simplify]: Simplify 0 into 0
1.470 * [backup-simplify]: Simplify 1 into 1
1.470 * [taylor]: Taking taylor expansion of PI in n
1.470 * [backup-simplify]: Simplify PI into PI
1.470 * [backup-simplify]: Simplify (* 0 PI) into 0
1.471 * [backup-simplify]: Simplify (* 2 0) into 0
1.472 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.474 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.475 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.475 * [backup-simplify]: Simplify (- k) into (- k)
1.476 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.476 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.477 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.478 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.479 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.479 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.479 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.479 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.479 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.479 * [taylor]: Taking taylor expansion of 1/2 in n
1.479 * [backup-simplify]: Simplify 1/2 into 1/2
1.479 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.479 * [taylor]: Taking taylor expansion of 1 in n
1.479 * [backup-simplify]: Simplify 1 into 1
1.480 * [taylor]: Taking taylor expansion of k in n
1.480 * [backup-simplify]: Simplify k into k
1.480 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.480 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.480 * [taylor]: Taking taylor expansion of 2 in n
1.480 * [backup-simplify]: Simplify 2 into 2
1.480 * [taylor]: Taking taylor expansion of (* n PI) in n
1.480 * [taylor]: Taking taylor expansion of n in n
1.480 * [backup-simplify]: Simplify 0 into 0
1.480 * [backup-simplify]: Simplify 1 into 1
1.480 * [taylor]: Taking taylor expansion of PI in n
1.480 * [backup-simplify]: Simplify PI into PI
1.480 * [backup-simplify]: Simplify (* 0 PI) into 0
1.481 * [backup-simplify]: Simplify (* 2 0) into 0
1.482 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.484 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.485 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.485 * [backup-simplify]: Simplify (- k) into (- k)
1.485 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.485 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.486 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.487 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.488 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.489 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
1.489 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
1.489 * [taylor]: Taking taylor expansion of 1/2 in k
1.489 * [backup-simplify]: Simplify 1/2 into 1/2
1.489 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
1.489 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.489 * [taylor]: Taking taylor expansion of 1 in k
1.489 * [backup-simplify]: Simplify 1 into 1
1.489 * [taylor]: Taking taylor expansion of k in k
1.489 * [backup-simplify]: Simplify 0 into 0
1.489 * [backup-simplify]: Simplify 1 into 1
1.489 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.489 * [taylor]: Taking taylor expansion of (log n) in k
1.489 * [taylor]: Taking taylor expansion of n in k
1.489 * [backup-simplify]: Simplify n into n
1.489 * [backup-simplify]: Simplify (log n) into (log n)
1.489 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.489 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.489 * [taylor]: Taking taylor expansion of 2 in k
1.489 * [backup-simplify]: Simplify 2 into 2
1.489 * [taylor]: Taking taylor expansion of PI in k
1.489 * [backup-simplify]: Simplify PI into PI
1.490 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.491 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.491 * [backup-simplify]: Simplify (- 0) into 0
1.491 * [backup-simplify]: Simplify (+ 1 0) into 1
1.492 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.493 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
1.494 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.496 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.497 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.498 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.499 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.500 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.501 * [backup-simplify]: Simplify (- 0) into 0
1.501 * [backup-simplify]: Simplify (+ 0 0) into 0
1.502 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
1.503 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.504 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.506 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.506 * [taylor]: Taking taylor expansion of 0 in k
1.506 * [backup-simplify]: Simplify 0 into 0
1.506 * [backup-simplify]: Simplify 0 into 0
1.507 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.508 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.510 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.510 * [backup-simplify]: Simplify (+ 0 0) into 0
1.511 * [backup-simplify]: Simplify (- 1) into -1
1.511 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.513 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
1.515 * [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)))))
1.518 * [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)))))))
1.521 * [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)))))))
1.523 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.524 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.527 * [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
1.527 * [backup-simplify]: Simplify (- 0) into 0
1.528 * [backup-simplify]: Simplify (+ 0 0) into 0
1.532 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
1.534 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.535 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.538 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.538 * [taylor]: Taking taylor expansion of 0 in k
1.538 * [backup-simplify]: Simplify 0 into 0
1.538 * [backup-simplify]: Simplify 0 into 0
1.538 * [backup-simplify]: Simplify 0 into 0
1.539 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.540 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.542 * [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
1.542 * [backup-simplify]: Simplify (+ 0 0) into 0
1.542 * [backup-simplify]: Simplify (- 0) into 0
1.542 * [backup-simplify]: Simplify (+ 0 0) into 0
1.544 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.545 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.547 * [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)))))
1.550 * [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)))))
1.556 * [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)))))
1.556 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
1.556 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
1.556 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
1.556 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
1.556 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
1.556 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
1.556 * [taylor]: Taking taylor expansion of 1/2 in k
1.556 * [backup-simplify]: Simplify 1/2 into 1/2
1.556 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.556 * [taylor]: Taking taylor expansion of 1 in k
1.556 * [backup-simplify]: Simplify 1 into 1
1.556 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.556 * [taylor]: Taking taylor expansion of k in k
1.556 * [backup-simplify]: Simplify 0 into 0
1.556 * [backup-simplify]: Simplify 1 into 1
1.557 * [backup-simplify]: Simplify (/ 1 1) into 1
1.557 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
1.557 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
1.557 * [taylor]: Taking taylor expansion of 2 in k
1.557 * [backup-simplify]: Simplify 2 into 2
1.557 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.557 * [taylor]: Taking taylor expansion of PI in k
1.557 * [backup-simplify]: Simplify PI into PI
1.557 * [taylor]: Taking taylor expansion of n in k
1.557 * [backup-simplify]: Simplify n into n
1.557 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.557 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
1.557 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
1.557 * [backup-simplify]: Simplify (- 1) into -1
1.557 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.558 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
1.558 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
1.558 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
1.558 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.558 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.558 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.558 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
1.558 * [taylor]: Taking taylor expansion of 1/2 in n
1.558 * [backup-simplify]: Simplify 1/2 into 1/2
1.558 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
1.558 * [taylor]: Taking taylor expansion of 1 in n
1.558 * [backup-simplify]: Simplify 1 into 1
1.558 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.558 * [taylor]: Taking taylor expansion of k in n
1.558 * [backup-simplify]: Simplify k into k
1.558 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.558 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.558 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.558 * [taylor]: Taking taylor expansion of 2 in n
1.558 * [backup-simplify]: Simplify 2 into 2
1.558 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.558 * [taylor]: Taking taylor expansion of PI in n
1.558 * [backup-simplify]: Simplify PI into PI
1.558 * [taylor]: Taking taylor expansion of n in n
1.558 * [backup-simplify]: Simplify 0 into 0
1.558 * [backup-simplify]: Simplify 1 into 1
1.558 * [backup-simplify]: Simplify (/ PI 1) into PI
1.559 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.559 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.559 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.560 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.560 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.560 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.561 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.562 * [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)))))
1.562 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.562 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.562 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.562 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
1.562 * [taylor]: Taking taylor expansion of 1/2 in n
1.562 * [backup-simplify]: Simplify 1/2 into 1/2
1.562 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
1.562 * [taylor]: Taking taylor expansion of 1 in n
1.562 * [backup-simplify]: Simplify 1 into 1
1.562 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.562 * [taylor]: Taking taylor expansion of k in n
1.562 * [backup-simplify]: Simplify k into k
1.562 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.562 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.562 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.562 * [taylor]: Taking taylor expansion of 2 in n
1.562 * [backup-simplify]: Simplify 2 into 2
1.562 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.562 * [taylor]: Taking taylor expansion of PI in n
1.562 * [backup-simplify]: Simplify PI into PI
1.562 * [taylor]: Taking taylor expansion of n in n
1.562 * [backup-simplify]: Simplify 0 into 0
1.562 * [backup-simplify]: Simplify 1 into 1
1.562 * [backup-simplify]: Simplify (/ PI 1) into PI
1.563 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.563 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.563 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.563 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.563 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.564 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.565 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.566 * [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)))))
1.566 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
1.566 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
1.566 * [taylor]: Taking taylor expansion of 1/2 in k
1.566 * [backup-simplify]: Simplify 1/2 into 1/2
1.566 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
1.566 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.566 * [taylor]: Taking taylor expansion of 1 in k
1.566 * [backup-simplify]: Simplify 1 into 1
1.566 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.566 * [taylor]: Taking taylor expansion of k in k
1.566 * [backup-simplify]: Simplify 0 into 0
1.566 * [backup-simplify]: Simplify 1 into 1
1.566 * [backup-simplify]: Simplify (/ 1 1) into 1
1.566 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
1.566 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.566 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.566 * [taylor]: Taking taylor expansion of 2 in k
1.566 * [backup-simplify]: Simplify 2 into 2
1.566 * [taylor]: Taking taylor expansion of PI in k
1.566 * [backup-simplify]: Simplify PI into PI
1.567 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.567 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.568 * [taylor]: Taking taylor expansion of (log n) in k
1.568 * [taylor]: Taking taylor expansion of n in k
1.568 * [backup-simplify]: Simplify n into n
1.568 * [backup-simplify]: Simplify (log n) into (log n)
1.568 * [backup-simplify]: Simplify (- 1) into -1
1.568 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.569 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.570 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
1.571 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
1.572 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
1.573 * [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)))))
1.574 * [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)))))
1.575 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.576 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.578 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.578 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.578 * [backup-simplify]: Simplify (- 0) into 0
1.579 * [backup-simplify]: Simplify (+ 0 0) into 0
1.579 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
1.581 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.582 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
1.584 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.584 * [taylor]: Taking taylor expansion of 0 in k
1.584 * [backup-simplify]: Simplify 0 into 0
1.584 * [backup-simplify]: Simplify 0 into 0
1.584 * [backup-simplify]: Simplify 0 into 0
1.585 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.586 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.589 * [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
1.589 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.590 * [backup-simplify]: Simplify (- 0) into 0
1.590 * [backup-simplify]: Simplify (+ 0 0) into 0
1.591 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
1.593 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.594 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
1.596 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.596 * [taylor]: Taking taylor expansion of 0 in k
1.597 * [backup-simplify]: Simplify 0 into 0
1.597 * [backup-simplify]: Simplify 0 into 0
1.597 * [backup-simplify]: Simplify 0 into 0
1.597 * [backup-simplify]: Simplify 0 into 0
1.598 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.599 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.604 * [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
1.605 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.605 * [backup-simplify]: Simplify (- 0) into 0
1.606 * [backup-simplify]: Simplify (+ 0 0) into 0
1.607 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
1.609 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.611 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
1.613 * [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
1.613 * [taylor]: Taking taylor expansion of 0 in k
1.613 * [backup-simplify]: Simplify 0 into 0
1.613 * [backup-simplify]: Simplify 0 into 0
1.615 * [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))))))
1.615 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
1.615 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
1.615 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
1.615 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
1.615 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
1.615 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
1.615 * [taylor]: Taking taylor expansion of 1/2 in k
1.615 * [backup-simplify]: Simplify 1/2 into 1/2
1.615 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
1.616 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.616 * [taylor]: Taking taylor expansion of k in k
1.616 * [backup-simplify]: Simplify 0 into 0
1.616 * [backup-simplify]: Simplify 1 into 1
1.616 * [backup-simplify]: Simplify (/ 1 1) into 1
1.616 * [taylor]: Taking taylor expansion of 1 in k
1.616 * [backup-simplify]: Simplify 1 into 1
1.616 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
1.616 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
1.616 * [taylor]: Taking taylor expansion of -2 in k
1.616 * [backup-simplify]: Simplify -2 into -2
1.616 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.616 * [taylor]: Taking taylor expansion of PI in k
1.616 * [backup-simplify]: Simplify PI into PI
1.616 * [taylor]: Taking taylor expansion of n in k
1.616 * [backup-simplify]: Simplify n into n
1.616 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.616 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
1.617 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
1.617 * [backup-simplify]: Simplify (+ 1 0) into 1
1.617 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.617 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
1.618 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
1.618 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.618 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.618 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.618 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.618 * [taylor]: Taking taylor expansion of 1/2 in n
1.618 * [backup-simplify]: Simplify 1/2 into 1/2
1.618 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.618 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.618 * [taylor]: Taking taylor expansion of k in n
1.618 * [backup-simplify]: Simplify k into k
1.618 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.618 * [taylor]: Taking taylor expansion of 1 in n
1.618 * [backup-simplify]: Simplify 1 into 1
1.618 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.618 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.618 * [taylor]: Taking taylor expansion of -2 in n
1.618 * [backup-simplify]: Simplify -2 into -2
1.618 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.618 * [taylor]: Taking taylor expansion of PI in n
1.618 * [backup-simplify]: Simplify PI into PI
1.618 * [taylor]: Taking taylor expansion of n in n
1.618 * [backup-simplify]: Simplify 0 into 0
1.618 * [backup-simplify]: Simplify 1 into 1
1.619 * [backup-simplify]: Simplify (/ PI 1) into PI
1.619 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.620 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.620 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.620 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
1.622 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.623 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
1.624 * [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)))))
1.624 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.625 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.625 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.625 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.625 * [taylor]: Taking taylor expansion of 1/2 in n
1.625 * [backup-simplify]: Simplify 1/2 into 1/2
1.625 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.625 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.625 * [taylor]: Taking taylor expansion of k in n
1.625 * [backup-simplify]: Simplify k into k
1.625 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.625 * [taylor]: Taking taylor expansion of 1 in n
1.625 * [backup-simplify]: Simplify 1 into 1
1.625 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.625 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.625 * [taylor]: Taking taylor expansion of -2 in n
1.625 * [backup-simplify]: Simplify -2 into -2
1.625 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.625 * [taylor]: Taking taylor expansion of PI in n
1.625 * [backup-simplify]: Simplify PI into PI
1.625 * [taylor]: Taking taylor expansion of n in n
1.625 * [backup-simplify]: Simplify 0 into 0
1.625 * [backup-simplify]: Simplify 1 into 1
1.626 * [backup-simplify]: Simplify (/ PI 1) into PI
1.626 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.627 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.627 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.627 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
1.629 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.630 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
1.631 * [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)))))
1.631 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
1.631 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
1.631 * [taylor]: Taking taylor expansion of 1/2 in k
1.631 * [backup-simplify]: Simplify 1/2 into 1/2
1.631 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
1.631 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
1.632 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.632 * [taylor]: Taking taylor expansion of k in k
1.632 * [backup-simplify]: Simplify 0 into 0
1.632 * [backup-simplify]: Simplify 1 into 1
1.632 * [backup-simplify]: Simplify (/ 1 1) into 1
1.632 * [taylor]: Taking taylor expansion of 1 in k
1.632 * [backup-simplify]: Simplify 1 into 1
1.632 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
1.632 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
1.632 * [taylor]: Taking taylor expansion of (* -2 PI) in k
1.632 * [taylor]: Taking taylor expansion of -2 in k
1.632 * [backup-simplify]: Simplify -2 into -2
1.632 * [taylor]: Taking taylor expansion of PI in k
1.632 * [backup-simplify]: Simplify PI into PI
1.633 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.634 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.634 * [taylor]: Taking taylor expansion of (log n) in k
1.634 * [taylor]: Taking taylor expansion of n in k
1.634 * [backup-simplify]: Simplify n into n
1.634 * [backup-simplify]: Simplify (log n) into (log n)
1.635 * [backup-simplify]: Simplify (+ 1 0) into 1
1.635 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.636 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
1.637 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
1.638 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
1.639 * [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)))))
1.640 * [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)))))
1.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.642 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.644 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
1.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.644 * [backup-simplify]: Simplify (+ 0 0) into 0
1.645 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
1.646 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.647 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
1.649 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.649 * [taylor]: Taking taylor expansion of 0 in k
1.649 * [backup-simplify]: Simplify 0 into 0
1.649 * [backup-simplify]: Simplify 0 into 0
1.649 * [backup-simplify]: Simplify 0 into 0
1.650 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.651 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.657 * [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
1.657 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.658 * [backup-simplify]: Simplify (+ 0 0) into 0
1.659 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
1.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.661 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
1.662 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.662 * [taylor]: Taking taylor expansion of 0 in k
1.662 * [backup-simplify]: Simplify 0 into 0
1.662 * [backup-simplify]: Simplify 0 into 0
1.662 * [backup-simplify]: Simplify 0 into 0
1.662 * [backup-simplify]: Simplify 0 into 0
1.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.663 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.667 * [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
1.667 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.667 * [backup-simplify]: Simplify (+ 0 0) into 0
1.668 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
1.669 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.670 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
1.671 * [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
1.671 * [taylor]: Taking taylor expansion of 0 in k
1.671 * [backup-simplify]: Simplify 0 into 0
1.671 * [backup-simplify]: Simplify 0 into 0
1.672 * [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))))))
1.672 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
1.673 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
1.673 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
1.673 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.673 * [taylor]: Taking taylor expansion of 2 in n
1.673 * [backup-simplify]: Simplify 2 into 2
1.673 * [taylor]: Taking taylor expansion of (* n PI) in n
1.673 * [taylor]: Taking taylor expansion of n in n
1.673 * [backup-simplify]: Simplify 0 into 0
1.673 * [backup-simplify]: Simplify 1 into 1
1.673 * [taylor]: Taking taylor expansion of PI in n
1.673 * [backup-simplify]: Simplify PI into PI
1.673 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.673 * [taylor]: Taking taylor expansion of 2 in n
1.673 * [backup-simplify]: Simplify 2 into 2
1.673 * [taylor]: Taking taylor expansion of (* n PI) in n
1.673 * [taylor]: Taking taylor expansion of n in n
1.673 * [backup-simplify]: Simplify 0 into 0
1.673 * [backup-simplify]: Simplify 1 into 1
1.673 * [taylor]: Taking taylor expansion of PI in n
1.673 * [backup-simplify]: Simplify PI into PI
1.673 * [backup-simplify]: Simplify (* 0 PI) into 0
1.673 * [backup-simplify]: Simplify (* 2 0) into 0
1.673 * [backup-simplify]: Simplify 0 into 0
1.674 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.675 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.676 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.676 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.677 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.677 * [backup-simplify]: Simplify 0 into 0
1.677 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.678 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.678 * [backup-simplify]: Simplify 0 into 0
1.679 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.680 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
1.680 * [backup-simplify]: Simplify 0 into 0
1.681 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.681 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
1.681 * [backup-simplify]: Simplify 0 into 0
1.682 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.683 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
1.683 * [backup-simplify]: Simplify 0 into 0
1.684 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
1.685 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
1.685 * [backup-simplify]: Simplify 0 into 0
1.686 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
1.686 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
1.686 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
1.686 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.686 * [taylor]: Taking taylor expansion of 2 in n
1.686 * [backup-simplify]: Simplify 2 into 2
1.686 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.686 * [taylor]: Taking taylor expansion of PI in n
1.686 * [backup-simplify]: Simplify PI into PI
1.686 * [taylor]: Taking taylor expansion of n in n
1.686 * [backup-simplify]: Simplify 0 into 0
1.686 * [backup-simplify]: Simplify 1 into 1
1.686 * [backup-simplify]: Simplify (/ PI 1) into PI
1.686 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.687 * [taylor]: Taking taylor expansion of 2 in n
1.687 * [backup-simplify]: Simplify 2 into 2
1.687 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.687 * [taylor]: Taking taylor expansion of PI in n
1.687 * [backup-simplify]: Simplify PI into PI
1.687 * [taylor]: Taking taylor expansion of n in n
1.687 * [backup-simplify]: Simplify 0 into 0
1.687 * [backup-simplify]: Simplify 1 into 1
1.687 * [backup-simplify]: Simplify (/ PI 1) into PI
1.688 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.688 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.689 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.690 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.690 * [backup-simplify]: Simplify 0 into 0
1.691 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.692 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.692 * [backup-simplify]: Simplify 0 into 0
1.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.695 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.695 * [backup-simplify]: Simplify 0 into 0
1.696 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.697 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.697 * [backup-simplify]: Simplify 0 into 0
1.699 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.700 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.700 * [backup-simplify]: Simplify 0 into 0
1.702 * [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
1.703 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.703 * [backup-simplify]: Simplify 0 into 0
1.703 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
1.704 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
1.704 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
1.704 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.704 * [taylor]: Taking taylor expansion of -2 in n
1.704 * [backup-simplify]: Simplify -2 into -2
1.704 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.704 * [taylor]: Taking taylor expansion of PI in n
1.704 * [backup-simplify]: Simplify PI into PI
1.704 * [taylor]: Taking taylor expansion of n in n
1.704 * [backup-simplify]: Simplify 0 into 0
1.704 * [backup-simplify]: Simplify 1 into 1
1.704 * [backup-simplify]: Simplify (/ PI 1) into PI
1.704 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.704 * [taylor]: Taking taylor expansion of -2 in n
1.704 * [backup-simplify]: Simplify -2 into -2
1.704 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.704 * [taylor]: Taking taylor expansion of PI in n
1.704 * [backup-simplify]: Simplify PI into PI
1.704 * [taylor]: Taking taylor expansion of n in n
1.704 * [backup-simplify]: Simplify 0 into 0
1.704 * [backup-simplify]: Simplify 1 into 1
1.705 * [backup-simplify]: Simplify (/ PI 1) into PI
1.705 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.705 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.706 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.706 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.706 * [backup-simplify]: Simplify 0 into 0
1.707 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.707 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.708 * [backup-simplify]: Simplify 0 into 0
1.708 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.709 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.709 * [backup-simplify]: Simplify 0 into 0
1.709 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.710 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.710 * [backup-simplify]: Simplify 0 into 0
1.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.712 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.712 * [backup-simplify]: Simplify 0 into 0
1.712 * [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
1.713 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.713 * [backup-simplify]: Simplify 0 into 0
1.714 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
1.714 * * * * [progress]: [ 3 / 3 ] generating series at (2)
1.714 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
1.714 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (n k) around 0
1.714 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
1.714 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
1.714 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
1.714 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
1.714 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
1.714 * [taylor]: Taking taylor expansion of 1/2 in k
1.714 * [backup-simplify]: Simplify 1/2 into 1/2
1.714 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.714 * [taylor]: Taking taylor expansion of 1 in k
1.714 * [backup-simplify]: Simplify 1 into 1
1.714 * [taylor]: Taking taylor expansion of k in k
1.714 * [backup-simplify]: Simplify 0 into 0
1.715 * [backup-simplify]: Simplify 1 into 1
1.715 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.715 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.715 * [taylor]: Taking taylor expansion of 2 in k
1.715 * [backup-simplify]: Simplify 2 into 2
1.715 * [taylor]: Taking taylor expansion of (* n PI) in k
1.715 * [taylor]: Taking taylor expansion of n in k
1.715 * [backup-simplify]: Simplify n into n
1.715 * [taylor]: Taking taylor expansion of PI in k
1.715 * [backup-simplify]: Simplify PI into PI
1.715 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.715 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.715 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.715 * [backup-simplify]: Simplify (- 0) into 0
1.715 * [backup-simplify]: Simplify (+ 1 0) into 1
1.716 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.716 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.716 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.716 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.716 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.716 * [taylor]: Taking taylor expansion of k in k
1.716 * [backup-simplify]: Simplify 0 into 0
1.716 * [backup-simplify]: Simplify 1 into 1
1.716 * [backup-simplify]: Simplify (/ 1 1) into 1
1.716 * [backup-simplify]: Simplify (sqrt 0) into 0
1.717 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.717 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
1.717 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.717 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.717 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.717 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.717 * [taylor]: Taking taylor expansion of 1/2 in n
1.717 * [backup-simplify]: Simplify 1/2 into 1/2
1.717 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.717 * [taylor]: Taking taylor expansion of 1 in n
1.717 * [backup-simplify]: Simplify 1 into 1
1.717 * [taylor]: Taking taylor expansion of k in n
1.717 * [backup-simplify]: Simplify k into k
1.717 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.717 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.718 * [taylor]: Taking taylor expansion of 2 in n
1.718 * [backup-simplify]: Simplify 2 into 2
1.718 * [taylor]: Taking taylor expansion of (* n PI) in n
1.718 * [taylor]: Taking taylor expansion of n in n
1.718 * [backup-simplify]: Simplify 0 into 0
1.718 * [backup-simplify]: Simplify 1 into 1
1.718 * [taylor]: Taking taylor expansion of PI in n
1.718 * [backup-simplify]: Simplify PI into PI
1.718 * [backup-simplify]: Simplify (* 0 PI) into 0
1.718 * [backup-simplify]: Simplify (* 2 0) into 0
1.719 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.720 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.721 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.721 * [backup-simplify]: Simplify (- k) into (- k)
1.721 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.721 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.722 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.722 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.723 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.723 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
1.723 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.723 * [taylor]: Taking taylor expansion of k in n
1.723 * [backup-simplify]: Simplify k into k
1.723 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.723 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
1.723 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.723 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
1.723 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
1.723 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.724 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.724 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.724 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.724 * [taylor]: Taking taylor expansion of 1/2 in n
1.724 * [backup-simplify]: Simplify 1/2 into 1/2
1.724 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.724 * [taylor]: Taking taylor expansion of 1 in n
1.724 * [backup-simplify]: Simplify 1 into 1
1.724 * [taylor]: Taking taylor expansion of k in n
1.724 * [backup-simplify]: Simplify k into k
1.724 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.724 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.724 * [taylor]: Taking taylor expansion of 2 in n
1.724 * [backup-simplify]: Simplify 2 into 2
1.724 * [taylor]: Taking taylor expansion of (* n PI) in n
1.724 * [taylor]: Taking taylor expansion of n in n
1.724 * [backup-simplify]: Simplify 0 into 0
1.724 * [backup-simplify]: Simplify 1 into 1
1.724 * [taylor]: Taking taylor expansion of PI in n
1.724 * [backup-simplify]: Simplify PI into PI
1.724 * [backup-simplify]: Simplify (* 0 PI) into 0
1.724 * [backup-simplify]: Simplify (* 2 0) into 0
1.725 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.726 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.727 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.727 * [backup-simplify]: Simplify (- k) into (- k)
1.727 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.727 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.728 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.728 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.729 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.729 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
1.729 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.729 * [taylor]: Taking taylor expansion of k in n
1.729 * [backup-simplify]: Simplify k into k
1.729 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.729 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
1.729 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.729 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
1.730 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
1.730 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
1.730 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
1.730 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
1.730 * [taylor]: Taking taylor expansion of 1/2 in k
1.730 * [backup-simplify]: Simplify 1/2 into 1/2
1.730 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
1.730 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.730 * [taylor]: Taking taylor expansion of 1 in k
1.730 * [backup-simplify]: Simplify 1 into 1
1.730 * [taylor]: Taking taylor expansion of k in k
1.730 * [backup-simplify]: Simplify 0 into 0
1.730 * [backup-simplify]: Simplify 1 into 1
1.730 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.730 * [taylor]: Taking taylor expansion of (log n) in k
1.730 * [taylor]: Taking taylor expansion of n in k
1.730 * [backup-simplify]: Simplify n into n
1.730 * [backup-simplify]: Simplify (log n) into (log n)
1.730 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.730 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.730 * [taylor]: Taking taylor expansion of 2 in k
1.730 * [backup-simplify]: Simplify 2 into 2
1.730 * [taylor]: Taking taylor expansion of PI in k
1.730 * [backup-simplify]: Simplify PI into PI
1.731 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.732 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.732 * [backup-simplify]: Simplify (- 0) into 0
1.733 * [backup-simplify]: Simplify (+ 1 0) into 1
1.734 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.735 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
1.736 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.737 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.737 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.737 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.737 * [taylor]: Taking taylor expansion of k in k
1.737 * [backup-simplify]: Simplify 0 into 0
1.737 * [backup-simplify]: Simplify 1 into 1
1.738 * [backup-simplify]: Simplify (/ 1 1) into 1
1.738 * [backup-simplify]: Simplify (sqrt 0) into 0
1.740 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.741 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
1.741 * [backup-simplify]: Simplify 0 into 0
1.742 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.743 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.744 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.745 * [backup-simplify]: Simplify (- 0) into 0
1.745 * [backup-simplify]: Simplify (+ 0 0) into 0
1.746 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
1.747 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.748 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.750 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.751 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
1.751 * [taylor]: Taking taylor expansion of 0 in k
1.752 * [backup-simplify]: Simplify 0 into 0
1.752 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.753 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.755 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.756 * [backup-simplify]: Simplify (+ 0 0) into 0
1.756 * [backup-simplify]: Simplify (- 1) into -1
1.756 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.758 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
1.760 * [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)))))
1.765 * [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)))))))
1.769 * [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)))))))
1.770 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.770 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.771 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
1.772 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.772 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.774 * [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
1.774 * [backup-simplify]: Simplify (- 0) into 0
1.775 * [backup-simplify]: Simplify (+ 0 0) into 0
1.775 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
1.776 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.777 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.778 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.779 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
1.779 * [taylor]: Taking taylor expansion of 0 in k
1.779 * [backup-simplify]: Simplify 0 into 0
1.779 * [backup-simplify]: Simplify 0 into 0
1.780 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
1.782 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
1.783 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.783 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.785 * [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
1.785 * [backup-simplify]: Simplify (+ 0 0) into 0
1.786 * [backup-simplify]: Simplify (- 0) into 0
1.786 * [backup-simplify]: Simplify (+ 0 0) into 0
1.787 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.789 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.791 * [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)))))
1.796 * [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))))))))
1.799 * [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))))))))
1.799 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.800 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
1.801 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.803 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
1.809 * [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
1.810 * [backup-simplify]: Simplify (- 0) into 0
1.810 * [backup-simplify]: Simplify (+ 0 0) into 0
1.811 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
1.813 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.815 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
1.818 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.820 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
1.820 * [taylor]: Taking taylor expansion of 0 in k
1.820 * [backup-simplify]: Simplify 0 into 0
1.820 * [backup-simplify]: Simplify 0 into 0
1.820 * [backup-simplify]: Simplify 0 into 0
1.821 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.826 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
1.828 * [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
1.830 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.836 * [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
1.836 * [backup-simplify]: Simplify (+ 0 0) into 0
1.837 * [backup-simplify]: Simplify (- 0) into 0
1.837 * [backup-simplify]: Simplify (+ 0 0) into 0
1.840 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
1.843 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
1.850 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.867 * [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))))))))))))))
1.878 * [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))))))))))))))
1.900 * [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))))))))))))))))))))))
1.901 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
1.901 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (n k) around 0
1.901 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
1.901 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
1.901 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
1.901 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
1.901 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
1.901 * [taylor]: Taking taylor expansion of 1/2 in k
1.901 * [backup-simplify]: Simplify 1/2 into 1/2
1.901 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.901 * [taylor]: Taking taylor expansion of 1 in k
1.901 * [backup-simplify]: Simplify 1 into 1
1.901 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.901 * [taylor]: Taking taylor expansion of k in k
1.901 * [backup-simplify]: Simplify 0 into 0
1.901 * [backup-simplify]: Simplify 1 into 1
1.902 * [backup-simplify]: Simplify (/ 1 1) into 1
1.902 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
1.902 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
1.902 * [taylor]: Taking taylor expansion of 2 in k
1.902 * [backup-simplify]: Simplify 2 into 2
1.902 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.902 * [taylor]: Taking taylor expansion of PI in k
1.902 * [backup-simplify]: Simplify PI into PI
1.902 * [taylor]: Taking taylor expansion of n in k
1.902 * [backup-simplify]: Simplify n into n
1.902 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.902 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
1.902 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
1.903 * [backup-simplify]: Simplify (- 1) into -1
1.903 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.904 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
1.904 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
1.904 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
1.904 * [taylor]: Taking taylor expansion of (sqrt k) in k
1.904 * [taylor]: Taking taylor expansion of k in k
1.904 * [backup-simplify]: Simplify 0 into 0
1.904 * [backup-simplify]: Simplify 1 into 1
1.904 * [backup-simplify]: Simplify (sqrt 0) into 0
1.906 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.906 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
1.906 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.906 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.906 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.906 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
1.906 * [taylor]: Taking taylor expansion of 1/2 in n
1.906 * [backup-simplify]: Simplify 1/2 into 1/2
1.906 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
1.906 * [taylor]: Taking taylor expansion of 1 in n
1.906 * [backup-simplify]: Simplify 1 into 1
1.906 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.906 * [taylor]: Taking taylor expansion of k in n
1.906 * [backup-simplify]: Simplify k into k
1.907 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.907 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.907 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.907 * [taylor]: Taking taylor expansion of 2 in n
1.907 * [backup-simplify]: Simplify 2 into 2
1.907 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.907 * [taylor]: Taking taylor expansion of PI in n
1.907 * [backup-simplify]: Simplify PI into PI
1.907 * [taylor]: Taking taylor expansion of n in n
1.907 * [backup-simplify]: Simplify 0 into 0
1.907 * [backup-simplify]: Simplify 1 into 1
1.907 * [backup-simplify]: Simplify (/ PI 1) into PI
1.908 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.909 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.909 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.909 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.909 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.910 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.911 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.912 * [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)))))
1.912 * [taylor]: Taking taylor expansion of (sqrt k) in n
1.912 * [taylor]: Taking taylor expansion of k in n
1.912 * [backup-simplify]: Simplify k into k
1.912 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
1.912 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
1.912 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
1.912 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.912 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.912 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.912 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
1.912 * [taylor]: Taking taylor expansion of 1/2 in n
1.912 * [backup-simplify]: Simplify 1/2 into 1/2
1.912 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
1.912 * [taylor]: Taking taylor expansion of 1 in n
1.912 * [backup-simplify]: Simplify 1 into 1
1.912 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.912 * [taylor]: Taking taylor expansion of k in n
1.912 * [backup-simplify]: Simplify k into k
1.912 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.912 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.912 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.912 * [taylor]: Taking taylor expansion of 2 in n
1.912 * [backup-simplify]: Simplify 2 into 2
1.912 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.912 * [taylor]: Taking taylor expansion of PI in n
1.912 * [backup-simplify]: Simplify PI into PI
1.912 * [taylor]: Taking taylor expansion of n in n
1.912 * [backup-simplify]: Simplify 0 into 0
1.912 * [backup-simplify]: Simplify 1 into 1
1.913 * [backup-simplify]: Simplify (/ PI 1) into PI
1.913 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.914 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.914 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.914 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.914 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.915 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.915 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.916 * [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)))))
1.916 * [taylor]: Taking taylor expansion of (sqrt k) in n
1.916 * [taylor]: Taking taylor expansion of k in n
1.916 * [backup-simplify]: Simplify k into k
1.916 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
1.916 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
1.917 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
1.917 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
1.917 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
1.917 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
1.917 * [taylor]: Taking taylor expansion of 1/2 in k
1.917 * [backup-simplify]: Simplify 1/2 into 1/2
1.917 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
1.917 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.917 * [taylor]: Taking taylor expansion of 1 in k
1.917 * [backup-simplify]: Simplify 1 into 1
1.917 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.917 * [taylor]: Taking taylor expansion of k in k
1.917 * [backup-simplify]: Simplify 0 into 0
1.917 * [backup-simplify]: Simplify 1 into 1
1.917 * [backup-simplify]: Simplify (/ 1 1) into 1
1.917 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
1.917 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.917 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.917 * [taylor]: Taking taylor expansion of 2 in k
1.917 * [backup-simplify]: Simplify 2 into 2
1.917 * [taylor]: Taking taylor expansion of PI in k
1.917 * [backup-simplify]: Simplify PI into PI
1.918 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.918 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.918 * [taylor]: Taking taylor expansion of (log n) in k
1.918 * [taylor]: Taking taylor expansion of n in k
1.918 * [backup-simplify]: Simplify n into n
1.918 * [backup-simplify]: Simplify (log n) into (log n)
1.919 * [backup-simplify]: Simplify (- 1) into -1
1.919 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.919 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.920 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
1.920 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
1.921 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
1.922 * [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)))))
1.922 * [taylor]: Taking taylor expansion of (sqrt k) in k
1.922 * [taylor]: Taking taylor expansion of k in k
1.922 * [backup-simplify]: Simplify 0 into 0
1.922 * [backup-simplify]: Simplify 1 into 1
1.922 * [backup-simplify]: Simplify (sqrt 0) into 0
1.923 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.923 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
1.923 * [backup-simplify]: Simplify 0 into 0
1.924 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.924 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.925 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.926 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.926 * [backup-simplify]: Simplify (- 0) into 0
1.926 * [backup-simplify]: Simplify (+ 0 0) into 0
1.926 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
1.927 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.928 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
1.929 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.930 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
1.930 * [taylor]: Taking taylor expansion of 0 in k
1.930 * [backup-simplify]: Simplify 0 into 0
1.930 * [backup-simplify]: Simplify 0 into 0
1.931 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
1.932 * [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)))))))
1.932 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
1.933 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.933 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.935 * [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
1.935 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.936 * [backup-simplify]: Simplify (- 0) into 0
1.936 * [backup-simplify]: Simplify (+ 0 0) into 0
1.936 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
1.937 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.938 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
1.940 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.942 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
1.942 * [taylor]: Taking taylor expansion of 0 in k
1.942 * [backup-simplify]: Simplify 0 into 0
1.942 * [backup-simplify]: Simplify 0 into 0
1.943 * [backup-simplify]: Simplify 0 into 0
1.945 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
1.947 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
1.948 * [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)))))))
1.949 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
1.951 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.952 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.958 * [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
1.958 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.959 * [backup-simplify]: Simplify (- 0) into 0
1.959 * [backup-simplify]: Simplify (+ 0 0) into 0
1.961 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
1.962 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.964 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
1.967 * [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
1.969 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
1.969 * [taylor]: Taking taylor expansion of 0 in k
1.969 * [backup-simplify]: Simplify 0 into 0
1.969 * [backup-simplify]: Simplify 0 into 0
1.969 * [backup-simplify]: Simplify 0 into 0
1.969 * [backup-simplify]: Simplify 0 into 0
1.973 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
1.975 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
1.976 * [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)))))))
1.981 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
1.981 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
1.981 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0
1.982 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
1.982 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
1.982 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
1.982 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
1.982 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
1.982 * [taylor]: Taking taylor expansion of 1/2 in k
1.982 * [backup-simplify]: Simplify 1/2 into 1/2
1.982 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
1.982 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.982 * [taylor]: Taking taylor expansion of k in k
1.982 * [backup-simplify]: Simplify 0 into 0
1.982 * [backup-simplify]: Simplify 1 into 1
1.982 * [backup-simplify]: Simplify (/ 1 1) into 1
1.982 * [taylor]: Taking taylor expansion of 1 in k
1.982 * [backup-simplify]: Simplify 1 into 1
1.982 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
1.982 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
1.982 * [taylor]: Taking taylor expansion of -2 in k
1.982 * [backup-simplify]: Simplify -2 into -2
1.982 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.982 * [taylor]: Taking taylor expansion of PI in k
1.982 * [backup-simplify]: Simplify PI into PI
1.983 * [taylor]: Taking taylor expansion of n in k
1.983 * [backup-simplify]: Simplify n into n
1.983 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.983 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
1.983 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
1.983 * [backup-simplify]: Simplify (+ 1 0) into 1
1.984 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.984 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
1.984 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
1.984 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
1.984 * [taylor]: Taking taylor expansion of (/ -1 k) in k
1.984 * [taylor]: Taking taylor expansion of -1 in k
1.984 * [backup-simplify]: Simplify -1 into -1
1.984 * [taylor]: Taking taylor expansion of k in k
1.984 * [backup-simplify]: Simplify 0 into 0
1.984 * [backup-simplify]: Simplify 1 into 1
1.985 * [backup-simplify]: Simplify (/ -1 1) into -1
1.985 * [backup-simplify]: Simplify (sqrt 0) into 0
1.987 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
1.987 * [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)))))
1.987 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
1.987 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.987 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.987 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.987 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.987 * [taylor]: Taking taylor expansion of 1/2 in n
1.987 * [backup-simplify]: Simplify 1/2 into 1/2
1.987 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.987 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.987 * [taylor]: Taking taylor expansion of k in n
1.987 * [backup-simplify]: Simplify k into k
1.987 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.987 * [taylor]: Taking taylor expansion of 1 in n
1.987 * [backup-simplify]: Simplify 1 into 1
1.987 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.987 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.987 * [taylor]: Taking taylor expansion of -2 in n
1.987 * [backup-simplify]: Simplify -2 into -2
1.987 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.987 * [taylor]: Taking taylor expansion of PI in n
1.988 * [backup-simplify]: Simplify PI into PI
1.988 * [taylor]: Taking taylor expansion of n in n
1.988 * [backup-simplify]: Simplify 0 into 0
1.988 * [backup-simplify]: Simplify 1 into 1
1.988 * [backup-simplify]: Simplify (/ PI 1) into PI
1.989 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.990 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.990 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.990 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
1.991 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.992 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
1.993 * [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)))))
1.994 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
1.994 * [taylor]: Taking taylor expansion of (/ -1 k) in n
1.994 * [taylor]: Taking taylor expansion of -1 in n
1.994 * [backup-simplify]: Simplify -1 into -1
1.994 * [taylor]: Taking taylor expansion of k in n
1.994 * [backup-simplify]: Simplify k into k
1.994 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
1.994 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
1.994 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
1.994 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
1.995 * [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)))
1.995 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
1.995 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.995 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.995 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.995 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.995 * [taylor]: Taking taylor expansion of 1/2 in n
1.996 * [backup-simplify]: Simplify 1/2 into 1/2
1.996 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.996 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.996 * [taylor]: Taking taylor expansion of k in n
1.996 * [backup-simplify]: Simplify k into k
1.996 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.996 * [taylor]: Taking taylor expansion of 1 in n
1.996 * [backup-simplify]: Simplify 1 into 1
1.996 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.996 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.996 * [taylor]: Taking taylor expansion of -2 in n
1.996 * [backup-simplify]: Simplify -2 into -2
1.996 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.996 * [taylor]: Taking taylor expansion of PI in n
1.996 * [backup-simplify]: Simplify PI into PI
1.996 * [taylor]: Taking taylor expansion of n in n
1.996 * [backup-simplify]: Simplify 0 into 0
1.996 * [backup-simplify]: Simplify 1 into 1
1.996 * [backup-simplify]: Simplify (/ PI 1) into PI
1.997 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.998 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.998 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.998 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
2.000 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.001 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
2.002 * [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)))))
2.002 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.002 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.002 * [taylor]: Taking taylor expansion of -1 in n
2.002 * [backup-simplify]: Simplify -1 into -1
2.002 * [taylor]: Taking taylor expansion of k in n
2.002 * [backup-simplify]: Simplify k into k
2.002 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.002 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.002 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.002 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.004 * [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)))
2.004 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
2.004 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
2.004 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
2.004 * [taylor]: Taking taylor expansion of 1/2 in k
2.004 * [backup-simplify]: Simplify 1/2 into 1/2
2.004 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
2.004 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
2.004 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.004 * [taylor]: Taking taylor expansion of k in k
2.004 * [backup-simplify]: Simplify 0 into 0
2.004 * [backup-simplify]: Simplify 1 into 1
2.004 * [backup-simplify]: Simplify (/ 1 1) into 1
2.004 * [taylor]: Taking taylor expansion of 1 in k
2.005 * [backup-simplify]: Simplify 1 into 1
2.005 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.005 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.005 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.005 * [taylor]: Taking taylor expansion of -2 in k
2.005 * [backup-simplify]: Simplify -2 into -2
2.005 * [taylor]: Taking taylor expansion of PI in k
2.005 * [backup-simplify]: Simplify PI into PI
2.005 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.006 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.006 * [taylor]: Taking taylor expansion of (log n) in k
2.006 * [taylor]: Taking taylor expansion of n in k
2.006 * [backup-simplify]: Simplify n into n
2.006 * [backup-simplify]: Simplify (log n) into (log n)
2.007 * [backup-simplify]: Simplify (+ 1 0) into 1
2.007 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.008 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.009 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
2.013 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.014 * [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)))))
2.014 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.014 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.015 * [taylor]: Taking taylor expansion of -1 in k
2.015 * [backup-simplify]: Simplify -1 into -1
2.015 * [taylor]: Taking taylor expansion of k in k
2.015 * [backup-simplify]: Simplify 0 into 0
2.015 * [backup-simplify]: Simplify 1 into 1
2.015 * [backup-simplify]: Simplify (/ -1 1) into -1
2.016 * [backup-simplify]: Simplify (sqrt 0) into 0
2.017 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.018 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
2.019 * [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))))))
2.021 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.021 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.023 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.023 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.024 * [backup-simplify]: Simplify (+ 0 0) into 0
2.024 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
2.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.027 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.029 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.030 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
2.031 * [taylor]: Taking taylor expansion of 0 in k
2.031 * [backup-simplify]: Simplify 0 into 0
2.031 * [backup-simplify]: Simplify 0 into 0
2.032 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.035 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.037 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.038 * [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)))))))
2.039 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.040 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.043 * [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
2.044 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.044 * [backup-simplify]: Simplify (+ 0 0) into 0
2.045 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
2.047 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.048 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.051 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.051 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.052 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
2.053 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
2.053 * [taylor]: Taking taylor expansion of 0 in k
2.053 * [backup-simplify]: Simplify 0 into 0
2.053 * [backup-simplify]: Simplify 0 into 0
2.053 * [backup-simplify]: Simplify 0 into 0
2.054 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.059 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.062 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.063 * [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)))))))
2.068 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
2.068 * * * [progress]: simplifying candidates
2.068 * * * * [progress]: [ 1 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.068 * * * * [progress]: [ 2 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.068 * * * * [progress]: [ 3 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 4 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 5 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 6 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 7 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 8 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 9 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 10 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 11 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 12 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 13 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 14 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 15 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (sqrt k)))>
2.069 * * * * [progress]: [ 16 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (sqrt k)))>
2.069 * * * * [progress]: [ 17 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (sqrt k)))>
2.070 * * * * [progress]: [ 18 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (sqrt k)))>
2.070 * * * * [progress]: [ 19 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
2.070 * * * * [progress]: [ 20 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
2.070 * * * * [progress]: [ 21 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
2.070 * * * * [progress]: [ 22 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (sqrt k)))>
2.070 * * * * [progress]: [ 23 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (sqrt k)))>
2.070 * * * * [progress]: [ 24 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (sqrt k)))>
2.070 * * * * [progress]: [ 25 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (sqrt k)))>
2.070 * * * * [progress]: [ 26 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (sqrt k)))>
2.070 * * * * [progress]: [ 27 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k)))>
2.070 * * * * [progress]: [ 28 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
2.071 * * * * [progress]: [ 29 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
2.071 * * * * [progress]: [ 30 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
2.071 * * * * [progress]: [ 31 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
2.071 * * * * [progress]: [ 32 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1 k)) (/ 1 2)) (sqrt k)))>
2.071 * * * * [progress]: [ 33 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)))>
2.071 * * * * [progress]: [ 34 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
2.071 * * * * [progress]: [ 35 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.071 * * * * [progress]: [ 36 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.071 * * * * [progress]: [ 37 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.071 * * * * [progress]: [ 38 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.071 * * * * [progress]: [ 39 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.071 * * * * [progress]: [ 40 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))>
2.071 * * * * [progress]: [ 41 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
2.071 * * * * [progress]: [ 42 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.072 * * * * [progress]: [ 43 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 44 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 45 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 46 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 47 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 48 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 49 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 50 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 51 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 52 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 53 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 54 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 55 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.072 * * * * [progress]: [ 56 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.073 * * * * [progress]: [ 57 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
2.073 * * * * [progress]: [ 58 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))>
2.073 * * * * [progress]: [ 59 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
2.073 * * * * [progress]: [ 60 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
2.073 * * * * [progress]: [ 61 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
2.073 * * * * [progress]: [ 62 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.073 * * * * [progress]: [ 63 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))>
2.073 * * * * [progress]: [ 64 / 133 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.073 * * * * [progress]: [ 65 / 133 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.073 * * * * [progress]: [ 66 / 133 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) 1))>
2.073 * * * * [progress]: [ 67 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
2.073 * * * * [progress]: [ 68 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
2.073 * * * * [progress]: [ 69 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
2.073 * * * * [progress]: [ 70 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
2.073 * * * * [progress]: [ 71 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))))>
2.073 * * * * [progress]: [ 72 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.074 * * * * [progress]: [ 73 / 133 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.074 * * * * [progress]: [ 74 / 133 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
2.074 * * * * [progress]: [ 75 / 133 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.074 * * * * [progress]: [ 76 / 133 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.074 * * * * [progress]: [ 77 / 133 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.074 * * * * [progress]: [ 78 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- (sqrt k))))>
2.074 * * * * [progress]: [ 79 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
2.074 * * * * [progress]: [ 80 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
2.074 * * * * [progress]: [ 81 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
2.074 * * * * [progress]: [ 82 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
2.074 * * * * [progress]: [ 83 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
2.074 * * * * [progress]: [ 84 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
2.074 * * * * [progress]: [ 85 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
2.074 * * * * [progress]: [ 86 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
2.075 * * * * [progress]: [ 87 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
2.075 * * * * [progress]: [ 88 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
2.075 * * * * [progress]: [ 89 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
2.075 * * * * [progress]: [ 90 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
2.075 * * * * [progress]: [ 91 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
2.075 * * * * [progress]: [ 92 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
2.075 * * * * [progress]: [ 93 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
2.075 * * * * [progress]: [ 94 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
2.075 * * * * [progress]: [ 95 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
2.075 * * * * [progress]: [ 96 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
2.075 * * * * [progress]: [ 97 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
2.075 * * * * [progress]: [ 98 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
2.075 * * * * [progress]: [ 99 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
2.075 * * * * [progress]: [ 100 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))>
2.076 * * * * [progress]: [ 101 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
2.076 * * * * [progress]: [ 102 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))>
2.076 * * * * [progress]: [ 103 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))>
2.076 * * * * [progress]: [ 104 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))>
2.076 * * * * [progress]: [ 105 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
2.076 * * * * [progress]: [ 106 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
2.076 * * * * [progress]: [ 107 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
2.076 * * * * [progress]: [ 108 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
2.076 * * * * [progress]: [ 109 / 133 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))>
2.076 * * * * [progress]: [ 110 / 133 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
2.076 * * * * [progress]: [ 111 / 133 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
2.076 * * * * [progress]: [ 112 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
2.076 * * * * [progress]: [ 113 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
2.076 * * * * [progress]: [ 114 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.077 * * * * [progress]: [ 115 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt 1)) (sqrt k)))>
2.077 * * * * [progress]: [ 116 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.077 * * * * [progress]: [ 117 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
2.077 * * * * [progress]: [ 118 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))))>
2.077 * * * * [progress]: [ 119 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
2.077 * * * * [progress]: [ 120 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
2.077 * * * * [progress]: [ 121 / 133 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
2.077 * * * * [progress]: [ 122 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
2.077 * * * * [progress]: [ 123 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))>
2.077 * * * * [progress]: [ 124 / 133 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.077 * * * * [progress]: [ 125 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
2.077 * * * * [progress]: [ 126 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))>
2.077 * * * * [progress]: [ 127 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))>
2.077 * * * * [progress]: [ 128 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
2.077 * * * * [progress]: [ 129 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
2.078 * * * * [progress]: [ 130 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
2.078 * * * * [progress]: [ 131 / 133 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
2.078 * * * * [progress]: [ 132 / 133 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
2.078 * * * * [progress]: [ 133 / 133 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
2.081 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* n (* 2 PI)) (/ 1 2))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (expm1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))
  (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) 1)
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1)
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1)
  (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))
  (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))
  (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
2.086 * * [simplify]: iteration 1: (293 enodes)
2.252 * * [simplify]: iteration 2: (1283 enodes)
2.652 * * [simplify]: Extracting #0: cost 104 inf + 0
2.653 * * [simplify]: Extracting #1: cost 497 inf + 1
2.663 * * [simplify]: Extracting #2: cost 810 inf + 14867
2.678 * * [simplify]: Extracting #3: cost 702 inf + 99401
2.723 * * [simplify]: Extracting #4: cost 365 inf + 232639
2.788 * * [simplify]: Extracting #5: cost 166 inf + 319584
2.860 * * [simplify]: Extracting #6: cost 117 inf + 352160
2.973 * * [simplify]: Extracting #7: cost 45 inf + 400424
3.080 * * [simplify]: Extracting #8: cost 4 inf + 433511
3.218 * * [simplify]: Extracting #9: cost 0 inf + 434477
3.356 * * [simplify]: Extracting #10: cost 0 inf + 432772
3.485 * * [simplify]: Extracting #11: cost 0 inf + 432482
3.601 * [simplify]: Simplified to:
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (cbrt (- 1 k)) (/ (sqrt 2) (cbrt (- 1 k)))))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* PI 2) (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (expm1 (* (* PI 2) n))
  (log1p (* (* PI 2) n))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* (* (* n n) n) (* (* PI PI) PI)) 8)
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* (* PI 2) (cbrt n))
  (* (* (sqrt n) PI) 2)
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (expm1 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* PI 2) n))) (log (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (/ (/ (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3) (sqrt k)) k)
  (* (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (* (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow n (/ (- 1 k) 2))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow n (/ (- 1 k) 2))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (* (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (fabs (cbrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 4))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 4)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 4)))
  (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k))
  (real->posit16 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (fma (* (* (* (sqrt (* (* PI 2) n)) (log (* PI 2))) (log n)) (* k k)) 1/4 (- (fma (* 1/8 (sqrt (* (* PI 2) n))) (* (* (log n) k) (* (log n) k)) (fma (* (* k k) (* (log (* PI 2)) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))) 1/8 (sqrt (* (* PI 2) n)))) (* (* k (+ (* (log n) (sqrt (* (* PI 2) n))) (* (sqrt (* (* PI 2) n)) (log (* PI 2))))) 1/2)))
  (exp (* (* (log (* (* PI 2) n)) (- 1 k)) 1/2))
  (exp (* (* 1/2 (- (log (* PI -2)) (log (/ -1 n)))) (- 1 k)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (+ (fma (* (log (* PI 2)) +nan.0) (* (* k k) (sqrt (* (* PI 2) n))) (+ (fma +nan.0 (* k (sqrt (* (* PI 2) n))) (+ (- (* (* (* k k) (sqrt (* (* PI 2) n))) (* (* (log (* PI 2)) +nan.0) (log (* PI 2)))) (fma (* (* k k) (* (log n) (sqrt (* (* PI 2) n)))) +nan.0 (+ (* (- +nan.0) (* (* k k) (sqrt (* (* PI 2) n)))) (* +nan.0 (- (* (* (log (* PI 2)) k) (sqrt (* (* PI 2) n))) (* k (* (log n) (sqrt (* (* PI 2) n))))))))) (* (sqrt (* (* PI 2) n)) (- +nan.0)))) (* (* (sqrt (* (* PI 2) n)) (- +nan.0)) (* (* (log n) k) (* (log n) k))))) (* (- (* (log (* PI 2)) +nan.0)) (* (* k k) (* (log n) (sqrt (* (* PI 2) n))))))
  (+ (/ (- (* (exp (* (* (log (* (* PI 2) n)) (- 1 k)) 1/2)) +nan.0)) k) (* +nan.0 (- (/ (exp (* (* (log (* (* PI 2) n)) (- 1 k)) 1/2)) (* k k)) (/ (/ (exp (* (* (log (* (* PI 2) n)) (- 1 k)) 1/2)) (* k k)) k))))
  (+ (* +nan.0 (- (/ (exp (* (* 1/2 (- (log (* PI -2)) (log (/ -1 n)))) (- 1 k))) (* k k)) (exp (* (* 1/2 (- (log (* PI -2)) (log (/ -1 n)))) (- 1 k))))) (- (/ (exp (* (* 1/2 (- (log (* PI -2)) (log (/ -1 n)))) (- 1 k))) (/ k +nan.0))))
3.610 * * * [progress]: adding candidates to table
5.176 * * [progress]: iteration 2 / 4
5.176 * * * [progress]: picking best candidate
5.204 * * * * [pick]: Picked  #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
5.204 * * * [progress]: localizing error
5.258 * * * [progress]: generating rewritten candidates
5.258 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
5.281 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1)
5.294 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
5.303 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
5.350 * * * [progress]: generating series expansions
5.350 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
5.351 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
5.351 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
5.351 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.352 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.352 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.352 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.352 * [taylor]: Taking taylor expansion of 1/2 in k
5.352 * [backup-simplify]: Simplify 1/2 into 1/2
5.352 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.352 * [taylor]: Taking taylor expansion of 1 in k
5.352 * [backup-simplify]: Simplify 1 into 1
5.352 * [taylor]: Taking taylor expansion of k in k
5.352 * [backup-simplify]: Simplify 0 into 0
5.352 * [backup-simplify]: Simplify 1 into 1
5.352 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.352 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.352 * [taylor]: Taking taylor expansion of 2 in k
5.352 * [backup-simplify]: Simplify 2 into 2
5.352 * [taylor]: Taking taylor expansion of (* n PI) in k
5.352 * [taylor]: Taking taylor expansion of n in k
5.352 * [backup-simplify]: Simplify n into n
5.352 * [taylor]: Taking taylor expansion of PI in k
5.352 * [backup-simplify]: Simplify PI into PI
5.352 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.352 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.352 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.353 * [backup-simplify]: Simplify (- 0) into 0
5.353 * [backup-simplify]: Simplify (+ 1 0) into 1
5.354 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.354 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.354 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.354 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.354 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.354 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.354 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.354 * [taylor]: Taking taylor expansion of 1/2 in n
5.354 * [backup-simplify]: Simplify 1/2 into 1/2
5.354 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.354 * [taylor]: Taking taylor expansion of 1 in n
5.354 * [backup-simplify]: Simplify 1 into 1
5.354 * [taylor]: Taking taylor expansion of k in n
5.354 * [backup-simplify]: Simplify k into k
5.354 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.354 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.354 * [taylor]: Taking taylor expansion of 2 in n
5.354 * [backup-simplify]: Simplify 2 into 2
5.354 * [taylor]: Taking taylor expansion of (* n PI) in n
5.354 * [taylor]: Taking taylor expansion of n in n
5.354 * [backup-simplify]: Simplify 0 into 0
5.354 * [backup-simplify]: Simplify 1 into 1
5.355 * [taylor]: Taking taylor expansion of PI in n
5.355 * [backup-simplify]: Simplify PI into PI
5.355 * [backup-simplify]: Simplify (* 0 PI) into 0
5.355 * [backup-simplify]: Simplify (* 2 0) into 0
5.357 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.359 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.360 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.360 * [backup-simplify]: Simplify (- k) into (- k)
5.360 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.360 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.361 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.362 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.363 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.363 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.363 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.363 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.363 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.363 * [taylor]: Taking taylor expansion of 1/2 in n
5.363 * [backup-simplify]: Simplify 1/2 into 1/2
5.363 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.363 * [taylor]: Taking taylor expansion of 1 in n
5.363 * [backup-simplify]: Simplify 1 into 1
5.364 * [taylor]: Taking taylor expansion of k in n
5.364 * [backup-simplify]: Simplify k into k
5.364 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.364 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.364 * [taylor]: Taking taylor expansion of 2 in n
5.364 * [backup-simplify]: Simplify 2 into 2
5.364 * [taylor]: Taking taylor expansion of (* n PI) in n
5.364 * [taylor]: Taking taylor expansion of n in n
5.364 * [backup-simplify]: Simplify 0 into 0
5.364 * [backup-simplify]: Simplify 1 into 1
5.364 * [taylor]: Taking taylor expansion of PI in n
5.364 * [backup-simplify]: Simplify PI into PI
5.364 * [backup-simplify]: Simplify (* 0 PI) into 0
5.365 * [backup-simplify]: Simplify (* 2 0) into 0
5.366 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.368 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.369 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.369 * [backup-simplify]: Simplify (- k) into (- k)
5.369 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.369 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.370 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.371 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.372 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.372 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
5.372 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
5.372 * [taylor]: Taking taylor expansion of 1/2 in k
5.372 * [backup-simplify]: Simplify 1/2 into 1/2
5.372 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
5.373 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.373 * [taylor]: Taking taylor expansion of 1 in k
5.373 * [backup-simplify]: Simplify 1 into 1
5.373 * [taylor]: Taking taylor expansion of k in k
5.373 * [backup-simplify]: Simplify 0 into 0
5.373 * [backup-simplify]: Simplify 1 into 1
5.373 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
5.373 * [taylor]: Taking taylor expansion of (log n) in k
5.373 * [taylor]: Taking taylor expansion of n in k
5.373 * [backup-simplify]: Simplify n into n
5.373 * [backup-simplify]: Simplify (log n) into (log n)
5.373 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.373 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.373 * [taylor]: Taking taylor expansion of 2 in k
5.373 * [backup-simplify]: Simplify 2 into 2
5.373 * [taylor]: Taking taylor expansion of PI in k
5.373 * [backup-simplify]: Simplify PI into PI
5.373 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.374 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.375 * [backup-simplify]: Simplify (- 0) into 0
5.375 * [backup-simplify]: Simplify (+ 1 0) into 1
5.376 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.377 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
5.378 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
5.379 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.380 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.381 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.382 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.384 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.384 * [backup-simplify]: Simplify (- 0) into 0
5.385 * [backup-simplify]: Simplify (+ 0 0) into 0
5.385 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
5.387 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.388 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.389 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.389 * [taylor]: Taking taylor expansion of 0 in k
5.389 * [backup-simplify]: Simplify 0 into 0
5.389 * [backup-simplify]: Simplify 0 into 0
5.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.390 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.391 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.391 * [backup-simplify]: Simplify (+ 0 0) into 0
5.392 * [backup-simplify]: Simplify (- 1) into -1
5.392 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.393 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
5.394 * [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)))))
5.396 * [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)))))))
5.398 * [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)))))))
5.398 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.399 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.401 * [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
5.401 * [backup-simplify]: Simplify (- 0) into 0
5.401 * [backup-simplify]: Simplify (+ 0 0) into 0
5.402 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
5.403 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.404 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.405 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.405 * [taylor]: Taking taylor expansion of 0 in k
5.405 * [backup-simplify]: Simplify 0 into 0
5.405 * [backup-simplify]: Simplify 0 into 0
5.405 * [backup-simplify]: Simplify 0 into 0
5.406 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.407 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.408 * [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
5.409 * [backup-simplify]: Simplify (+ 0 0) into 0
5.409 * [backup-simplify]: Simplify (- 0) into 0
5.409 * [backup-simplify]: Simplify (+ 0 0) into 0
5.410 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.412 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.414 * [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)))))
5.418 * [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)))))
5.427 * [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)))))
5.428 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
5.428 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
5.428 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.428 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.429 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.429 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.429 * [taylor]: Taking taylor expansion of 1/2 in k
5.429 * [backup-simplify]: Simplify 1/2 into 1/2
5.429 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.429 * [taylor]: Taking taylor expansion of 1 in k
5.429 * [backup-simplify]: Simplify 1 into 1
5.429 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.429 * [taylor]: Taking taylor expansion of k in k
5.429 * [backup-simplify]: Simplify 0 into 0
5.429 * [backup-simplify]: Simplify 1 into 1
5.429 * [backup-simplify]: Simplify (/ 1 1) into 1
5.429 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.429 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.429 * [taylor]: Taking taylor expansion of 2 in k
5.429 * [backup-simplify]: Simplify 2 into 2
5.429 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.429 * [taylor]: Taking taylor expansion of PI in k
5.429 * [backup-simplify]: Simplify PI into PI
5.429 * [taylor]: Taking taylor expansion of n in k
5.429 * [backup-simplify]: Simplify n into n
5.430 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.430 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.430 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.430 * [backup-simplify]: Simplify (- 1) into -1
5.431 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.431 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.431 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.431 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.431 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.431 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.431 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.432 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.432 * [taylor]: Taking taylor expansion of 1/2 in n
5.432 * [backup-simplify]: Simplify 1/2 into 1/2
5.432 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.432 * [taylor]: Taking taylor expansion of 1 in n
5.432 * [backup-simplify]: Simplify 1 into 1
5.432 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.432 * [taylor]: Taking taylor expansion of k in n
5.432 * [backup-simplify]: Simplify k into k
5.432 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.432 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.432 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.432 * [taylor]: Taking taylor expansion of 2 in n
5.432 * [backup-simplify]: Simplify 2 into 2
5.432 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.432 * [taylor]: Taking taylor expansion of PI in n
5.432 * [backup-simplify]: Simplify PI into PI
5.432 * [taylor]: Taking taylor expansion of n in n
5.432 * [backup-simplify]: Simplify 0 into 0
5.432 * [backup-simplify]: Simplify 1 into 1
5.433 * [backup-simplify]: Simplify (/ PI 1) into PI
5.433 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.434 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.434 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.434 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.434 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.436 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.437 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.438 * [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)))))
5.438 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.438 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.438 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.438 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.438 * [taylor]: Taking taylor expansion of 1/2 in n
5.438 * [backup-simplify]: Simplify 1/2 into 1/2
5.438 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.438 * [taylor]: Taking taylor expansion of 1 in n
5.438 * [backup-simplify]: Simplify 1 into 1
5.438 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.438 * [taylor]: Taking taylor expansion of k in n
5.438 * [backup-simplify]: Simplify k into k
5.438 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.438 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.438 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.438 * [taylor]: Taking taylor expansion of 2 in n
5.438 * [backup-simplify]: Simplify 2 into 2
5.438 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.438 * [taylor]: Taking taylor expansion of PI in n
5.438 * [backup-simplify]: Simplify PI into PI
5.438 * [taylor]: Taking taylor expansion of n in n
5.439 * [backup-simplify]: Simplify 0 into 0
5.439 * [backup-simplify]: Simplify 1 into 1
5.439 * [backup-simplify]: Simplify (/ PI 1) into PI
5.440 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.441 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.441 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.441 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.441 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.442 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.443 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.444 * [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)))))
5.444 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
5.444 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
5.445 * [taylor]: Taking taylor expansion of 1/2 in k
5.445 * [backup-simplify]: Simplify 1/2 into 1/2
5.445 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
5.445 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.445 * [taylor]: Taking taylor expansion of 1 in k
5.445 * [backup-simplify]: Simplify 1 into 1
5.445 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.445 * [taylor]: Taking taylor expansion of k in k
5.445 * [backup-simplify]: Simplify 0 into 0
5.445 * [backup-simplify]: Simplify 1 into 1
5.445 * [backup-simplify]: Simplify (/ 1 1) into 1
5.445 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
5.445 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.445 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.445 * [taylor]: Taking taylor expansion of 2 in k
5.445 * [backup-simplify]: Simplify 2 into 2
5.445 * [taylor]: Taking taylor expansion of PI in k
5.445 * [backup-simplify]: Simplify PI into PI
5.446 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.447 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.447 * [taylor]: Taking taylor expansion of (log n) in k
5.447 * [taylor]: Taking taylor expansion of n in k
5.447 * [backup-simplify]: Simplify n into n
5.447 * [backup-simplify]: Simplify (log n) into (log n)
5.448 * [backup-simplify]: Simplify (- 1) into -1
5.448 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.448 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.449 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
5.450 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
5.451 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
5.452 * [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)))))
5.454 * [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)))))
5.455 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.455 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.457 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.457 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.458 * [backup-simplify]: Simplify (- 0) into 0
5.458 * [backup-simplify]: Simplify (+ 0 0) into 0
5.458 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
5.460 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.461 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.463 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.463 * [taylor]: Taking taylor expansion of 0 in k
5.463 * [backup-simplify]: Simplify 0 into 0
5.463 * [backup-simplify]: Simplify 0 into 0
5.463 * [backup-simplify]: Simplify 0 into 0
5.464 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.465 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.474 * [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
5.474 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.475 * [backup-simplify]: Simplify (- 0) into 0
5.475 * [backup-simplify]: Simplify (+ 0 0) into 0
5.476 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
5.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.479 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
5.481 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.481 * [taylor]: Taking taylor expansion of 0 in k
5.482 * [backup-simplify]: Simplify 0 into 0
5.482 * [backup-simplify]: Simplify 0 into 0
5.482 * [backup-simplify]: Simplify 0 into 0
5.482 * [backup-simplify]: Simplify 0 into 0
5.483 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.484 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.490 * [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
5.490 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.491 * [backup-simplify]: Simplify (- 0) into 0
5.491 * [backup-simplify]: Simplify (+ 0 0) into 0
5.492 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
5.492 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.494 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
5.495 * [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
5.495 * [taylor]: Taking taylor expansion of 0 in k
5.495 * [backup-simplify]: Simplify 0 into 0
5.495 * [backup-simplify]: Simplify 0 into 0
5.496 * [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))))))
5.496 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
5.496 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
5.496 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.496 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.496 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.496 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.496 * [taylor]: Taking taylor expansion of 1/2 in k
5.496 * [backup-simplify]: Simplify 1/2 into 1/2
5.496 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.496 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.496 * [taylor]: Taking taylor expansion of k in k
5.496 * [backup-simplify]: Simplify 0 into 0
5.496 * [backup-simplify]: Simplify 1 into 1
5.497 * [backup-simplify]: Simplify (/ 1 1) into 1
5.497 * [taylor]: Taking taylor expansion of 1 in k
5.497 * [backup-simplify]: Simplify 1 into 1
5.497 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.497 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.497 * [taylor]: Taking taylor expansion of -2 in k
5.497 * [backup-simplify]: Simplify -2 into -2
5.497 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.497 * [taylor]: Taking taylor expansion of PI in k
5.497 * [backup-simplify]: Simplify PI into PI
5.497 * [taylor]: Taking taylor expansion of n in k
5.497 * [backup-simplify]: Simplify n into n
5.497 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.497 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.497 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.498 * [backup-simplify]: Simplify (+ 1 0) into 1
5.498 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.498 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.498 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.498 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.498 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.498 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.498 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.498 * [taylor]: Taking taylor expansion of 1/2 in n
5.498 * [backup-simplify]: Simplify 1/2 into 1/2
5.498 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.498 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.498 * [taylor]: Taking taylor expansion of k in n
5.498 * [backup-simplify]: Simplify k into k
5.498 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.498 * [taylor]: Taking taylor expansion of 1 in n
5.498 * [backup-simplify]: Simplify 1 into 1
5.498 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.498 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.498 * [taylor]: Taking taylor expansion of -2 in n
5.498 * [backup-simplify]: Simplify -2 into -2
5.498 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.498 * [taylor]: Taking taylor expansion of PI in n
5.498 * [backup-simplify]: Simplify PI into PI
5.498 * [taylor]: Taking taylor expansion of n in n
5.498 * [backup-simplify]: Simplify 0 into 0
5.498 * [backup-simplify]: Simplify 1 into 1
5.499 * [backup-simplify]: Simplify (/ PI 1) into PI
5.499 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.500 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.500 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.500 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.500 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.501 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.502 * [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)))))
5.502 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.502 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.502 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.502 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.502 * [taylor]: Taking taylor expansion of 1/2 in n
5.502 * [backup-simplify]: Simplify 1/2 into 1/2
5.502 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.502 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.502 * [taylor]: Taking taylor expansion of k in n
5.502 * [backup-simplify]: Simplify k into k
5.502 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.502 * [taylor]: Taking taylor expansion of 1 in n
5.502 * [backup-simplify]: Simplify 1 into 1
5.502 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.502 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.502 * [taylor]: Taking taylor expansion of -2 in n
5.502 * [backup-simplify]: Simplify -2 into -2
5.502 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.502 * [taylor]: Taking taylor expansion of PI in n
5.502 * [backup-simplify]: Simplify PI into PI
5.502 * [taylor]: Taking taylor expansion of n in n
5.502 * [backup-simplify]: Simplify 0 into 0
5.502 * [backup-simplify]: Simplify 1 into 1
5.502 * [backup-simplify]: Simplify (/ PI 1) into PI
5.503 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.503 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.503 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.503 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.504 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.505 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.506 * [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)))))
5.506 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
5.506 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
5.506 * [taylor]: Taking taylor expansion of 1/2 in k
5.506 * [backup-simplify]: Simplify 1/2 into 1/2
5.506 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
5.506 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.506 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.506 * [taylor]: Taking taylor expansion of k in k
5.506 * [backup-simplify]: Simplify 0 into 0
5.506 * [backup-simplify]: Simplify 1 into 1
5.506 * [backup-simplify]: Simplify (/ 1 1) into 1
5.506 * [taylor]: Taking taylor expansion of 1 in k
5.506 * [backup-simplify]: Simplify 1 into 1
5.506 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
5.506 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
5.506 * [taylor]: Taking taylor expansion of (* -2 PI) in k
5.506 * [taylor]: Taking taylor expansion of -2 in k
5.506 * [backup-simplify]: Simplify -2 into -2
5.506 * [taylor]: Taking taylor expansion of PI in k
5.506 * [backup-simplify]: Simplify PI into PI
5.507 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.507 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.507 * [taylor]: Taking taylor expansion of (log n) in k
5.507 * [taylor]: Taking taylor expansion of n in k
5.507 * [backup-simplify]: Simplify n into n
5.507 * [backup-simplify]: Simplify (log n) into (log n)
5.508 * [backup-simplify]: Simplify (+ 1 0) into 1
5.508 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.508 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
5.509 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
5.509 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
5.510 * [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)))))
5.511 * [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)))))
5.511 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.512 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.513 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.513 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.513 * [backup-simplify]: Simplify (+ 0 0) into 0
5.513 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
5.514 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.515 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
5.516 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.516 * [taylor]: Taking taylor expansion of 0 in k
5.516 * [backup-simplify]: Simplify 0 into 0
5.516 * [backup-simplify]: Simplify 0 into 0
5.516 * [backup-simplify]: Simplify 0 into 0
5.517 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.517 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.519 * [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
5.519 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.520 * [backup-simplify]: Simplify (+ 0 0) into 0
5.520 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
5.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.522 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
5.524 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.524 * [taylor]: Taking taylor expansion of 0 in k
5.524 * [backup-simplify]: Simplify 0 into 0
5.524 * [backup-simplify]: Simplify 0 into 0
5.524 * [backup-simplify]: Simplify 0 into 0
5.524 * [backup-simplify]: Simplify 0 into 0
5.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.527 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.533 * [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
5.533 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.533 * [backup-simplify]: Simplify (+ 0 0) into 0
5.535 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
5.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.537 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
5.538 * [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
5.538 * [taylor]: Taking taylor expansion of 0 in k
5.538 * [backup-simplify]: Simplify 0 into 0
5.538 * [backup-simplify]: Simplify 0 into 0
5.539 * [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))))))
5.539 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1)
5.539 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
5.540 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
5.540 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.540 * [taylor]: Taking taylor expansion of 2 in n
5.540 * [backup-simplify]: Simplify 2 into 2
5.540 * [taylor]: Taking taylor expansion of (* n PI) in n
5.540 * [taylor]: Taking taylor expansion of n in n
5.540 * [backup-simplify]: Simplify 0 into 0
5.540 * [backup-simplify]: Simplify 1 into 1
5.540 * [taylor]: Taking taylor expansion of PI in n
5.540 * [backup-simplify]: Simplify PI into PI
5.540 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.540 * [taylor]: Taking taylor expansion of 2 in n
5.540 * [backup-simplify]: Simplify 2 into 2
5.540 * [taylor]: Taking taylor expansion of (* n PI) in n
5.540 * [taylor]: Taking taylor expansion of n in n
5.540 * [backup-simplify]: Simplify 0 into 0
5.540 * [backup-simplify]: Simplify 1 into 1
5.540 * [taylor]: Taking taylor expansion of PI in n
5.540 * [backup-simplify]: Simplify PI into PI
5.540 * [backup-simplify]: Simplify (* 0 PI) into 0
5.540 * [backup-simplify]: Simplify (* 2 0) into 0
5.540 * [backup-simplify]: Simplify 0 into 0
5.541 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.542 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.543 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.543 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.544 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.544 * [backup-simplify]: Simplify 0 into 0
5.545 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.545 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.545 * [backup-simplify]: Simplify 0 into 0
5.546 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.547 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.547 * [backup-simplify]: Simplify 0 into 0
5.548 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.549 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
5.549 * [backup-simplify]: Simplify 0 into 0
5.550 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.551 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
5.551 * [backup-simplify]: Simplify 0 into 0
5.552 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
5.553 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
5.553 * [backup-simplify]: Simplify 0 into 0
5.553 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
5.554 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
5.554 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
5.554 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.554 * [taylor]: Taking taylor expansion of 2 in n
5.554 * [backup-simplify]: Simplify 2 into 2
5.554 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.554 * [taylor]: Taking taylor expansion of PI in n
5.554 * [backup-simplify]: Simplify PI into PI
5.554 * [taylor]: Taking taylor expansion of n in n
5.554 * [backup-simplify]: Simplify 0 into 0
5.554 * [backup-simplify]: Simplify 1 into 1
5.554 * [backup-simplify]: Simplify (/ PI 1) into PI
5.554 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.554 * [taylor]: Taking taylor expansion of 2 in n
5.554 * [backup-simplify]: Simplify 2 into 2
5.554 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.554 * [taylor]: Taking taylor expansion of PI in n
5.554 * [backup-simplify]: Simplify PI into PI
5.554 * [taylor]: Taking taylor expansion of n in n
5.554 * [backup-simplify]: Simplify 0 into 0
5.554 * [backup-simplify]: Simplify 1 into 1
5.555 * [backup-simplify]: Simplify (/ PI 1) into PI
5.555 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.555 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.556 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.556 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.556 * [backup-simplify]: Simplify 0 into 0
5.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.557 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.558 * [backup-simplify]: Simplify 0 into 0
5.558 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.559 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.559 * [backup-simplify]: Simplify 0 into 0
5.559 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.560 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.560 * [backup-simplify]: Simplify 0 into 0
5.561 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.562 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.562 * [backup-simplify]: Simplify 0 into 0
5.562 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.563 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.563 * [backup-simplify]: Simplify 0 into 0
5.564 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
5.564 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
5.564 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
5.564 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.564 * [taylor]: Taking taylor expansion of -2 in n
5.564 * [backup-simplify]: Simplify -2 into -2
5.564 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.564 * [taylor]: Taking taylor expansion of PI in n
5.564 * [backup-simplify]: Simplify PI into PI
5.564 * [taylor]: Taking taylor expansion of n in n
5.564 * [backup-simplify]: Simplify 0 into 0
5.564 * [backup-simplify]: Simplify 1 into 1
5.565 * [backup-simplify]: Simplify (/ PI 1) into PI
5.565 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.565 * [taylor]: Taking taylor expansion of -2 in n
5.565 * [backup-simplify]: Simplify -2 into -2
5.565 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.565 * [taylor]: Taking taylor expansion of PI in n
5.565 * [backup-simplify]: Simplify PI into PI
5.565 * [taylor]: Taking taylor expansion of n in n
5.565 * [backup-simplify]: Simplify 0 into 0
5.565 * [backup-simplify]: Simplify 1 into 1
5.565 * [backup-simplify]: Simplify (/ PI 1) into PI
5.565 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.566 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.566 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.567 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.567 * [backup-simplify]: Simplify 0 into 0
5.568 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.569 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.569 * [backup-simplify]: Simplify 0 into 0
5.570 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.571 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.571 * [backup-simplify]: Simplify 0 into 0
5.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.574 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.574 * [backup-simplify]: Simplify 0 into 0
5.575 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.582 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.582 * [backup-simplify]: Simplify 0 into 0
5.583 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.585 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.585 * [backup-simplify]: Simplify 0 into 0
5.586 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
5.586 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
5.586 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) into (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k))
5.587 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in (k n) around 0
5.587 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in n
5.587 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in n
5.587 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.587 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.587 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.587 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.587 * [taylor]: Taking taylor expansion of 1/2 in n
5.587 * [backup-simplify]: Simplify 1/2 into 1/2
5.587 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.587 * [taylor]: Taking taylor expansion of 1 in n
5.587 * [backup-simplify]: Simplify 1 into 1
5.587 * [taylor]: Taking taylor expansion of k in n
5.587 * [backup-simplify]: Simplify k into k
5.587 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.587 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.587 * [taylor]: Taking taylor expansion of 2 in n
5.587 * [backup-simplify]: Simplify 2 into 2
5.587 * [taylor]: Taking taylor expansion of (* n PI) in n
5.587 * [taylor]: Taking taylor expansion of n in n
5.587 * [backup-simplify]: Simplify 0 into 0
5.587 * [backup-simplify]: Simplify 1 into 1
5.587 * [taylor]: Taking taylor expansion of PI in n
5.587 * [backup-simplify]: Simplify PI into PI
5.588 * [backup-simplify]: Simplify (* 0 PI) into 0
5.588 * [backup-simplify]: Simplify (* 2 0) into 0
5.590 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.591 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.592 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.592 * [backup-simplify]: Simplify (- k) into (- k)
5.592 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.592 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.594 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.595 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.596 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.597 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) into (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))
5.597 * [taylor]: Taking taylor expansion of (sqrt k) in n
5.597 * [taylor]: Taking taylor expansion of k in n
5.597 * [backup-simplify]: Simplify k into k
5.597 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
5.597 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
5.598 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in k
5.598 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in k
5.598 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.598 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.598 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.598 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.598 * [taylor]: Taking taylor expansion of 1/2 in k
5.598 * [backup-simplify]: Simplify 1/2 into 1/2
5.598 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.598 * [taylor]: Taking taylor expansion of 1 in k
5.598 * [backup-simplify]: Simplify 1 into 1
5.598 * [taylor]: Taking taylor expansion of k in k
5.598 * [backup-simplify]: Simplify 0 into 0
5.598 * [backup-simplify]: Simplify 1 into 1
5.598 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.598 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.598 * [taylor]: Taking taylor expansion of 2 in k
5.598 * [backup-simplify]: Simplify 2 into 2
5.598 * [taylor]: Taking taylor expansion of (* n PI) in k
5.598 * [taylor]: Taking taylor expansion of n in k
5.598 * [backup-simplify]: Simplify n into n
5.598 * [taylor]: Taking taylor expansion of PI in k
5.598 * [backup-simplify]: Simplify PI into PI
5.598 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.598 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.598 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.599 * [backup-simplify]: Simplify (- 0) into 0
5.599 * [backup-simplify]: Simplify (+ 1 0) into 1
5.600 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.600 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.600 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.600 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2))))
5.600 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.600 * [taylor]: Taking taylor expansion of k in k
5.600 * [backup-simplify]: Simplify 0 into 0
5.600 * [backup-simplify]: Simplify 1 into 1
5.600 * [backup-simplify]: Simplify (sqrt 0) into 0
5.602 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.602 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) (sqrt k)) in k
5.602 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in k
5.602 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.602 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.602 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.602 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.602 * [taylor]: Taking taylor expansion of 1/2 in k
5.602 * [backup-simplify]: Simplify 1/2 into 1/2
5.602 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.602 * [taylor]: Taking taylor expansion of 1 in k
5.602 * [backup-simplify]: Simplify 1 into 1
5.602 * [taylor]: Taking taylor expansion of k in k
5.602 * [backup-simplify]: Simplify 0 into 0
5.602 * [backup-simplify]: Simplify 1 into 1
5.602 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.602 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.602 * [taylor]: Taking taylor expansion of 2 in k
5.602 * [backup-simplify]: Simplify 2 into 2
5.602 * [taylor]: Taking taylor expansion of (* n PI) in k
5.602 * [taylor]: Taking taylor expansion of n in k
5.603 * [backup-simplify]: Simplify n into n
5.603 * [taylor]: Taking taylor expansion of PI in k
5.603 * [backup-simplify]: Simplify PI into PI
5.603 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.603 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.603 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.603 * [backup-simplify]: Simplify (- 0) into 0
5.604 * [backup-simplify]: Simplify (+ 1 0) into 1
5.604 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.605 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.605 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.605 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2))))
5.605 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.605 * [taylor]: Taking taylor expansion of k in k
5.605 * [backup-simplify]: Simplify 0 into 0
5.605 * [backup-simplify]: Simplify 1 into 1
5.605 * [backup-simplify]: Simplify (sqrt 0) into 0
5.607 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.607 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0
5.607 * [taylor]: Taking taylor expansion of 0 in n
5.607 * [backup-simplify]: Simplify 0 into 0
5.607 * [backup-simplify]: Simplify 0 into 0
5.608 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
5.608 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
5.609 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
5.609 * [backup-simplify]: Simplify (- 1) into -1
5.610 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.610 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
5.611 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
5.611 * [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)))))
5.612 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))
5.614 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))
5.614 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n
5.614 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
5.614 * [taylor]: Taking taylor expansion of +nan.0 in n
5.614 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.614 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
5.614 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
5.614 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
5.614 * [taylor]: Taking taylor expansion of (* n PI) in n
5.614 * [taylor]: Taking taylor expansion of n in n
5.614 * [backup-simplify]: Simplify 0 into 0
5.614 * [backup-simplify]: Simplify 1 into 1
5.614 * [taylor]: Taking taylor expansion of PI in n
5.614 * [backup-simplify]: Simplify PI into PI
5.615 * [backup-simplify]: Simplify (* 0 PI) into 0
5.616 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.616 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
5.617 * [backup-simplify]: Simplify (sqrt 0) into 0
5.619 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
5.619 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
5.619 * [taylor]: Taking taylor expansion of 1/2 in n
5.619 * [backup-simplify]: Simplify 1/2 into 1/2
5.619 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
5.620 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
5.623 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.624 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0
5.629 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.632 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.635 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.635 * [backup-simplify]: Simplify 0 into 0
5.638 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.639 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
5.640 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
5.642 * [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
5.642 * [backup-simplify]: Simplify (- 0) into 0
5.643 * [backup-simplify]: Simplify (+ 0 0) into 0
5.644 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
5.645 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
5.646 * [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)))
5.649 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))))
5.655 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))))
5.655 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n
5.655 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n
5.655 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n
5.655 * [taylor]: Taking taylor expansion of +nan.0 in n
5.655 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.655 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n
5.656 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n
5.656 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.656 * [taylor]: Taking taylor expansion of 2 in n
5.656 * [backup-simplify]: Simplify 2 into 2
5.656 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.657 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.657 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n
5.657 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.657 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.657 * [taylor]: Taking taylor expansion of 2 in n
5.657 * [backup-simplify]: Simplify 2 into 2
5.657 * [taylor]: Taking taylor expansion of (* n PI) in n
5.657 * [taylor]: Taking taylor expansion of n in n
5.657 * [backup-simplify]: Simplify 0 into 0
5.657 * [backup-simplify]: Simplify 1 into 1
5.657 * [taylor]: Taking taylor expansion of PI in n
5.657 * [backup-simplify]: Simplify PI into PI
5.657 * [backup-simplify]: Simplify (* 0 PI) into 0
5.658 * [backup-simplify]: Simplify (* 2 0) into 0
5.659 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.661 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.662 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.662 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n
5.662 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
5.662 * [taylor]: Taking taylor expansion of 1/2 in n
5.662 * [backup-simplify]: Simplify 1/2 into 1/2
5.663 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
5.663 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
5.663 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
5.664 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
5.664 * [taylor]: Taking taylor expansion of (* n PI) in n
5.664 * [taylor]: Taking taylor expansion of n in n
5.664 * [backup-simplify]: Simplify 0 into 0
5.664 * [backup-simplify]: Simplify 1 into 1
5.664 * [taylor]: Taking taylor expansion of PI in n
5.664 * [backup-simplify]: Simplify PI into PI
5.664 * [backup-simplify]: Simplify (* 0 PI) into 0
5.666 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.666 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
5.666 * [backup-simplify]: Simplify (sqrt 0) into 0
5.669 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
5.669 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n
5.669 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
5.669 * [taylor]: Taking taylor expansion of +nan.0 in n
5.669 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.669 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
5.669 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
5.669 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n
5.669 * [taylor]: Taking taylor expansion of (* n PI) in n
5.669 * [taylor]: Taking taylor expansion of n in n
5.669 * [backup-simplify]: Simplify 0 into 0
5.669 * [backup-simplify]: Simplify 1 into 1
5.669 * [taylor]: Taking taylor expansion of PI in n
5.669 * [backup-simplify]: Simplify PI into PI
5.669 * [backup-simplify]: Simplify (* 0 PI) into 0
5.671 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.671 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI)
5.672 * [backup-simplify]: Simplify (sqrt 0) into 0
5.674 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
5.674 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n
5.674 * [taylor]: Taking taylor expansion of 1/2 in n
5.674 * [backup-simplify]: Simplify 1/2 into 1/2
5.674 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2)
5.675 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
5.676 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.677 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2)
5.679 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))
5.682 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))
5.683 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.684 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0
5.685 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.686 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.688 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.689 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0
5.692 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0
5.695 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
5.697 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0
5.707 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
5.709 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.709 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0
5.712 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.720 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
5.735 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
5.754 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
5.774 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
5.776 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0
5.777 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.778 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0
5.782 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2))
5.789 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
5.798 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
5.803 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
5.807 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))
5.834 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))
5.834 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2))) into (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k)))
5.834 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0
5.834 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in n
5.835 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in n
5.835 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.835 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.835 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.835 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.835 * [taylor]: Taking taylor expansion of 1/2 in n
5.835 * [backup-simplify]: Simplify 1/2 into 1/2
5.835 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.835 * [taylor]: Taking taylor expansion of 1 in n
5.835 * [backup-simplify]: Simplify 1 into 1
5.835 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.835 * [taylor]: Taking taylor expansion of k in n
5.835 * [backup-simplify]: Simplify k into k
5.835 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.835 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.835 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.835 * [taylor]: Taking taylor expansion of 2 in n
5.835 * [backup-simplify]: Simplify 2 into 2
5.835 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.835 * [taylor]: Taking taylor expansion of PI in n
5.835 * [backup-simplify]: Simplify PI into PI
5.835 * [taylor]: Taking taylor expansion of n in n
5.835 * [backup-simplify]: Simplify 0 into 0
5.835 * [backup-simplify]: Simplify 1 into 1
5.836 * [backup-simplify]: Simplify (/ PI 1) into PI
5.836 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.837 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.837 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.837 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.837 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.839 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.840 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.841 * [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)))))
5.842 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.842 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
5.842 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.842 * [taylor]: Taking taylor expansion of k in n
5.842 * [backup-simplify]: Simplify k into k
5.842 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.842 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
5.843 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.843 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
5.843 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in k
5.843 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in k
5.843 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.843 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.843 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.843 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.843 * [taylor]: Taking taylor expansion of 1/2 in k
5.843 * [backup-simplify]: Simplify 1/2 into 1/2
5.843 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.843 * [taylor]: Taking taylor expansion of 1 in k
5.843 * [backup-simplify]: Simplify 1 into 1
5.843 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.843 * [taylor]: Taking taylor expansion of k in k
5.843 * [backup-simplify]: Simplify 0 into 0
5.843 * [backup-simplify]: Simplify 1 into 1
5.844 * [backup-simplify]: Simplify (/ 1 1) into 1
5.844 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.844 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.844 * [taylor]: Taking taylor expansion of 2 in k
5.844 * [backup-simplify]: Simplify 2 into 2
5.844 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.844 * [taylor]: Taking taylor expansion of PI in k
5.844 * [backup-simplify]: Simplify PI into PI
5.844 * [taylor]: Taking taylor expansion of n in k
5.844 * [backup-simplify]: Simplify n into n
5.844 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.844 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.844 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.845 * [backup-simplify]: Simplify (- 1) into -1
5.845 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.845 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.845 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.846 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.846 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
5.846 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.846 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.846 * [taylor]: Taking taylor expansion of k in k
5.846 * [backup-simplify]: Simplify 0 into 0
5.846 * [backup-simplify]: Simplify 1 into 1
5.846 * [backup-simplify]: Simplify (/ 1 1) into 1
5.847 * [backup-simplify]: Simplify (sqrt 0) into 0
5.848 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.848 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) (sqrt (/ 1 k))) in k
5.848 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in k
5.848 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.848 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.848 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.848 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.848 * [taylor]: Taking taylor expansion of 1/2 in k
5.848 * [backup-simplify]: Simplify 1/2 into 1/2
5.849 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.849 * [taylor]: Taking taylor expansion of 1 in k
5.849 * [backup-simplify]: Simplify 1 into 1
5.849 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.849 * [taylor]: Taking taylor expansion of k in k
5.849 * [backup-simplify]: Simplify 0 into 0
5.849 * [backup-simplify]: Simplify 1 into 1
5.849 * [backup-simplify]: Simplify (/ 1 1) into 1
5.849 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.849 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.849 * [taylor]: Taking taylor expansion of 2 in k
5.849 * [backup-simplify]: Simplify 2 into 2
5.849 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.849 * [taylor]: Taking taylor expansion of PI in k
5.849 * [backup-simplify]: Simplify PI into PI
5.849 * [taylor]: Taking taylor expansion of n in k
5.849 * [backup-simplify]: Simplify n into n
5.849 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.849 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.850 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.850 * [backup-simplify]: Simplify (- 1) into -1
5.850 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.851 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.851 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.851 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.851 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
5.851 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.852 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.852 * [taylor]: Taking taylor expansion of k in k
5.852 * [backup-simplify]: Simplify 0 into 0
5.852 * [backup-simplify]: Simplify 1 into 1
5.852 * [backup-simplify]: Simplify (/ 1 1) into 1
5.852 * [backup-simplify]: Simplify (sqrt 0) into 0
5.854 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.854 * [backup-simplify]: Simplify (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) 0) into 0
5.854 * [taylor]: Taking taylor expansion of 0 in n
5.854 * [backup-simplify]: Simplify 0 into 0
5.854 * [backup-simplify]: Simplify 0 into 0
5.855 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into 0
5.855 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
5.855 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) in n
5.855 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
5.855 * [taylor]: Taking taylor expansion of +nan.0 in n
5.855 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.855 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
5.855 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
5.855 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
5.856 * [taylor]: Taking taylor expansion of 1/2 in n
5.856 * [backup-simplify]: Simplify 1/2 into 1/2
5.856 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
5.856 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.856 * [taylor]: Taking taylor expansion of 1 in n
5.856 * [backup-simplify]: Simplify 1 into 1
5.856 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.856 * [taylor]: Taking taylor expansion of k in n
5.856 * [backup-simplify]: Simplify k into k
5.856 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.856 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.856 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.856 * [taylor]: Taking taylor expansion of 2 in n
5.856 * [backup-simplify]: Simplify 2 into 2
5.856 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.856 * [taylor]: Taking taylor expansion of PI in n
5.856 * [backup-simplify]: Simplify PI into PI
5.856 * [taylor]: Taking taylor expansion of n in n
5.856 * [backup-simplify]: Simplify 0 into 0
5.856 * [backup-simplify]: Simplify 1 into 1
5.857 * [backup-simplify]: Simplify (/ PI 1) into PI
5.857 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.858 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.858 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.858 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.860 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.867 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
5.868 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.869 * [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)))))
5.869 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.870 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.871 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
5.872 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
5.872 * [backup-simplify]: Simplify 0 into 0
5.872 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.874 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.874 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into 0
5.875 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
5.875 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) in n
5.875 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
5.875 * [taylor]: Taking taylor expansion of +nan.0 in n
5.875 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.875 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
5.875 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
5.875 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
5.875 * [taylor]: Taking taylor expansion of 1/2 in n
5.875 * [backup-simplify]: Simplify 1/2 into 1/2
5.875 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
5.875 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.875 * [taylor]: Taking taylor expansion of 1 in n
5.875 * [backup-simplify]: Simplify 1 into 1
5.875 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.875 * [taylor]: Taking taylor expansion of k in n
5.875 * [backup-simplify]: Simplify k into k
5.875 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.875 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.875 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.875 * [taylor]: Taking taylor expansion of 2 in n
5.875 * [backup-simplify]: Simplify 2 into 2
5.875 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.875 * [taylor]: Taking taylor expansion of PI in n
5.875 * [backup-simplify]: Simplify PI into PI
5.875 * [taylor]: Taking taylor expansion of n in n
5.875 * [backup-simplify]: Simplify 0 into 0
5.875 * [backup-simplify]: Simplify 1 into 1
5.876 * [backup-simplify]: Simplify (/ PI 1) into PI
5.876 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.876 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.876 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.877 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.878 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
5.879 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.880 * [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)))))
5.880 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.881 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.882 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
5.883 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
5.883 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.884 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.885 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.885 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.885 * [backup-simplify]: Simplify (- 0) into 0
5.885 * [backup-simplify]: Simplify (+ 0 0) into 0
5.886 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.887 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.889 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
5.891 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.893 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
5.894 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0
5.895 * [backup-simplify]: Simplify (- 0) into 0
5.895 * [backup-simplify]: Simplify 0 into 0
5.895 * [backup-simplify]: Simplify 0 into 0
5.896 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.900 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.901 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) (* 0 (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into 0
5.902 * [backup-simplify]: Simplify (+ (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
5.902 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) in n
5.902 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
5.902 * [taylor]: Taking taylor expansion of +nan.0 in n
5.902 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.902 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
5.902 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
5.902 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
5.902 * [taylor]: Taking taylor expansion of 1/2 in n
5.902 * [backup-simplify]: Simplify 1/2 into 1/2
5.902 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
5.903 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.903 * [taylor]: Taking taylor expansion of 1 in n
5.903 * [backup-simplify]: Simplify 1 into 1
5.903 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.903 * [taylor]: Taking taylor expansion of k in n
5.903 * [backup-simplify]: Simplify k into k
5.903 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.903 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.903 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.903 * [taylor]: Taking taylor expansion of 2 in n
5.903 * [backup-simplify]: Simplify 2 into 2
5.903 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.903 * [taylor]: Taking taylor expansion of PI in n
5.903 * [backup-simplify]: Simplify PI into PI
5.903 * [taylor]: Taking taylor expansion of n in n
5.903 * [backup-simplify]: Simplify 0 into 0
5.903 * [backup-simplify]: Simplify 1 into 1
5.903 * [backup-simplify]: Simplify (/ PI 1) into PI
5.904 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.905 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.905 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.905 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.907 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.908 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
5.909 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.910 * [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)))))
5.911 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.913 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.914 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
5.915 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
5.919 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))))) into (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))
5.920 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))))
5.920 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in (k n) around 0
5.920 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in n
5.920 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
5.920 * [taylor]: Taking taylor expansion of (/ -1 k) in n
5.920 * [taylor]: Taking taylor expansion of -1 in n
5.920 * [backup-simplify]: Simplify -1 into -1
5.920 * [taylor]: Taking taylor expansion of k in n
5.920 * [backup-simplify]: Simplify k into k
5.920 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
5.920 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
5.920 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
5.921 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
5.921 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.921 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.921 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.921 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.921 * [taylor]: Taking taylor expansion of 1/2 in n
5.921 * [backup-simplify]: Simplify 1/2 into 1/2
5.921 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.921 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.921 * [taylor]: Taking taylor expansion of k in n
5.921 * [backup-simplify]: Simplify k into k
5.921 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.921 * [taylor]: Taking taylor expansion of 1 in n
5.921 * [backup-simplify]: Simplify 1 into 1
5.921 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.921 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.921 * [taylor]: Taking taylor expansion of -2 in n
5.921 * [backup-simplify]: Simplify -2 into -2
5.921 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.921 * [taylor]: Taking taylor expansion of PI in n
5.921 * [backup-simplify]: Simplify PI into PI
5.921 * [taylor]: Taking taylor expansion of n in n
5.921 * [backup-simplify]: Simplify 0 into 0
5.921 * [backup-simplify]: Simplify 1 into 1
5.922 * [backup-simplify]: Simplify (/ PI 1) into PI
5.922 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.923 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.924 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.924 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.925 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.926 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.927 * [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)))))
5.929 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
5.929 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k
5.929 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.929 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.929 * [taylor]: Taking taylor expansion of -1 in k
5.929 * [backup-simplify]: Simplify -1 into -1
5.929 * [taylor]: Taking taylor expansion of k in k
5.929 * [backup-simplify]: Simplify 0 into 0
5.929 * [backup-simplify]: Simplify 1 into 1
5.930 * [backup-simplify]: Simplify (/ -1 1) into -1
5.930 * [backup-simplify]: Simplify (sqrt 0) into 0
5.932 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.932 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.932 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.932 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.932 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.932 * [taylor]: Taking taylor expansion of 1/2 in k
5.932 * [backup-simplify]: Simplify 1/2 into 1/2
5.932 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.932 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.932 * [taylor]: Taking taylor expansion of k in k
5.932 * [backup-simplify]: Simplify 0 into 0
5.932 * [backup-simplify]: Simplify 1 into 1
5.932 * [backup-simplify]: Simplify (/ 1 1) into 1
5.932 * [taylor]: Taking taylor expansion of 1 in k
5.932 * [backup-simplify]: Simplify 1 into 1
5.932 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.933 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.933 * [taylor]: Taking taylor expansion of -2 in k
5.933 * [backup-simplify]: Simplify -2 into -2
5.933 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.933 * [taylor]: Taking taylor expansion of PI in k
5.933 * [backup-simplify]: Simplify PI into PI
5.933 * [taylor]: Taking taylor expansion of n in k
5.933 * [backup-simplify]: Simplify n into n
5.933 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.933 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.933 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.933 * [backup-simplify]: Simplify (+ 1 0) into 1
5.934 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.934 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.934 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.934 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
5.934 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))) in k
5.935 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.935 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.935 * [taylor]: Taking taylor expansion of -1 in k
5.935 * [backup-simplify]: Simplify -1 into -1
5.935 * [taylor]: Taking taylor expansion of k in k
5.935 * [backup-simplify]: Simplify 0 into 0
5.935 * [backup-simplify]: Simplify 1 into 1
5.935 * [backup-simplify]: Simplify (/ -1 1) into -1
5.936 * [backup-simplify]: Simplify (sqrt 0) into 0
5.937 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.937 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.937 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.937 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.937 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.937 * [taylor]: Taking taylor expansion of 1/2 in k
5.937 * [backup-simplify]: Simplify 1/2 into 1/2
5.937 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.937 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.937 * [taylor]: Taking taylor expansion of k in k
5.937 * [backup-simplify]: Simplify 0 into 0
5.937 * [backup-simplify]: Simplify 1 into 1
5.938 * [backup-simplify]: Simplify (/ 1 1) into 1
5.938 * [taylor]: Taking taylor expansion of 1 in k
5.938 * [backup-simplify]: Simplify 1 into 1
5.938 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.938 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.938 * [taylor]: Taking taylor expansion of -2 in k
5.938 * [backup-simplify]: Simplify -2 into -2
5.938 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.938 * [taylor]: Taking taylor expansion of PI in k
5.938 * [backup-simplify]: Simplify PI into PI
5.938 * [taylor]: Taking taylor expansion of n in k
5.938 * [backup-simplify]: Simplify n into n
5.938 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.938 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.938 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.939 * [backup-simplify]: Simplify (+ 1 0) into 1
5.939 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.939 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.939 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.940 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
5.940 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
5.940 * [taylor]: Taking taylor expansion of +nan.0 in n
5.940 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.940 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
5.940 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
5.940 * [taylor]: Taking taylor expansion of 1/2 in n
5.940 * [backup-simplify]: Simplify 1/2 into 1/2
5.940 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
5.940 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.940 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.940 * [taylor]: Taking taylor expansion of -2 in n
5.940 * [backup-simplify]: Simplify -2 into -2
5.940 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.940 * [taylor]: Taking taylor expansion of PI in n
5.940 * [backup-simplify]: Simplify PI into PI
5.940 * [taylor]: Taking taylor expansion of n in n
5.940 * [backup-simplify]: Simplify 0 into 0
5.940 * [backup-simplify]: Simplify 1 into 1
5.941 * [backup-simplify]: Simplify (/ PI 1) into PI
5.941 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.942 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.942 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.942 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.942 * [taylor]: Taking taylor expansion of k in n
5.942 * [backup-simplify]: Simplify k into k
5.942 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.942 * [taylor]: Taking taylor expansion of 1 in n
5.942 * [backup-simplify]: Simplify 1 into 1
5.944 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.944 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.945 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
5.946 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.947 * [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)))))
5.949 * [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))))))
5.950 * [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))))))
5.951 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
5.954 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.955 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))
5.955 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) in n
5.955 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
5.955 * [taylor]: Taking taylor expansion of +nan.0 in n
5.955 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.955 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
5.955 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
5.955 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
5.955 * [taylor]: Taking taylor expansion of 1/2 in n
5.955 * [backup-simplify]: Simplify 1/2 into 1/2
5.955 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
5.955 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.955 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.955 * [taylor]: Taking taylor expansion of -2 in n
5.955 * [backup-simplify]: Simplify -2 into -2
5.955 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.955 * [taylor]: Taking taylor expansion of PI in n
5.955 * [backup-simplify]: Simplify PI into PI
5.955 * [taylor]: Taking taylor expansion of n in n
5.955 * [backup-simplify]: Simplify 0 into 0
5.955 * [backup-simplify]: Simplify 1 into 1
5.956 * [backup-simplify]: Simplify (/ PI 1) into PI
5.956 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.957 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.957 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.957 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.957 * [taylor]: Taking taylor expansion of k in n
5.957 * [backup-simplify]: Simplify k into k
5.957 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.957 * [taylor]: Taking taylor expansion of 1 in n
5.957 * [backup-simplify]: Simplify 1 into 1
5.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.959 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.960 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
5.961 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.963 * [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)))))
5.964 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
5.965 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
5.966 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
5.967 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
5.969 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.969 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.969 * [backup-simplify]: Simplify (+ 0 0) into 0
5.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.971 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.973 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.974 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
5.976 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
5.977 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.981 * [backup-simplify]: Simplify (- (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))) into 0
5.981 * [backup-simplify]: Simplify 0 into 0
5.982 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.987 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.988 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))
5.988 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) in n
5.988 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
5.988 * [taylor]: Taking taylor expansion of +nan.0 in n
5.988 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.988 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
5.988 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
5.988 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
5.988 * [taylor]: Taking taylor expansion of 1/2 in n
5.988 * [backup-simplify]: Simplify 1/2 into 1/2
5.988 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
5.988 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.988 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.988 * [taylor]: Taking taylor expansion of -2 in n
5.988 * [backup-simplify]: Simplify -2 into -2
5.988 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.988 * [taylor]: Taking taylor expansion of PI in n
5.988 * [backup-simplify]: Simplify PI into PI
5.988 * [taylor]: Taking taylor expansion of n in n
5.988 * [backup-simplify]: Simplify 0 into 0
5.989 * [backup-simplify]: Simplify 1 into 1
5.989 * [backup-simplify]: Simplify (/ PI 1) into PI
5.990 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.991 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.991 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.991 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.991 * [taylor]: Taking taylor expansion of k in n
5.991 * [backup-simplify]: Simplify k into k
5.991 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.991 * [taylor]: Taking taylor expansion of 1 in n
5.991 * [backup-simplify]: Simplify 1 into 1
5.992 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.992 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.994 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
5.995 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.996 * [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)))))
6.003 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
6.005 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
6.006 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
6.007 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
6.012 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))
6.012 * * * * [progress]: [ 4 / 4 ] generating series at (2)
6.012 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
6.013 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
6.013 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
6.013 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
6.013 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
6.013 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
6.013 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
6.013 * [taylor]: Taking taylor expansion of 1/2 in n
6.013 * [backup-simplify]: Simplify 1/2 into 1/2
6.013 * [taylor]: Taking taylor expansion of (- 1 k) in n
6.013 * [taylor]: Taking taylor expansion of 1 in n
6.013 * [backup-simplify]: Simplify 1 into 1
6.013 * [taylor]: Taking taylor expansion of k in n
6.013 * [backup-simplify]: Simplify k into k
6.013 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.013 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.013 * [taylor]: Taking taylor expansion of 2 in n
6.013 * [backup-simplify]: Simplify 2 into 2
6.013 * [taylor]: Taking taylor expansion of (* n PI) in n
6.013 * [taylor]: Taking taylor expansion of n in n
6.013 * [backup-simplify]: Simplify 0 into 0
6.013 * [backup-simplify]: Simplify 1 into 1
6.013 * [taylor]: Taking taylor expansion of PI in n
6.013 * [backup-simplify]: Simplify PI into PI
6.014 * [backup-simplify]: Simplify (* 0 PI) into 0
6.014 * [backup-simplify]: Simplify (* 2 0) into 0
6.016 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.017 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.018 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.018 * [backup-simplify]: Simplify (- k) into (- k)
6.018 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
6.018 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
6.020 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.021 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
6.022 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
6.022 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
6.022 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.022 * [taylor]: Taking taylor expansion of k in n
6.022 * [backup-simplify]: Simplify k into k
6.022 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.022 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
6.023 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.023 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
6.023 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
6.023 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
6.023 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
6.023 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
6.023 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
6.023 * [taylor]: Taking taylor expansion of 1/2 in k
6.023 * [backup-simplify]: Simplify 1/2 into 1/2
6.023 * [taylor]: Taking taylor expansion of (- 1 k) in k
6.023 * [taylor]: Taking taylor expansion of 1 in k
6.023 * [backup-simplify]: Simplify 1 into 1
6.023 * [taylor]: Taking taylor expansion of k in k
6.023 * [backup-simplify]: Simplify 0 into 0
6.023 * [backup-simplify]: Simplify 1 into 1
6.023 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
6.023 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
6.023 * [taylor]: Taking taylor expansion of 2 in k
6.023 * [backup-simplify]: Simplify 2 into 2
6.023 * [taylor]: Taking taylor expansion of (* n PI) in k
6.023 * [taylor]: Taking taylor expansion of n in k
6.023 * [backup-simplify]: Simplify n into n
6.023 * [taylor]: Taking taylor expansion of PI in k
6.023 * [backup-simplify]: Simplify PI into PI
6.023 * [backup-simplify]: Simplify (* n PI) into (* n PI)
6.023 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
6.024 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
6.024 * [backup-simplify]: Simplify (- 0) into 0
6.024 * [backup-simplify]: Simplify (+ 1 0) into 1
6.025 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.025 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
6.025 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
6.025 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.025 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.025 * [taylor]: Taking taylor expansion of k in k
6.025 * [backup-simplify]: Simplify 0 into 0
6.025 * [backup-simplify]: Simplify 1 into 1
6.026 * [backup-simplify]: Simplify (/ 1 1) into 1
6.026 * [backup-simplify]: Simplify (sqrt 0) into 0
6.027 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.027 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
6.028 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
6.028 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
6.028 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
6.028 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
6.028 * [taylor]: Taking taylor expansion of 1/2 in k
6.028 * [backup-simplify]: Simplify 1/2 into 1/2
6.028 * [taylor]: Taking taylor expansion of (- 1 k) in k
6.028 * [taylor]: Taking taylor expansion of 1 in k
6.028 * [backup-simplify]: Simplify 1 into 1
6.028 * [taylor]: Taking taylor expansion of k in k
6.028 * [backup-simplify]: Simplify 0 into 0
6.028 * [backup-simplify]: Simplify 1 into 1
6.028 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
6.028 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
6.028 * [taylor]: Taking taylor expansion of 2 in k
6.028 * [backup-simplify]: Simplify 2 into 2
6.028 * [taylor]: Taking taylor expansion of (* n PI) in k
6.028 * [taylor]: Taking taylor expansion of n in k
6.028 * [backup-simplify]: Simplify n into n
6.028 * [taylor]: Taking taylor expansion of PI in k
6.028 * [backup-simplify]: Simplify PI into PI
6.028 * [backup-simplify]: Simplify (* n PI) into (* n PI)
6.028 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
6.028 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
6.029 * [backup-simplify]: Simplify (- 0) into 0
6.029 * [backup-simplify]: Simplify (+ 1 0) into 1
6.030 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.030 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
6.030 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
6.030 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.030 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.030 * [taylor]: Taking taylor expansion of k in k
6.030 * [backup-simplify]: Simplify 0 into 0
6.030 * [backup-simplify]: Simplify 1 into 1
6.031 * [backup-simplify]: Simplify (/ 1 1) into 1
6.031 * [backup-simplify]: Simplify (sqrt 0) into 0
6.032 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.032 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
6.032 * [taylor]: Taking taylor expansion of 0 in n
6.032 * [backup-simplify]: Simplify 0 into 0
6.032 * [backup-simplify]: Simplify 0 into 0
6.032 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
6.033 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
6.033 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
6.033 * [backup-simplify]: Simplify (- 1) into -1
6.034 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.034 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
6.035 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
6.035 * [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)))))
6.035 * [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)))))
6.035 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
6.035 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
6.035 * [taylor]: Taking taylor expansion of +nan.0 in n
6.035 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.035 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
6.035 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.035 * [taylor]: Taking taylor expansion of 2 in n
6.035 * [backup-simplify]: Simplify 2 into 2
6.035 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.036 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.036 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.036 * [taylor]: Taking taylor expansion of (* n PI) in n
6.036 * [taylor]: Taking taylor expansion of n in n
6.036 * [backup-simplify]: Simplify 0 into 0
6.036 * [backup-simplify]: Simplify 1 into 1
6.036 * [taylor]: Taking taylor expansion of PI in n
6.036 * [backup-simplify]: Simplify PI into PI
6.036 * [backup-simplify]: Simplify (* 0 PI) into 0
6.037 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.038 * [backup-simplify]: Simplify (sqrt 0) into 0
6.038 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.039 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
6.039 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.039 * [backup-simplify]: Simplify (- 0) into 0
6.039 * [backup-simplify]: Simplify 0 into 0
6.039 * [backup-simplify]: Simplify 0 into 0
6.040 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
6.042 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.042 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
6.043 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
6.044 * [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
6.044 * [backup-simplify]: Simplify (- 0) into 0
6.044 * [backup-simplify]: Simplify (+ 0 0) into 0
6.045 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
6.045 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
6.046 * [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)))
6.047 * [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)))))))
6.047 * [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
6.047 * [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
6.047 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
6.047 * [taylor]: Taking taylor expansion of +nan.0 in n
6.047 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.047 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
6.047 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
6.047 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.047 * [taylor]: Taking taylor expansion of 2 in n
6.047 * [backup-simplify]: Simplify 2 into 2
6.047 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.047 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.047 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.047 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.048 * [taylor]: Taking taylor expansion of 2 in n
6.048 * [backup-simplify]: Simplify 2 into 2
6.048 * [taylor]: Taking taylor expansion of (* n PI) in n
6.048 * [taylor]: Taking taylor expansion of n in n
6.048 * [backup-simplify]: Simplify 0 into 0
6.048 * [backup-simplify]: Simplify 1 into 1
6.048 * [taylor]: Taking taylor expansion of PI in n
6.048 * [backup-simplify]: Simplify PI into PI
6.048 * [backup-simplify]: Simplify (* 0 PI) into 0
6.048 * [backup-simplify]: Simplify (* 2 0) into 0
6.049 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.050 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.051 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.051 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.051 * [taylor]: Taking taylor expansion of (* n PI) in n
6.051 * [taylor]: Taking taylor expansion of n in n
6.051 * [backup-simplify]: Simplify 0 into 0
6.051 * [backup-simplify]: Simplify 1 into 1
6.051 * [taylor]: Taking taylor expansion of PI in n
6.051 * [backup-simplify]: Simplify PI into PI
6.051 * [backup-simplify]: Simplify (* 0 PI) into 0
6.052 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.052 * [backup-simplify]: Simplify (sqrt 0) into 0
6.053 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.053 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
6.053 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
6.053 * [taylor]: Taking taylor expansion of +nan.0 in n
6.053 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.053 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
6.053 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.053 * [taylor]: Taking taylor expansion of 2 in n
6.053 * [backup-simplify]: Simplify 2 into 2
6.053 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.054 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.054 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.054 * [taylor]: Taking taylor expansion of (* n PI) in n
6.054 * [taylor]: Taking taylor expansion of n in n
6.054 * [backup-simplify]: Simplify 0 into 0
6.054 * [backup-simplify]: Simplify 1 into 1
6.054 * [taylor]: Taking taylor expansion of PI in n
6.054 * [backup-simplify]: Simplify PI into PI
6.054 * [backup-simplify]: Simplify (* 0 PI) into 0
6.055 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.055 * [backup-simplify]: Simplify (sqrt 0) into 0
6.056 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.057 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.058 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
6.059 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
6.059 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.060 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
6.060 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.061 * [backup-simplify]: Simplify (- 0) into 0
6.061 * [backup-simplify]: Simplify (+ 0 0) into 0
6.061 * [backup-simplify]: Simplify (- 0) into 0
6.061 * [backup-simplify]: Simplify 0 into 0
6.064 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
6.070 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
6.073 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
6.076 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
6.076 * [backup-simplify]: Simplify 0 into 0
6.077 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.082 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.083 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.084 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
6.087 * [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
6.088 * [backup-simplify]: Simplify (- 0) into 0
6.088 * [backup-simplify]: Simplify (+ 0 0) into 0
6.090 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
6.091 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
6.093 * [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)))
6.094 * [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)))))))))
6.094 * [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
6.094 * [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
6.094 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
6.094 * [taylor]: Taking taylor expansion of +nan.0 in n
6.094 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.094 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
6.094 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
6.094 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.094 * [taylor]: Taking taylor expansion of 2 in n
6.094 * [backup-simplify]: Simplify 2 into 2
6.095 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.095 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.096 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.096 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.096 * [taylor]: Taking taylor expansion of 2 in n
6.096 * [backup-simplify]: Simplify 2 into 2
6.096 * [taylor]: Taking taylor expansion of (* n PI) in n
6.096 * [taylor]: Taking taylor expansion of n in n
6.096 * [backup-simplify]: Simplify 0 into 0
6.096 * [backup-simplify]: Simplify 1 into 1
6.096 * [taylor]: Taking taylor expansion of PI in n
6.096 * [backup-simplify]: Simplify PI into PI
6.096 * [backup-simplify]: Simplify (* 0 PI) into 0
6.097 * [backup-simplify]: Simplify (* 2 0) into 0
6.098 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.100 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.101 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.101 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.101 * [taylor]: Taking taylor expansion of (* n PI) in n
6.101 * [taylor]: Taking taylor expansion of n in n
6.101 * [backup-simplify]: Simplify 0 into 0
6.101 * [backup-simplify]: Simplify 1 into 1
6.101 * [taylor]: Taking taylor expansion of PI in n
6.101 * [backup-simplify]: Simplify PI into PI
6.102 * [backup-simplify]: Simplify (* 0 PI) into 0
6.103 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.103 * [backup-simplify]: Simplify (sqrt 0) into 0
6.105 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.105 * [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
6.105 * [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
6.105 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
6.105 * [taylor]: Taking taylor expansion of +nan.0 in n
6.105 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.105 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
6.105 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.105 * [taylor]: Taking taylor expansion of 2 in n
6.105 * [backup-simplify]: Simplify 2 into 2
6.106 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.106 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.106 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.106 * [taylor]: Taking taylor expansion of (* n PI) in n
6.106 * [taylor]: Taking taylor expansion of n in n
6.106 * [backup-simplify]: Simplify 0 into 0
6.106 * [backup-simplify]: Simplify 1 into 1
6.106 * [taylor]: Taking taylor expansion of PI in n
6.106 * [backup-simplify]: Simplify PI into PI
6.107 * [backup-simplify]: Simplify (* 0 PI) into 0
6.109 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.109 * [backup-simplify]: Simplify (sqrt 0) into 0
6.110 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.111 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
6.111 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
6.111 * [taylor]: Taking taylor expansion of +nan.0 in n
6.111 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.111 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
6.111 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
6.111 * [taylor]: Taking taylor expansion of (sqrt 2) in n
6.111 * [taylor]: Taking taylor expansion of 2 in n
6.111 * [backup-simplify]: Simplify 2 into 2
6.111 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
6.112 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
6.112 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
6.112 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.112 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.112 * [taylor]: Taking taylor expansion of 2 in n
6.112 * [backup-simplify]: Simplify 2 into 2
6.112 * [taylor]: Taking taylor expansion of (* n PI) in n
6.112 * [taylor]: Taking taylor expansion of n in n
6.112 * [backup-simplify]: Simplify 0 into 0
6.112 * [backup-simplify]: Simplify 1 into 1
6.112 * [taylor]: Taking taylor expansion of PI in n
6.112 * [backup-simplify]: Simplify PI into PI
6.113 * [backup-simplify]: Simplify (* 0 PI) into 0
6.113 * [backup-simplify]: Simplify (* 2 0) into 0
6.115 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.116 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.117 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.119 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.119 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
6.119 * [taylor]: Taking taylor expansion of (* n PI) in n
6.119 * [taylor]: Taking taylor expansion of n in n
6.119 * [backup-simplify]: Simplify 0 into 0
6.119 * [backup-simplify]: Simplify 1 into 1
6.119 * [taylor]: Taking taylor expansion of PI in n
6.119 * [backup-simplify]: Simplify PI into PI
6.119 * [backup-simplify]: Simplify (* 0 PI) into 0
6.121 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.121 * [backup-simplify]: Simplify (sqrt 0) into 0
6.122 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
6.124 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.125 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
6.127 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
6.127 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.128 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
6.128 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.136 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.138 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.140 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
6.142 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
6.144 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
6.144 * [backup-simplify]: Simplify (* +nan.0 0) into 0
6.144 * [backup-simplify]: Simplify (- 0) into 0
6.145 * [backup-simplify]: Simplify (+ 0 0) into 0
6.145 * [backup-simplify]: Simplify (- 0) into 0
6.146 * [backup-simplify]: Simplify (+ 0 0) into 0
6.146 * [backup-simplify]: Simplify (- 0) into 0
6.146 * [backup-simplify]: Simplify 0 into 0
6.147 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
6.148 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
6.150 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.152 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.153 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
6.156 * [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))))))))
6.162 * [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))))))))
6.165 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
6.169 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
6.171 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
6.176 * [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))))))))))
6.181 * [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)))))))
6.185 * [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)))))))
6.186 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
6.190 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
6.192 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
6.197 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
6.206 * [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))))
6.211 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
6.214 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
6.223 * [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)))))))))))))
6.223 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
6.223 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
6.223 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
6.223 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
6.223 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
6.223 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
6.223 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
6.223 * [taylor]: Taking taylor expansion of 1/2 in n
6.223 * [backup-simplify]: Simplify 1/2 into 1/2
6.223 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.223 * [taylor]: Taking taylor expansion of 1 in n
6.223 * [backup-simplify]: Simplify 1 into 1
6.223 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.223 * [taylor]: Taking taylor expansion of k in n
6.223 * [backup-simplify]: Simplify k into k
6.224 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.224 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.224 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.224 * [taylor]: Taking taylor expansion of 2 in n
6.224 * [backup-simplify]: Simplify 2 into 2
6.224 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.224 * [taylor]: Taking taylor expansion of PI in n
6.224 * [backup-simplify]: Simplify PI into PI
6.224 * [taylor]: Taking taylor expansion of n in n
6.224 * [backup-simplify]: Simplify 0 into 0
6.224 * [backup-simplify]: Simplify 1 into 1
6.224 * [backup-simplify]: Simplify (/ PI 1) into PI
6.224 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.225 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.225 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.225 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.225 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
6.226 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.227 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.227 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.227 * [taylor]: Taking taylor expansion of (sqrt k) in n
6.227 * [taylor]: Taking taylor expansion of k in n
6.227 * [backup-simplify]: Simplify k into k
6.227 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
6.227 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
6.228 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
6.228 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
6.228 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
6.228 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
6.228 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
6.228 * [taylor]: Taking taylor expansion of 1/2 in k
6.228 * [backup-simplify]: Simplify 1/2 into 1/2
6.228 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
6.228 * [taylor]: Taking taylor expansion of 1 in k
6.228 * [backup-simplify]: Simplify 1 into 1
6.228 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.228 * [taylor]: Taking taylor expansion of k in k
6.228 * [backup-simplify]: Simplify 0 into 0
6.228 * [backup-simplify]: Simplify 1 into 1
6.228 * [backup-simplify]: Simplify (/ 1 1) into 1
6.228 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
6.228 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
6.228 * [taylor]: Taking taylor expansion of 2 in k
6.228 * [backup-simplify]: Simplify 2 into 2
6.228 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.228 * [taylor]: Taking taylor expansion of PI in k
6.228 * [backup-simplify]: Simplify PI into PI
6.228 * [taylor]: Taking taylor expansion of n in k
6.228 * [backup-simplify]: Simplify n into n
6.228 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.228 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
6.228 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
6.228 * [backup-simplify]: Simplify (- 1) into -1
6.229 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.229 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
6.229 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
6.229 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
6.229 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.229 * [taylor]: Taking taylor expansion of k in k
6.229 * [backup-simplify]: Simplify 0 into 0
6.229 * [backup-simplify]: Simplify 1 into 1
6.230 * [backup-simplify]: Simplify (sqrt 0) into 0
6.230 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.230 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
6.231 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
6.231 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
6.231 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
6.231 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
6.231 * [taylor]: Taking taylor expansion of 1/2 in k
6.231 * [backup-simplify]: Simplify 1/2 into 1/2
6.231 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
6.231 * [taylor]: Taking taylor expansion of 1 in k
6.231 * [backup-simplify]: Simplify 1 into 1
6.231 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.231 * [taylor]: Taking taylor expansion of k in k
6.231 * [backup-simplify]: Simplify 0 into 0
6.231 * [backup-simplify]: Simplify 1 into 1
6.231 * [backup-simplify]: Simplify (/ 1 1) into 1
6.231 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
6.231 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
6.231 * [taylor]: Taking taylor expansion of 2 in k
6.231 * [backup-simplify]: Simplify 2 into 2
6.231 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.231 * [taylor]: Taking taylor expansion of PI in k
6.231 * [backup-simplify]: Simplify PI into PI
6.231 * [taylor]: Taking taylor expansion of n in k
6.231 * [backup-simplify]: Simplify n into n
6.231 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.231 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
6.231 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
6.232 * [backup-simplify]: Simplify (- 1) into -1
6.232 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.232 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
6.232 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
6.232 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
6.232 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.232 * [taylor]: Taking taylor expansion of k in k
6.232 * [backup-simplify]: Simplify 0 into 0
6.232 * [backup-simplify]: Simplify 1 into 1
6.233 * [backup-simplify]: Simplify (sqrt 0) into 0
6.233 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.234 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
6.234 * [taylor]: Taking taylor expansion of 0 in n
6.234 * [backup-simplify]: Simplify 0 into 0
6.234 * [backup-simplify]: Simplify 0 into 0
6.234 * [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))))))))
6.234 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
6.234 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
6.234 * [taylor]: Taking taylor expansion of +nan.0 in n
6.234 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.234 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
6.234 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
6.234 * [taylor]: Taking taylor expansion of 1/2 in n
6.234 * [backup-simplify]: Simplify 1/2 into 1/2
6.234 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
6.234 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.234 * [taylor]: Taking taylor expansion of 1 in n
6.234 * [backup-simplify]: Simplify 1 into 1
6.234 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.234 * [taylor]: Taking taylor expansion of k in n
6.234 * [backup-simplify]: Simplify k into k
6.234 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.234 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.234 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.234 * [taylor]: Taking taylor expansion of 2 in n
6.234 * [backup-simplify]: Simplify 2 into 2
6.234 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.234 * [taylor]: Taking taylor expansion of PI in n
6.234 * [backup-simplify]: Simplify PI into PI
6.234 * [taylor]: Taking taylor expansion of n in n
6.234 * [backup-simplify]: Simplify 0 into 0
6.234 * [backup-simplify]: Simplify 1 into 1
6.235 * [backup-simplify]: Simplify (/ PI 1) into PI
6.235 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.236 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.236 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.236 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.237 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.237 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
6.238 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.239 * [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)))))
6.239 * [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))))))
6.240 * [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)))))))
6.241 * [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)))))))
6.241 * [backup-simplify]: Simplify 0 into 0
6.249 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.251 * [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))))))))
6.251 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
6.251 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
6.251 * [taylor]: Taking taylor expansion of +nan.0 in n
6.251 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.251 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
6.251 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
6.251 * [taylor]: Taking taylor expansion of 1/2 in n
6.251 * [backup-simplify]: Simplify 1/2 into 1/2
6.251 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
6.251 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.251 * [taylor]: Taking taylor expansion of 1 in n
6.251 * [backup-simplify]: Simplify 1 into 1
6.251 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.251 * [taylor]: Taking taylor expansion of k in n
6.251 * [backup-simplify]: Simplify k into k
6.251 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.251 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.251 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.251 * [taylor]: Taking taylor expansion of 2 in n
6.251 * [backup-simplify]: Simplify 2 into 2
6.251 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.252 * [taylor]: Taking taylor expansion of PI in n
6.252 * [backup-simplify]: Simplify PI into PI
6.252 * [taylor]: Taking taylor expansion of n in n
6.252 * [backup-simplify]: Simplify 0 into 0
6.252 * [backup-simplify]: Simplify 1 into 1
6.252 * [backup-simplify]: Simplify (/ PI 1) into PI
6.253 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.254 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.254 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.254 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.255 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.256 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
6.258 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.260 * [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)))))
6.261 * [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))))))
6.262 * [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)))))))
6.263 * [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)))))))
6.264 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.265 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
6.267 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.267 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.267 * [backup-simplify]: Simplify (- 0) into 0
6.268 * [backup-simplify]: Simplify (+ 0 0) into 0
6.269 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.270 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
6.272 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
6.274 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.275 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
6.275 * [backup-simplify]: Simplify (- 0) into 0
6.275 * [backup-simplify]: Simplify 0 into 0
6.276 * [backup-simplify]: Simplify 0 into 0
6.279 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.280 * [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))))))))
6.281 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
6.281 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
6.281 * [taylor]: Taking taylor expansion of +nan.0 in n
6.281 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.281 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
6.281 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
6.281 * [taylor]: Taking taylor expansion of 1/2 in n
6.281 * [backup-simplify]: Simplify 1/2 into 1/2
6.281 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
6.281 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.281 * [taylor]: Taking taylor expansion of 1 in n
6.281 * [backup-simplify]: Simplify 1 into 1
6.281 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.281 * [taylor]: Taking taylor expansion of k in n
6.281 * [backup-simplify]: Simplify k into k
6.281 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.281 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.281 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.281 * [taylor]: Taking taylor expansion of 2 in n
6.281 * [backup-simplify]: Simplify 2 into 2
6.281 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.281 * [taylor]: Taking taylor expansion of PI in n
6.281 * [backup-simplify]: Simplify PI into PI
6.281 * [taylor]: Taking taylor expansion of n in n
6.281 * [backup-simplify]: Simplify 0 into 0
6.281 * [backup-simplify]: Simplify 1 into 1
6.282 * [backup-simplify]: Simplify (/ PI 1) into PI
6.282 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.283 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.283 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.283 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.284 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.286 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
6.287 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.288 * [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)))))
6.289 * [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))))))
6.290 * [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)))))))
6.291 * [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)))))))
6.296 * [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))))))))
6.297 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
6.297 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
6.297 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
6.297 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
6.297 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
6.297 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
6.297 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
6.297 * [taylor]: Taking taylor expansion of 1/2 in n
6.297 * [backup-simplify]: Simplify 1/2 into 1/2
6.297 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.297 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.297 * [taylor]: Taking taylor expansion of k in n
6.297 * [backup-simplify]: Simplify k into k
6.297 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.297 * [taylor]: Taking taylor expansion of 1 in n
6.297 * [backup-simplify]: Simplify 1 into 1
6.297 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.297 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.297 * [taylor]: Taking taylor expansion of -2 in n
6.297 * [backup-simplify]: Simplify -2 into -2
6.297 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.297 * [taylor]: Taking taylor expansion of PI in n
6.297 * [backup-simplify]: Simplify PI into PI
6.297 * [taylor]: Taking taylor expansion of n in n
6.297 * [backup-simplify]: Simplify 0 into 0
6.297 * [backup-simplify]: Simplify 1 into 1
6.298 * [backup-simplify]: Simplify (/ PI 1) into PI
6.298 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.299 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.299 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.300 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
6.301 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.302 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.303 * [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)))))
6.303 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
6.303 * [taylor]: Taking taylor expansion of (/ -1 k) in n
6.303 * [taylor]: Taking taylor expansion of -1 in n
6.303 * [backup-simplify]: Simplify -1 into -1
6.303 * [taylor]: Taking taylor expansion of k in n
6.303 * [backup-simplify]: Simplify k into k
6.304 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
6.304 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
6.304 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
6.304 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
6.305 * [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)))
6.305 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
6.305 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
6.305 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
6.305 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
6.305 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
6.305 * [taylor]: Taking taylor expansion of 1/2 in k
6.305 * [backup-simplify]: Simplify 1/2 into 1/2
6.305 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
6.305 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.305 * [taylor]: Taking taylor expansion of k in k
6.305 * [backup-simplify]: Simplify 0 into 0
6.305 * [backup-simplify]: Simplify 1 into 1
6.306 * [backup-simplify]: Simplify (/ 1 1) into 1
6.306 * [taylor]: Taking taylor expansion of 1 in k
6.306 * [backup-simplify]: Simplify 1 into 1
6.306 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
6.306 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
6.306 * [taylor]: Taking taylor expansion of -2 in k
6.306 * [backup-simplify]: Simplify -2 into -2
6.306 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.306 * [taylor]: Taking taylor expansion of PI in k
6.306 * [backup-simplify]: Simplify PI into PI
6.306 * [taylor]: Taking taylor expansion of n in k
6.306 * [backup-simplify]: Simplify n into n
6.306 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.306 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
6.306 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
6.307 * [backup-simplify]: Simplify (+ 1 0) into 1
6.307 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.307 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
6.308 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
6.308 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.308 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.308 * [taylor]: Taking taylor expansion of -1 in k
6.308 * [backup-simplify]: Simplify -1 into -1
6.308 * [taylor]: Taking taylor expansion of k in k
6.308 * [backup-simplify]: Simplify 0 into 0
6.308 * [backup-simplify]: Simplify 1 into 1
6.308 * [backup-simplify]: Simplify (/ -1 1) into -1
6.309 * [backup-simplify]: Simplify (sqrt 0) into 0
6.311 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.311 * [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)))))
6.311 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
6.311 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
6.311 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
6.311 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
6.311 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
6.311 * [taylor]: Taking taylor expansion of 1/2 in k
6.311 * [backup-simplify]: Simplify 1/2 into 1/2
6.311 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
6.311 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.311 * [taylor]: Taking taylor expansion of k in k
6.311 * [backup-simplify]: Simplify 0 into 0
6.311 * [backup-simplify]: Simplify 1 into 1
6.312 * [backup-simplify]: Simplify (/ 1 1) into 1
6.312 * [taylor]: Taking taylor expansion of 1 in k
6.312 * [backup-simplify]: Simplify 1 into 1
6.312 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
6.312 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
6.312 * [taylor]: Taking taylor expansion of -2 in k
6.312 * [backup-simplify]: Simplify -2 into -2
6.312 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.312 * [taylor]: Taking taylor expansion of PI in k
6.312 * [backup-simplify]: Simplify PI into PI
6.312 * [taylor]: Taking taylor expansion of n in k
6.312 * [backup-simplify]: Simplify n into n
6.312 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.312 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
6.312 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
6.313 * [backup-simplify]: Simplify (+ 1 0) into 1
6.313 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.313 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
6.313 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
6.313 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.314 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.314 * [taylor]: Taking taylor expansion of -1 in k
6.314 * [backup-simplify]: Simplify -1 into -1
6.314 * [taylor]: Taking taylor expansion of k in k
6.314 * [backup-simplify]: Simplify 0 into 0
6.314 * [backup-simplify]: Simplify 1 into 1
6.314 * [backup-simplify]: Simplify (/ -1 1) into -1
6.315 * [backup-simplify]: Simplify (sqrt 0) into 0
6.316 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.316 * [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)))))
6.316 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
6.316 * [taylor]: Taking taylor expansion of +nan.0 in n
6.316 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.316 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
6.316 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
6.316 * [taylor]: Taking taylor expansion of 1/2 in n
6.317 * [backup-simplify]: Simplify 1/2 into 1/2
6.317 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
6.317 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.317 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.317 * [taylor]: Taking taylor expansion of -2 in n
6.317 * [backup-simplify]: Simplify -2 into -2
6.317 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.317 * [taylor]: Taking taylor expansion of PI in n
6.317 * [backup-simplify]: Simplify PI into PI
6.317 * [taylor]: Taking taylor expansion of n in n
6.317 * [backup-simplify]: Simplify 0 into 0
6.317 * [backup-simplify]: Simplify 1 into 1
6.317 * [backup-simplify]: Simplify (/ PI 1) into PI
6.318 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.319 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.319 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.319 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.319 * [taylor]: Taking taylor expansion of k in n
6.319 * [backup-simplify]: Simplify k into k
6.319 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.319 * [taylor]: Taking taylor expansion of 1 in n
6.319 * [backup-simplify]: Simplify 1 into 1
6.320 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.321 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.322 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
6.323 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.324 * [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)))))
6.325 * [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))))))
6.327 * [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))))))
6.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.331 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.333 * [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))))))
6.333 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
6.333 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
6.333 * [taylor]: Taking taylor expansion of +nan.0 in n
6.333 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.333 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
6.333 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
6.333 * [taylor]: Taking taylor expansion of 1/2 in n
6.333 * [backup-simplify]: Simplify 1/2 into 1/2
6.333 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
6.333 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.333 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.333 * [taylor]: Taking taylor expansion of -2 in n
6.333 * [backup-simplify]: Simplify -2 into -2
6.333 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.333 * [taylor]: Taking taylor expansion of PI in n
6.333 * [backup-simplify]: Simplify PI into PI
6.333 * [taylor]: Taking taylor expansion of n in n
6.333 * [backup-simplify]: Simplify 0 into 0
6.333 * [backup-simplify]: Simplify 1 into 1
6.334 * [backup-simplify]: Simplify (/ PI 1) into PI
6.334 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.335 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.335 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.335 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.335 * [taylor]: Taking taylor expansion of k in n
6.336 * [backup-simplify]: Simplify k into k
6.336 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.336 * [taylor]: Taking taylor expansion of 1 in n
6.336 * [backup-simplify]: Simplify 1 into 1
6.337 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.337 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.338 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
6.339 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.341 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.342 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
6.343 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
6.344 * [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)))))))
6.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.346 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.346 * [backup-simplify]: Simplify (+ 0 0) into 0
6.347 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.348 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
6.350 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
6.351 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
6.353 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
6.354 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.356 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
6.356 * [backup-simplify]: Simplify 0 into 0
6.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.361 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.363 * [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))))))
6.363 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
6.363 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
6.363 * [taylor]: Taking taylor expansion of +nan.0 in n
6.363 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.363 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
6.363 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
6.363 * [taylor]: Taking taylor expansion of 1/2 in n
6.363 * [backup-simplify]: Simplify 1/2 into 1/2
6.363 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
6.363 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.363 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.363 * [taylor]: Taking taylor expansion of -2 in n
6.363 * [backup-simplify]: Simplify -2 into -2
6.363 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.363 * [taylor]: Taking taylor expansion of PI in n
6.363 * [backup-simplify]: Simplify PI into PI
6.363 * [taylor]: Taking taylor expansion of n in n
6.363 * [backup-simplify]: Simplify 0 into 0
6.363 * [backup-simplify]: Simplify 1 into 1
6.364 * [backup-simplify]: Simplify (/ PI 1) into PI
6.364 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.365 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.365 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.365 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.365 * [taylor]: Taking taylor expansion of k in n
6.365 * [backup-simplify]: Simplify k into k
6.365 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.365 * [taylor]: Taking taylor expansion of 1 in n
6.366 * [backup-simplify]: Simplify 1 into 1
6.367 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.367 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.368 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
6.369 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.370 * [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)))))
6.372 * [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))))))
6.373 * [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)))))))
6.374 * [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)))))))
6.379 * [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))))))))))))
6.379 * * * [progress]: simplifying candidates
6.379 * * * * [progress]: [ 1 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.379 * * * * [progress]: [ 2 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.379 * * * * [progress]: [ 3 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
6.379 * * * * [progress]: [ 4 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
6.379 * * * * [progress]: [ 5 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.379 * * * * [progress]: [ 6 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.379 * * * * [progress]: [ 7 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))))))>
6.380 * * * * [progress]: [ 8 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))))))>
6.380 * * * * [progress]: [ 9 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))))))>
6.380 * * * * [progress]: [ 10 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))))))>
6.380 * * * * [progress]: [ 11 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))))>
6.380 * * * * [progress]: [ 12 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))))>
6.380 * * * * [progress]: [ 13 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))))))>
6.380 * * * * [progress]: [ 14 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))))))>
6.380 * * * * [progress]: [ 15 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)))))>
6.380 * * * * [progress]: [ 16 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))))))>
6.380 * * * * [progress]: [ 17 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))))))>
6.380 * * * * [progress]: [ 18 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)))))>
6.380 * * * * [progress]: [ 19 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))))))>
6.380 * * * * [progress]: [ 20 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))))))>
6.380 * * * * [progress]: [ 21 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)))))>
6.381 * * * * [progress]: [ 22 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))))))>
6.381 * * * * [progress]: [ 23 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))))))>
6.381 * * * * [progress]: [ 24 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)))))>
6.381 * * * * [progress]: [ 25 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))))))>
6.381 * * * * [progress]: [ 26 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))))))>
6.381 * * * * [progress]: [ 27 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)))))>
6.381 * * * * [progress]: [ 28 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))))))>
6.381 * * * * [progress]: [ 29 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))))))>
6.381 * * * * [progress]: [ 30 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)))))>
6.381 * * * * [progress]: [ 31 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)))))>
6.381 * * * * [progress]: [ 32 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (- 1 k)) (/ 1 2)))))>
6.381 * * * * [progress]: [ 33 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.381 * * * * [progress]: [ 34 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1))))>
6.382 * * * * [progress]: [ 35 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.382 * * * * [progress]: [ 36 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (log (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.382 * * * * [progress]: [ 37 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.382 * * * * [progress]: [ 38 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.382 * * * * [progress]: [ 39 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.382 * * * * [progress]: [ 40 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.382 * * * * [progress]: [ 41 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.382 * * * * [progress]: [ 42 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.382 * * * * [progress]: [ 43 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
6.382 * * * * [progress]: [ 44 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
6.382 * * * * [progress]: [ 45 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)))))>
6.382 * * * * [progress]: [ 46 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)))))>
6.382 * * * * [progress]: [ 47 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)))))>
6.382 * * * * [progress]: [ 48 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1 k) 2)))))>
6.382 * * * * [progress]: [ 49 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 50 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (log (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 51 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (log (exp (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 52 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 53 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 54 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 55 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 56 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 57 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 58 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 59 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 60 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 61 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 62 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1 k) 2)))))>
6.383 * * * * [progress]: [ 63 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
6.384 * * * * [progress]: [ 64 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (log1p (expm1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.384 * * * * [progress]: [ 65 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (expm1 (log1p (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.384 * * * * [progress]: [ 66 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (pow (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)))>
6.384 * * * * [progress]: [ 67 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
6.384 * * * * [progress]: [ 68 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
6.384 * * * * [progress]: [ 69 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.384 * * * * [progress]: [ 70 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.384 * * * * [progress]: [ 71 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.384 * * * * [progress]: [ 72 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.384 * * * * [progress]: [ 73 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (log (exp (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.384 * * * * [progress]: [ 74 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.384 * * * * [progress]: [ 75 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.384 * * * * [progress]: [ 76 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.385 * * * * [progress]: [ 77 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.385 * * * * [progress]: [ 78 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (- (sqrt k)) (- (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.385 * * * * [progress]: [ 79 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.385 * * * * [progress]: [ 80 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.385 * * * * [progress]: [ 81 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.385 * * * * [progress]: [ 82 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.385 * * * * [progress]: [ 83 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.385 * * * * [progress]: [ 84 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2))) (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.385 * * * * [progress]: [ 85 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.385 * * * * [progress]: [ 86 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.385 * * * * [progress]: [ 87 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.385 * * * * [progress]: [ 88 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.386 * * * * [progress]: [ 89 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.386 * * * * [progress]: [ 90 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.386 * * * * [progress]: [ 91 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.386 * * * * [progress]: [ 92 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.386 * * * * [progress]: [ 93 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.386 * * * * [progress]: [ 94 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.386 * * * * [progress]: [ 95 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.386 * * * * [progress]: [ 96 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.386 * * * * [progress]: [ 97 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.386 * * * * [progress]: [ 98 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.386 * * * * [progress]: [ 99 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.386 * * * * [progress]: [ 100 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.387 * * * * [progress]: [ 101 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.387 * * * * [progress]: [ 102 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.387 * * * * [progress]: [ 103 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.387 * * * * [progress]: [ 104 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.387 * * * * [progress]: [ 105 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.387 * * * * [progress]: [ 106 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.387 * * * * [progress]: [ 107 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.387 * * * * [progress]: [ 108 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.387 * * * * [progress]: [ 109 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.387 * * * * [progress]: [ 110 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.387 * * * * [progress]: [ 111 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
6.387 * * * * [progress]: [ 112 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow n (/ (- 1 k) 2))) (pow (* 2 PI) (/ (- 1 k) 2)))))>
6.387 * * * * [progress]: [ 113 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.388 * * * * [progress]: [ 114 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.388 * * * * [progress]: [ 115 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
6.388 * * * * [progress]: [ 116 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
6.388 * * * * [progress]: [ 117 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
6.388 * * * * [progress]: [ 118 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k))))))>
6.388 * * * * [progress]: [ 119 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
6.388 * * * * [progress]: [ 120 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
6.388 * * * * [progress]: [ 121 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
6.388 * * * * [progress]: [ 122 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
6.388 * * * * [progress]: [ 123 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2))) (pow (* n (* 2 PI)) (/ k 2)))))>
6.388 * * * * [progress]: [ 124 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (posit16->real (real->posit16 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.388 * * * * [progress]: [ 125 / 315 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.388 * * * * [progress]: [ 126 / 315 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.388 * * * * [progress]: [ 127 / 315 ] simplifiying candidate #<alt (λ (k n) (pow (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) -1))>
6.389 * * * * [progress]: [ 128 / 315 ] simplifiying candidate #<alt (λ (k n) (pow (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- 1)))>
6.389 * * * * [progress]: [ 129 / 315 ] simplifiying candidate #<alt (λ (k n) (pow (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1))>
6.389 * * * * [progress]: [ 130 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
6.389 * * * * [progress]: [ 131 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
6.389 * * * * [progress]: [ 132 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.389 * * * * [progress]: [ 133 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.389 * * * * [progress]: [ 134 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.389 * * * * [progress]: [ 135 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.389 * * * * [progress]: [ 136 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
6.389 * * * * [progress]: [ 137 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
6.389 * * * * [progress]: [ 138 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.389 * * * * [progress]: [ 139 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.389 * * * * [progress]: [ 140 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 141 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- 0 (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 142 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))))))>
6.390 * * * * [progress]: [ 143 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))))))>
6.390 * * * * [progress]: [ 144 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.390 * * * * [progress]: [ 145 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2))))))>
6.390 * * * * [progress]: [ 146 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 147 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (- (log 1) (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 148 / 315 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 149 / 315 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 150 / 315 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* 1 1) 1) (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 151 / 315 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* 1 1) 1) (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 152 / 315 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 153 / 315 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.390 * * * * [progress]: [ 154 / 315 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (sqrt (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.391 * * * * [progress]: [ 155 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (- 1) (- (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.391 * * * * [progress]: [ 156 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.391 * * * * [progress]: [ 157 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.391 * * * * [progress]: [ 158 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.391 * * * * [progress]: [ 159 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.391 * * * * [progress]: [ 160 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.391 * * * * [progress]: [ 161 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.391 * * * * [progress]: [ 162 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.391 * * * * [progress]: [ 163 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.391 * * * * [progress]: [ 164 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.392 * * * * [progress]: [ 165 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.392 * * * * [progress]: [ 166 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.392 * * * * [progress]: [ 167 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.392 * * * * [progress]: [ 168 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.392 * * * * [progress]: [ 169 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.392 * * * * [progress]: [ 170 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.392 * * * * [progress]: [ 171 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) 1)) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.392 * * * * [progress]: [ 172 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.392 * * * * [progress]: [ 173 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.392 * * * * [progress]: [ 174 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.392 * * * * [progress]: [ 175 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.393 * * * * [progress]: [ 176 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) 1)) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.393 * * * * [progress]: [ 177 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.393 * * * * [progress]: [ 178 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.393 * * * * [progress]: [ 179 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.393 * * * * [progress]: [ 180 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.393 * * * * [progress]: [ 181 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) 1)) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.393 * * * * [progress]: [ 182 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.393 * * * * [progress]: [ 183 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow n (/ (- 1 k) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.394 * * * * [progress]: [ 184 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.394 * * * * [progress]: [ 185 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.394 * * * * [progress]: [ 186 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 1)) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.394 * * * * [progress]: [ 187 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.394 * * * * [progress]: [ 188 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.395 * * * * [progress]: [ 189 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt k)) (/ (cbrt 1) (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.395 * * * * [progress]: [ 190 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2)))) (/ (cbrt 1) (pow (* n (* 2 PI)) (/ k 2)))))>
6.395 * * * * [progress]: [ 191 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.395 * * * * [progress]: [ 192 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.395 * * * * [progress]: [ 193 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.395 * * * * [progress]: [ 194 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.395 * * * * [progress]: [ 195 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.395 * * * * [progress]: [ 196 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.395 * * * * [progress]: [ 197 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.395 * * * * [progress]: [ 198 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.395 * * * * [progress]: [ 199 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.395 * * * * [progress]: [ 200 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.396 * * * * [progress]: [ 201 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.396 * * * * [progress]: [ 202 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.396 * * * * [progress]: [ 203 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.396 * * * * [progress]: [ 204 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.396 * * * * [progress]: [ 205 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.396 * * * * [progress]: [ 206 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) 1)) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.396 * * * * [progress]: [ 207 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.396 * * * * [progress]: [ 208 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.396 * * * * [progress]: [ 209 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.396 * * * * [progress]: [ 210 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.396 * * * * [progress]: [ 211 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) 1)) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.396 * * * * [progress]: [ 212 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.396 * * * * [progress]: [ 213 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.396 * * * * [progress]: [ 214 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.397 * * * * [progress]: [ 215 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.397 * * * * [progress]: [ 216 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) 1)) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.397 * * * * [progress]: [ 217 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.397 * * * * [progress]: [ 218 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow n (/ (- 1 k) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.397 * * * * [progress]: [ 219 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.397 * * * * [progress]: [ 220 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt 1) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.397 * * * * [progress]: [ 221 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 1)) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.397 * * * * [progress]: [ 222 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.397 * * * * [progress]: [ 223 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.397 * * * * [progress]: [ 224 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt k)) (/ (sqrt 1) (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.397 * * * * [progress]: [ 225 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2)))) (/ (sqrt 1) (pow (* n (* 2 PI)) (/ k 2)))))>
6.397 * * * * [progress]: [ 226 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.397 * * * * [progress]: [ 227 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.397 * * * * [progress]: [ 228 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.398 * * * * [progress]: [ 229 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.398 * * * * [progress]: [ 230 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.398 * * * * [progress]: [ 231 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.398 * * * * [progress]: [ 232 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.398 * * * * [progress]: [ 233 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.398 * * * * [progress]: [ 234 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.398 * * * * [progress]: [ 235 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.398 * * * * [progress]: [ 236 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.398 * * * * [progress]: [ 237 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.398 * * * * [progress]: [ 238 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.398 * * * * [progress]: [ 239 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.398 * * * * [progress]: [ 240 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.398 * * * * [progress]: [ 241 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.399 * * * * [progress]: [ 242 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.399 * * * * [progress]: [ 243 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.399 * * * * [progress]: [ 244 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.399 * * * * [progress]: [ 245 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.399 * * * * [progress]: [ 246 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) 1)) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.399 * * * * [progress]: [ 247 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.399 * * * * [progress]: [ 248 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.399 * * * * [progress]: [ 249 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.399 * * * * [progress]: [ 250 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.399 * * * * [progress]: [ 251 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.399 * * * * [progress]: [ 252 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.399 * * * * [progress]: [ 253 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow n (/ (- 1 k) 2)))) (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))))>
6.399 * * * * [progress]: [ 254 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.400 * * * * [progress]: [ 255 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.400 * * * * [progress]: [ 256 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 1)) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.400 * * * * [progress]: [ 257 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))))>
6.400 * * * * [progress]: [ 258 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.400 * * * * [progress]: [ 259 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.400 * * * * [progress]: [ 260 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2)))) (/ 1 (pow (* n (* 2 PI)) (/ k 2)))))>
6.400 * * * * [progress]: [ 261 / 315 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.400 * * * * [progress]: [ 262 / 315 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.400 * * * * [progress]: [ 263 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)))>
6.400 * * * * [progress]: [ 264 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.400 * * * * [progress]: [ 265 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.400 * * * * [progress]: [ 266 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))))>
6.400 * * * * [progress]: [ 267 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.400 * * * * [progress]: [ 268 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.401 * * * * [progress]: [ 269 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
6.401 * * * * [progress]: [ 270 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
6.401 * * * * [progress]: [ 271 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))) (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))))>
6.401 * * * * [progress]: [ 272 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.401 * * * * [progress]: [ 273 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.401 * * * * [progress]: [ 274 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1)) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
6.401 * * * * [progress]: [ 275 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
6.401 * * * * [progress]: [ 276 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))))>
6.401 * * * * [progress]: [ 277 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.401 * * * * [progress]: [ 278 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.401 * * * * [progress]: [ 279 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
6.401 * * * * [progress]: [ 280 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
6.402 * * * * [progress]: [ 281 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow n (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))))>
6.402 * * * * [progress]: [ 282 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.402 * * * * [progress]: [ 283 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.402 * * * * [progress]: [ 284 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
6.402 * * * * [progress]: [ 285 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
6.402 * * * * [progress]: [ 286 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))))>
6.402 * * * * [progress]: [ 287 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.402 * * * * [progress]: [ 288 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.403 * * * * [progress]: [ 289 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
6.403 * * * * [progress]: [ 290 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
6.403 * * * * [progress]: [ 291 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow n (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))))>
6.403 * * * * [progress]: [ 292 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.403 * * * * [progress]: [ 293 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
6.403 * * * * [progress]: [ 294 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
6.403 * * * * [progress]: [ 295 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
6.403 * * * * [progress]: [ 296 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
6.403 * * * * [progress]: [ 297 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
6.403 * * * * [progress]: [ 298 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2)))) (pow (* n (* 2 PI)) (/ k 2))))>
6.403 * * * * [progress]: [ 299 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt 1) (cbrt 1)) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt 1))))>
6.403 * * * * [progress]: [ 300 / 315 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt 1) (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))))>
6.403 * * * * [progress]: [ 301 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)))>
6.403 * * * * [progress]: [ 302 / 315 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
6.404 * * * * [progress]: [ 303 / 315 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))>
6.404 * * * * [progress]: [ 304 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))))))>
6.404 * * * * [progress]: [ 305 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))))>
6.404 * * * * [progress]: [ 306 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))>
6.404 * * * * [progress]: [ 307 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
6.404 * * * * [progress]: [ 308 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
6.404 * * * * [progress]: [ 309 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
6.404 * * * * [progress]: [ 310 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))))>
6.404 * * * * [progress]: [ 311 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))))>
6.404 * * * * [progress]: [ 312 / 315 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))))>
6.404 * * * * [progress]: [ 313 / 315 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))>
6.404 * * * * [progress]: [ 314 / 315 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
6.405 * * * * [progress]: [ 315 / 315 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
6.420 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* n (* 2 PI)) (/ 1 2))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (expm1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (log1p (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (- (log (sqrt k)) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)))
  (- (log (sqrt k)) (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)))
  (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2)))
  (- (log (sqrt k)) (* (log (* n (* 2 PI))) (/ (- 1 k) 2)))
  (- (log (sqrt k)) (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (log (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (exp (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (- (sqrt k))
  (- (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))
  (/ (cbrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (/ (cbrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2)))
  (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
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  (/ 1 (/ (sqrt (cbrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (cbrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (cbrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (cbrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt 1) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt 1) 1))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))
  (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ 1 1))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 1)
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (sqrt k))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2))))
  (/ 1 (pow (* n (* 2 PI)) (/ k 2)))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt 1) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt 1) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt 1) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt 1) 1))
  (/ 1 (/ (sqrt 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
  (/ 1 (/ 1 (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
  (/ 1 (/ 1 (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (/ 1 (/ 1 1))
  (/ 1 (/ 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ 1 2))))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt 1))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))
  (/ (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)
  (/ 1 (sqrt k))
  (real->posit16 (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI)))))))))))
  (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))
  (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
6.427 * * [simplify]: iteration 1: (535 enodes)
7.443 * * [simplify]: Extracting #0: cost 173 inf + 0
7.444 * * [simplify]: Extracting #1: cost 574 inf + 2
7.448 * * [simplify]: Extracting #2: cost 633 inf + 15385
7.463 * * [simplify]: Extracting #3: cost 528 inf + 75130
7.505 * * [simplify]: Extracting #4: cost 352 inf + 174310
7.567 * * [simplify]: Extracting #5: cost 264 inf + 236378
7.617 * * [simplify]: Extracting #6: cost 219 inf + 266422
7.678 * * [simplify]: Extracting #7: cost 179 inf + 284880
7.750 * * [simplify]: Extracting #8: cost 135 inf + 301652
7.829 * * [simplify]: Extracting #9: cost 79 inf + 328147
7.899 * * [simplify]: Extracting #10: cost 28 inf + 361426
8.009 * * [simplify]: Extracting #11: cost 10 inf + 374430
8.078 * * [simplify]: Extracting #12: cost 2 inf + 383052
8.166 * * [simplify]: Extracting #13: cost 0 inf + 385296
8.257 * [simplify]: Simplified to:
  (expm1 (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (log1p (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (- 1 k) 2) (log (* 2 (* n PI))))
  (* (/ (- 1 k) 2) (log (* 2 (* n PI))))
  (* (/ (- 1 k) 2) (log (* 2 (* n PI))))
  (* (/ (- 1 k) 2) (log (* 2 (* n PI))))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (pow (* 2 (* n PI)) 1/2)
  (pow (* 2 (* n PI)) (/ k 2))
  (pow (* 2 (* n PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* 2 (* n PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* 2 (* n PI)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* 2 (* n PI)) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* 2 (* n PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* 2 (* n PI)) (sqrt (- 1 k)))
  (pow (* 2 (* n PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ 1 (sqrt 2)))
  (* 2 (* n PI))
  (pow (* 2 (* n PI)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* 2 (* n PI)) (+ (sqrt k) 1))
  (pow (* 2 (* n PI)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* 2 (* n PI)) (+ (sqrt k) 1))
  (pow (* 2 (* n PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ 1 (sqrt 2)))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (pow (* 2 (* n PI)) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* PI 2) (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* 2 (* n PI))))
  (exp (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (pow (* 2 (* n PI)) (/ (- 1 k) 4))
  (pow (* 2 (* n PI)) (/ (- 1 k) 4))
  (real->posit16 (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (expm1 (* 2 (* n PI)))
  (log1p (* 2 (* n PI)))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (log (* 2 (* n PI)))
  (log (* 2 (* n PI)))
  (log (* 2 (* n PI)))
  (exp (* 2 (* n PI)))
  (* (* (* n n) n) (* 4 (* 2 (* (* PI PI) PI))))
  (* (* n n) (* n (* (* PI 2) (* (* PI 2) (* PI 2)))))
  (* (cbrt (* 2 (* n PI))) (cbrt (* 2 (* n PI))))
  (cbrt (* 2 (* n PI)))
  (* (* (* 2 (* n PI)) (* 2 (* n PI))) (* 2 (* n PI)))
  (sqrt (* 2 (* n PI)))
  (sqrt (* 2 (* n PI)))
  (* n 2)
  (* (* PI 2) (cbrt n))
  (* (* (sqrt n) 2) PI)
  (* 2 (* n PI))
  (real->posit16 (* 2 (* n PI)))
  (expm1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (log1p (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI)))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI)))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI)))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI)))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI)))))
  (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI)))))
  (exp (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ k (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (cbrt (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
  (cbrt (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (* (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
  (sqrt (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (sqrt (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (- (sqrt k))
  (- (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))
  (/ (cbrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
  (* (/ (cbrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (cbrt (sqrt k)) (/ (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (cbrt (sqrt k)) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (fabs (cbrt k)) (pow n (/ (- 1 k) 2)))
  (/ (sqrt (cbrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (fabs (cbrt k)) (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (fabs (cbrt k)) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (fabs (cbrt k))
  (/ (sqrt (cbrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (/ (fabs (cbrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (sqrt (cbrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (/ (sqrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ 1 (pow n (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ 1 (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
  (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ 1 (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  1
  (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (/ 1 (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (/ (sqrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ 1 (pow n (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ 1 (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
  (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ 1 (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  1
  (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (/ 1 (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ 1 (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (sqrt k) (pow n (/ (- 1 k) 2)))
  (/ (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (sqrt k)
  (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 4)))
  (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (sqrt k) (pow (* 2 (* n PI)) 1/2))
  (real->posit16 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (expm1 (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (log1p (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  -1
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI))))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI))))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI))))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI))))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI))))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI))))))
  (- (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* 2 (* n PI))))))
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  (- (- (/ (* +nan.0 (* (sqrt 2) (* (* k k) (* (log (* PI 2)) (* (sqrt 1/2) (sqrt 1/2)))))) PI) (- (* (/ (* (sqrt 1/2) (* k k)) PI) +nan.0) (- (* +nan.0 (/ (* n (* k (sqrt 1/2))) (* PI PI))) (- (* +nan.0 (/ (log n) (/ PI (* (sqrt 2) (* (* (sqrt 1/2) (sqrt 1/2)) (* k k)))))) (/ (* +nan.0 (* k (sqrt 1/2))) PI))))))
  (- (fma +nan.0 (/ 1 (exp (* (* 1/2 (- 1 k)) (- (log (* PI 2)) (- (log n)))))) (- (fma +nan.0 (/ (/ 1 (exp (* (* 1/2 (- 1 k)) (- (log (* PI 2)) (- (log n)))))) (* k k)) (* +nan.0 (- (/ (/ 1 (exp (* (* 1/2 (- 1 k)) (- (log (* PI 2)) (- (log n)))))) k)))))))
  (- (- (* (/ (/ 1 (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k))))) k) +nan.0) (- (/ (* +nan.0 1) (* (* k k) (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))))) (/ (* +nan.0 1) (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k))))))))
  (- (- (* (* +nan.0 (sqrt 2)) (* (* n PI) k)) (- (* (* +nan.0 (sqrt 2)) (* n PI)) (- (* +nan.0 (* (log (* PI 2)) (* (sqrt 2) (* (* n PI) k)))) (- (* (* (* (sqrt 2) n) (* (* (log n) k) PI)) +nan.0) (* (* +nan.0 (sqrt 2)) (* (* PI PI) (* n n))))))))
  (- (- (* (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI 2)) (- (log n))))) k) +nan.0) (- (* +nan.0 (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI 2)) (- (log n))))) (* k k))) (* +nan.0 (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI 2)) (- (log n))))) (* k (* k k)))))))
  (- (- (* (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) k) +nan.0) (- (/ (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) +nan.0) (* k k)) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) +nan.0))))
8.289 * * * [progress]: adding candidates to table
11.987 * * [progress]: iteration 3 / 4
11.987 * * * [progress]: picking best candidate
12.013 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.013 * * * [progress]: localizing error
12.037 * * * [progress]: generating rewritten candidates
12.037 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
12.060 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
12.069 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 2)
12.078 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
12.142 * * * [progress]: generating series expansions
12.142 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
12.143 * [backup-simplify]: Simplify (pow (* 2 (* n PI)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
12.143 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
12.143 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
12.143 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
12.143 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
12.143 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
12.143 * [taylor]: Taking taylor expansion of 1/2 in k
12.143 * [backup-simplify]: Simplify 1/2 into 1/2
12.143 * [taylor]: Taking taylor expansion of (- 1 k) in k
12.143 * [taylor]: Taking taylor expansion of 1 in k
12.143 * [backup-simplify]: Simplify 1 into 1
12.143 * [taylor]: Taking taylor expansion of k in k
12.143 * [backup-simplify]: Simplify 0 into 0
12.143 * [backup-simplify]: Simplify 1 into 1
12.143 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.143 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.143 * [taylor]: Taking taylor expansion of 2 in k
12.143 * [backup-simplify]: Simplify 2 into 2
12.143 * [taylor]: Taking taylor expansion of (* n PI) in k
12.143 * [taylor]: Taking taylor expansion of n in k
12.143 * [backup-simplify]: Simplify n into n
12.143 * [taylor]: Taking taylor expansion of PI in k
12.143 * [backup-simplify]: Simplify PI into PI
12.143 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.143 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.143 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.144 * [backup-simplify]: Simplify (- 0) into 0
12.145 * [backup-simplify]: Simplify (+ 1 0) into 1
12.145 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.145 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.145 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.145 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
12.145 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
12.145 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
12.145 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
12.145 * [taylor]: Taking taylor expansion of 1/2 in n
12.146 * [backup-simplify]: Simplify 1/2 into 1/2
12.146 * [taylor]: Taking taylor expansion of (- 1 k) in n
12.146 * [taylor]: Taking taylor expansion of 1 in n
12.146 * [backup-simplify]: Simplify 1 into 1
12.146 * [taylor]: Taking taylor expansion of k in n
12.146 * [backup-simplify]: Simplify k into k
12.146 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.146 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.146 * [taylor]: Taking taylor expansion of 2 in n
12.146 * [backup-simplify]: Simplify 2 into 2
12.146 * [taylor]: Taking taylor expansion of (* n PI) in n
12.146 * [taylor]: Taking taylor expansion of n in n
12.146 * [backup-simplify]: Simplify 0 into 0
12.146 * [backup-simplify]: Simplify 1 into 1
12.146 * [taylor]: Taking taylor expansion of PI in n
12.146 * [backup-simplify]: Simplify PI into PI
12.146 * [backup-simplify]: Simplify (* 0 PI) into 0
12.147 * [backup-simplify]: Simplify (* 2 0) into 0
12.148 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.151 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.152 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.152 * [backup-simplify]: Simplify (- k) into (- k)
12.153 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
12.153 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
12.154 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.155 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
12.156 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
12.156 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
12.156 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
12.156 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
12.156 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
12.157 * [taylor]: Taking taylor expansion of 1/2 in n
12.157 * [backup-simplify]: Simplify 1/2 into 1/2
12.157 * [taylor]: Taking taylor expansion of (- 1 k) in n
12.157 * [taylor]: Taking taylor expansion of 1 in n
12.157 * [backup-simplify]: Simplify 1 into 1
12.157 * [taylor]: Taking taylor expansion of k in n
12.157 * [backup-simplify]: Simplify k into k
12.157 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.157 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.157 * [taylor]: Taking taylor expansion of 2 in n
12.157 * [backup-simplify]: Simplify 2 into 2
12.157 * [taylor]: Taking taylor expansion of (* n PI) in n
12.157 * [taylor]: Taking taylor expansion of n in n
12.157 * [backup-simplify]: Simplify 0 into 0
12.157 * [backup-simplify]: Simplify 1 into 1
12.157 * [taylor]: Taking taylor expansion of PI in n
12.157 * [backup-simplify]: Simplify PI into PI
12.157 * [backup-simplify]: Simplify (* 0 PI) into 0
12.158 * [backup-simplify]: Simplify (* 2 0) into 0
12.159 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.161 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.162 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.162 * [backup-simplify]: Simplify (- k) into (- k)
12.162 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
12.162 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
12.164 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.165 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
12.166 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
12.166 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
12.166 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
12.166 * [taylor]: Taking taylor expansion of 1/2 in k
12.166 * [backup-simplify]: Simplify 1/2 into 1/2
12.166 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
12.166 * [taylor]: Taking taylor expansion of (- 1 k) in k
12.166 * [taylor]: Taking taylor expansion of 1 in k
12.166 * [backup-simplify]: Simplify 1 into 1
12.166 * [taylor]: Taking taylor expansion of k in k
12.166 * [backup-simplify]: Simplify 0 into 0
12.167 * [backup-simplify]: Simplify 1 into 1
12.167 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
12.167 * [taylor]: Taking taylor expansion of (log n) in k
12.167 * [taylor]: Taking taylor expansion of n in k
12.167 * [backup-simplify]: Simplify n into n
12.167 * [backup-simplify]: Simplify (log n) into (log n)
12.167 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.167 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.167 * [taylor]: Taking taylor expansion of 2 in k
12.167 * [backup-simplify]: Simplify 2 into 2
12.167 * [taylor]: Taking taylor expansion of PI in k
12.167 * [backup-simplify]: Simplify PI into PI
12.167 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.173 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.174 * [backup-simplify]: Simplify (- 0) into 0
12.174 * [backup-simplify]: Simplify (+ 1 0) into 1
12.175 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.176 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
12.177 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
12.178 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.179 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.180 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.181 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.183 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.183 * [backup-simplify]: Simplify (- 0) into 0
12.184 * [backup-simplify]: Simplify (+ 0 0) into 0
12.184 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
12.186 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.187 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.188 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.188 * [taylor]: Taking taylor expansion of 0 in k
12.189 * [backup-simplify]: Simplify 0 into 0
12.189 * [backup-simplify]: Simplify 0 into 0
12.189 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.190 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.192 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.192 * [backup-simplify]: Simplify (+ 0 0) into 0
12.193 * [backup-simplify]: Simplify (- 1) into -1
12.193 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.194 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
12.197 * [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)))))
12.200 * [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)))))))
12.202 * [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)))))))
12.204 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.205 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.208 * [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
12.208 * [backup-simplify]: Simplify (- 0) into 0
12.209 * [backup-simplify]: Simplify (+ 0 0) into 0
12.210 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
12.211 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.213 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.215 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) 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
12.217 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.218 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.221 * [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
12.221 * [backup-simplify]: Simplify (+ 0 0) into 0
12.222 * [backup-simplify]: Simplify (- 0) into 0
12.222 * [backup-simplify]: Simplify (+ 0 0) into 0
12.224 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.227 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 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 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)))))
12.235 * [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)))))
12.244 * [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)))))
12.244 * [backup-simplify]: Simplify (pow (* 2 (* (/ 1 n) PI)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
12.244 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
12.244 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
12.244 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.244 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.244 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
12.244 * [taylor]: Taking taylor expansion of 1/2 in k
12.244 * [backup-simplify]: Simplify 1/2 into 1/2
12.244 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
12.244 * [taylor]: Taking taylor expansion of 1 in k
12.244 * [backup-simplify]: Simplify 1 into 1
12.244 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.244 * [taylor]: Taking taylor expansion of k in k
12.244 * [backup-simplify]: Simplify 0 into 0
12.244 * [backup-simplify]: Simplify 1 into 1
12.244 * [backup-simplify]: Simplify (/ 1 1) into 1
12.244 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.244 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.244 * [taylor]: Taking taylor expansion of 2 in k
12.244 * [backup-simplify]: Simplify 2 into 2
12.244 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.244 * [taylor]: Taking taylor expansion of PI in k
12.244 * [backup-simplify]: Simplify PI into PI
12.245 * [taylor]: Taking taylor expansion of n in k
12.245 * [backup-simplify]: Simplify n into n
12.245 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.245 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.245 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.245 * [backup-simplify]: Simplify (- 1) into -1
12.246 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.246 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
12.246 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.246 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
12.246 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
12.246 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.246 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.246 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
12.246 * [taylor]: Taking taylor expansion of 1/2 in n
12.246 * [backup-simplify]: Simplify 1/2 into 1/2
12.246 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.246 * [taylor]: Taking taylor expansion of 1 in n
12.246 * [backup-simplify]: Simplify 1 into 1
12.247 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.247 * [taylor]: Taking taylor expansion of k in n
12.247 * [backup-simplify]: Simplify k into k
12.247 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.247 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.247 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.247 * [taylor]: Taking taylor expansion of 2 in n
12.247 * [backup-simplify]: Simplify 2 into 2
12.247 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.247 * [taylor]: Taking taylor expansion of PI in n
12.247 * [backup-simplify]: Simplify PI into PI
12.247 * [taylor]: Taking taylor expansion of n in n
12.247 * [backup-simplify]: Simplify 0 into 0
12.247 * [backup-simplify]: Simplify 1 into 1
12.248 * [backup-simplify]: Simplify (/ PI 1) into PI
12.248 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.249 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.249 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.250 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.250 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
12.251 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.252 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.253 * [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)))))
12.254 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
12.254 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.254 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.254 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
12.254 * [taylor]: Taking taylor expansion of 1/2 in n
12.254 * [backup-simplify]: Simplify 1/2 into 1/2
12.254 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.254 * [taylor]: Taking taylor expansion of 1 in n
12.254 * [backup-simplify]: Simplify 1 into 1
12.254 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.254 * [taylor]: Taking taylor expansion of k in n
12.254 * [backup-simplify]: Simplify k into k
12.254 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.254 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.254 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.254 * [taylor]: Taking taylor expansion of 2 in n
12.254 * [backup-simplify]: Simplify 2 into 2
12.254 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.254 * [taylor]: Taking taylor expansion of PI in n
12.254 * [backup-simplify]: Simplify PI into PI
12.254 * [taylor]: Taking taylor expansion of n in n
12.254 * [backup-simplify]: Simplify 0 into 0
12.254 * [backup-simplify]: Simplify 1 into 1
12.255 * [backup-simplify]: Simplify (/ PI 1) into PI
12.255 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.256 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.256 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.256 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.256 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
12.258 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.259 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.260 * [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)))))
12.260 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
12.260 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
12.260 * [taylor]: Taking taylor expansion of 1/2 in k
12.260 * [backup-simplify]: Simplify 1/2 into 1/2
12.260 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
12.260 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
12.260 * [taylor]: Taking taylor expansion of 1 in k
12.260 * [backup-simplify]: Simplify 1 into 1
12.260 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.260 * [taylor]: Taking taylor expansion of k in k
12.260 * [backup-simplify]: Simplify 0 into 0
12.260 * [backup-simplify]: Simplify 1 into 1
12.261 * [backup-simplify]: Simplify (/ 1 1) into 1
12.261 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.261 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.261 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.261 * [taylor]: Taking taylor expansion of 2 in k
12.261 * [backup-simplify]: Simplify 2 into 2
12.261 * [taylor]: Taking taylor expansion of PI in k
12.261 * [backup-simplify]: Simplify PI into PI
12.262 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.263 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.263 * [taylor]: Taking taylor expansion of (log n) in k
12.263 * [taylor]: Taking taylor expansion of n in k
12.263 * [backup-simplify]: Simplify n into n
12.263 * [backup-simplify]: Simplify (log n) into (log n)
12.263 * [backup-simplify]: Simplify (- 1) into -1
12.263 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.264 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.265 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.266 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
12.267 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.268 * [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)))))
12.269 * [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)))))
12.270 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.271 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.273 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.273 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.273 * [backup-simplify]: Simplify (- 0) into 0
12.274 * [backup-simplify]: Simplify (+ 0 0) into 0
12.274 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
12.276 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.277 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.279 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.279 * [taylor]: Taking taylor expansion of 0 in k
12.279 * [backup-simplify]: Simplify 0 into 0
12.279 * [backup-simplify]: Simplify 0 into 0
12.279 * [backup-simplify]: Simplify 0 into 0
12.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.281 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.284 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
12.284 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.285 * [backup-simplify]: Simplify (- 0) into 0
12.285 * [backup-simplify]: Simplify (+ 0 0) into 0
12.286 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
12.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.289 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.291 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.291 * [taylor]: Taking taylor expansion of 0 in k
12.291 * [backup-simplify]: Simplify 0 into 0
12.291 * [backup-simplify]: Simplify 0 into 0
12.292 * [backup-simplify]: Simplify 0 into 0
12.292 * [backup-simplify]: Simplify 0 into 0
12.293 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.294 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.300 * [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
12.300 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.301 * [backup-simplify]: Simplify (- 0) into 0
12.301 * [backup-simplify]: Simplify (+ 0 0) into 0
12.302 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
12.304 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.306 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.309 * [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
12.309 * [taylor]: Taking taylor expansion of 0 in k
12.309 * [backup-simplify]: Simplify 0 into 0
12.309 * [backup-simplify]: Simplify 0 into 0
12.310 * [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))))))
12.311 * [backup-simplify]: Simplify (pow (* 2 (* (/ 1 (- n)) PI)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
12.311 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
12.311 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
12.311 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
12.311 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
12.311 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
12.311 * [taylor]: Taking taylor expansion of 1/2 in k
12.311 * [backup-simplify]: Simplify 1/2 into 1/2
12.311 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.311 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.311 * [taylor]: Taking taylor expansion of k in k
12.311 * [backup-simplify]: Simplify 0 into 0
12.311 * [backup-simplify]: Simplify 1 into 1
12.316 * [backup-simplify]: Simplify (/ 1 1) into 1
12.317 * [taylor]: Taking taylor expansion of 1 in k
12.317 * [backup-simplify]: Simplify 1 into 1
12.317 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.317 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.317 * [taylor]: Taking taylor expansion of -2 in k
12.317 * [backup-simplify]: Simplify -2 into -2
12.317 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.317 * [taylor]: Taking taylor expansion of PI in k
12.317 * [backup-simplify]: Simplify PI into PI
12.317 * [taylor]: Taking taylor expansion of n in k
12.317 * [backup-simplify]: Simplify n into n
12.317 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.317 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.317 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.318 * [backup-simplify]: Simplify (+ 1 0) into 1
12.318 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.318 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.319 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
12.319 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
12.319 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
12.319 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
12.319 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
12.319 * [taylor]: Taking taylor expansion of 1/2 in n
12.319 * [backup-simplify]: Simplify 1/2 into 1/2
12.319 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.319 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.319 * [taylor]: Taking taylor expansion of k in n
12.319 * [backup-simplify]: Simplify k into k
12.319 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.319 * [taylor]: Taking taylor expansion of 1 in n
12.319 * [backup-simplify]: Simplify 1 into 1
12.319 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.319 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.319 * [taylor]: Taking taylor expansion of -2 in n
12.319 * [backup-simplify]: Simplify -2 into -2
12.319 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.319 * [taylor]: Taking taylor expansion of PI in n
12.319 * [backup-simplify]: Simplify PI into PI
12.319 * [taylor]: Taking taylor expansion of n in n
12.319 * [backup-simplify]: Simplify 0 into 0
12.319 * [backup-simplify]: Simplify 1 into 1
12.320 * [backup-simplify]: Simplify (/ PI 1) into PI
12.320 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.321 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.321 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.321 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
12.322 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.324 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.325 * [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)))))
12.325 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
12.325 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
12.325 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
12.325 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
12.325 * [taylor]: Taking taylor expansion of 1/2 in n
12.325 * [backup-simplify]: Simplify 1/2 into 1/2
12.325 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.325 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.325 * [taylor]: Taking taylor expansion of k in n
12.325 * [backup-simplify]: Simplify k into k
12.325 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.325 * [taylor]: Taking taylor expansion of 1 in n
12.325 * [backup-simplify]: Simplify 1 into 1
12.325 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.325 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.325 * [taylor]: Taking taylor expansion of -2 in n
12.325 * [backup-simplify]: Simplify -2 into -2
12.325 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.325 * [taylor]: Taking taylor expansion of PI in n
12.325 * [backup-simplify]: Simplify PI into PI
12.325 * [taylor]: Taking taylor expansion of n in n
12.325 * [backup-simplify]: Simplify 0 into 0
12.325 * [backup-simplify]: Simplify 1 into 1
12.326 * [backup-simplify]: Simplify (/ PI 1) into PI
12.326 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.327 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.327 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.327 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
12.328 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.330 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.331 * [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)))))
12.331 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
12.331 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
12.331 * [taylor]: Taking taylor expansion of 1/2 in k
12.331 * [backup-simplify]: Simplify 1/2 into 1/2
12.331 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
12.331 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.331 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.331 * [taylor]: Taking taylor expansion of k in k
12.331 * [backup-simplify]: Simplify 0 into 0
12.331 * [backup-simplify]: Simplify 1 into 1
12.332 * [backup-simplify]: Simplify (/ 1 1) into 1
12.332 * [taylor]: Taking taylor expansion of 1 in k
12.332 * [backup-simplify]: Simplify 1 into 1
12.332 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.332 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.332 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.332 * [taylor]: Taking taylor expansion of -2 in k
12.332 * [backup-simplify]: Simplify -2 into -2
12.332 * [taylor]: Taking taylor expansion of PI in k
12.332 * [backup-simplify]: Simplify PI into PI
12.332 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.333 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.333 * [taylor]: Taking taylor expansion of (log n) in k
12.333 * [taylor]: Taking taylor expansion of n in k
12.334 * [backup-simplify]: Simplify n into n
12.334 * [backup-simplify]: Simplify (log n) into (log n)
12.334 * [backup-simplify]: Simplify (+ 1 0) into 1
12.334 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.335 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.336 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
12.337 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
12.339 * [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)))))
12.340 * [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)))))
12.341 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.342 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.343 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.344 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.344 * [backup-simplify]: Simplify (+ 0 0) into 0
12.345 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
12.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.347 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.349 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.349 * [taylor]: Taking taylor expansion of 0 in k
12.349 * [backup-simplify]: Simplify 0 into 0
12.349 * [backup-simplify]: Simplify 0 into 0
12.349 * [backup-simplify]: Simplify 0 into 0
12.351 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.351 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.353 * [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
12.353 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.354 * [backup-simplify]: Simplify (+ 0 0) into 0
12.354 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
12.355 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.356 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.357 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.357 * [taylor]: Taking taylor expansion of 0 in k
12.357 * [backup-simplify]: Simplify 0 into 0
12.357 * [backup-simplify]: Simplify 0 into 0
12.357 * [backup-simplify]: Simplify 0 into 0
12.357 * [backup-simplify]: Simplify 0 into 0
12.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.359 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.362 * [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
12.362 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.362 * [backup-simplify]: Simplify (+ 0 0) into 0
12.363 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
12.364 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.365 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
12.367 * [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
12.367 * [taylor]: Taking taylor expansion of 0 in k
12.367 * [backup-simplify]: Simplify 0 into 0
12.367 * [backup-simplify]: Simplify 0 into 0
12.368 * [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))))))
12.368 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
12.368 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
12.368 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
12.368 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
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
12.369 * [backup-simplify]: Simplify (sqrt 0) into 0
12.369 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.369 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.370 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.370 * [taylor]: Taking taylor expansion of k in k
12.370 * [backup-simplify]: Simplify 0 into 0
12.370 * [backup-simplify]: Simplify 1 into 1
12.370 * [backup-simplify]: Simplify (/ 1 1) into 1
12.370 * [backup-simplify]: Simplify (sqrt 0) into 0
12.371 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.371 * [backup-simplify]: Simplify 0 into 0
12.371 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.371 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.373 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.373 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.374 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.377 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.377 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.378 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
12.378 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
12.378 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
12.378 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.378 * [taylor]: Taking taylor expansion of k in k
12.378 * [backup-simplify]: Simplify 0 into 0
12.378 * [backup-simplify]: Simplify 1 into 1
12.378 * [backup-simplify]: Simplify (sqrt 0) into 0
12.380 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.380 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.380 * [taylor]: Taking taylor expansion of k in k
12.380 * [backup-simplify]: Simplify 0 into 0
12.380 * [backup-simplify]: Simplify 1 into 1
12.380 * [backup-simplify]: Simplify (sqrt 0) into 0
12.382 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.382 * [backup-simplify]: Simplify 0 into 0
12.382 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.385 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.385 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.389 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.390 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.390 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 k) 3)) (+ (* +nan.0 (pow (/ 1 k) 2)) (* +nan.0 (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
12.390 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
12.390 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
12.390 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
12.390 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.390 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.390 * [taylor]: Taking taylor expansion of -1 in k
12.390 * [backup-simplify]: Simplify -1 into -1
12.390 * [taylor]: Taking taylor expansion of k in k
12.390 * [backup-simplify]: Simplify 0 into 0
12.390 * [backup-simplify]: Simplify 1 into 1
12.391 * [backup-simplify]: Simplify (/ -1 1) into -1
12.392 * [backup-simplify]: Simplify (sqrt 0) into 0
12.394 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.394 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
12.394 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
12.394 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.394 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.394 * [taylor]: Taking taylor expansion of -1 in k
12.395 * [backup-simplify]: Simplify -1 into -1
12.395 * [taylor]: Taking taylor expansion of k in k
12.395 * [backup-simplify]: Simplify 0 into 0
12.395 * [backup-simplify]: Simplify 1 into 1
12.395 * [backup-simplify]: Simplify (/ -1 1) into -1
12.396 * [backup-simplify]: Simplify (sqrt 0) into 0
12.397 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.398 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
12.398 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.399 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.401 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.402 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
12.402 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.403 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.405 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.408 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
12.408 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.409 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
12.409 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 2)
12.409 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.409 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0
12.409 * [taylor]: Taking taylor expansion of (* n PI) in n
12.409 * [taylor]: Taking taylor expansion of n in n
12.409 * [backup-simplify]: Simplify 0 into 0
12.409 * [backup-simplify]: Simplify 1 into 1
12.409 * [taylor]: Taking taylor expansion of PI in n
12.409 * [backup-simplify]: Simplify PI into PI
12.409 * [taylor]: Taking taylor expansion of (* n PI) in n
12.409 * [taylor]: Taking taylor expansion of n in n
12.409 * [backup-simplify]: Simplify 0 into 0
12.409 * [backup-simplify]: Simplify 1 into 1
12.409 * [taylor]: Taking taylor expansion of PI in n
12.409 * [backup-simplify]: Simplify PI into PI
12.409 * [backup-simplify]: Simplify (* 0 PI) into 0
12.409 * [backup-simplify]: Simplify 0 into 0
12.410 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.410 * [backup-simplify]: Simplify PI into PI
12.411 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.411 * [backup-simplify]: Simplify 0 into 0
12.412 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.412 * [backup-simplify]: Simplify 0 into 0
12.412 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.412 * [backup-simplify]: Simplify 0 into 0
12.413 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.413 * [backup-simplify]: Simplify 0 into 0
12.414 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.414 * [backup-simplify]: Simplify 0 into 0
12.415 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
12.415 * [backup-simplify]: Simplify 0 into 0
12.415 * [backup-simplify]: Simplify (* PI n) into (* n PI)
12.415 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n)
12.415 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0
12.415 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.415 * [taylor]: Taking taylor expansion of PI in n
12.415 * [backup-simplify]: Simplify PI into PI
12.415 * [taylor]: Taking taylor expansion of n in n
12.415 * [backup-simplify]: Simplify 0 into 0
12.416 * [backup-simplify]: Simplify 1 into 1
12.416 * [backup-simplify]: Simplify (/ PI 1) into PI
12.416 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.416 * [taylor]: Taking taylor expansion of PI in n
12.416 * [backup-simplify]: Simplify PI into PI
12.416 * [taylor]: Taking taylor expansion of n in n
12.416 * [backup-simplify]: Simplify 0 into 0
12.416 * [backup-simplify]: Simplify 1 into 1
12.416 * [backup-simplify]: Simplify (/ PI 1) into PI
12.416 * [backup-simplify]: Simplify PI into PI
12.417 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.417 * [backup-simplify]: Simplify 0 into 0
12.417 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.417 * [backup-simplify]: Simplify 0 into 0
12.418 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.418 * [backup-simplify]: Simplify 0 into 0
12.419 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.419 * [backup-simplify]: Simplify 0 into 0
12.420 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.420 * [backup-simplify]: Simplify 0 into 0
12.420 * [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
12.420 * [backup-simplify]: Simplify 0 into 0
12.420 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI)
12.420 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n))
12.420 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0
12.420 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
12.420 * [taylor]: Taking taylor expansion of -1 in n
12.421 * [backup-simplify]: Simplify -1 into -1
12.421 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.421 * [taylor]: Taking taylor expansion of PI in n
12.421 * [backup-simplify]: Simplify PI into PI
12.421 * [taylor]: Taking taylor expansion of n in n
12.421 * [backup-simplify]: Simplify 0 into 0
12.421 * [backup-simplify]: Simplify 1 into 1
12.421 * [backup-simplify]: Simplify (/ PI 1) into PI
12.421 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n
12.421 * [taylor]: Taking taylor expansion of -1 in n
12.421 * [backup-simplify]: Simplify -1 into -1
12.421 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.421 * [taylor]: Taking taylor expansion of PI in n
12.421 * [backup-simplify]: Simplify PI into PI
12.421 * [taylor]: Taking taylor expansion of n in n
12.421 * [backup-simplify]: Simplify 0 into 0
12.421 * [backup-simplify]: Simplify 1 into 1
12.421 * [backup-simplify]: Simplify (/ PI 1) into PI
12.422 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
12.422 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI)
12.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.423 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0
12.423 * [backup-simplify]: Simplify 0 into 0
12.424 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.424 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0
12.424 * [backup-simplify]: Simplify 0 into 0
12.425 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.425 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.425 * [backup-simplify]: Simplify 0 into 0
12.426 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.433 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.433 * [backup-simplify]: Simplify 0 into 0
12.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.436 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.436 * [backup-simplify]: Simplify 0 into 0
12.437 * [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
12.439 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.439 * [backup-simplify]: Simplify 0 into 0
12.440 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
12.440 * * * * [progress]: [ 4 / 4 ] generating series at (2)
12.440 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
12.440 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
12.440 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
12.440 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
12.440 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
12.440 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
12.440 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
12.440 * [taylor]: Taking taylor expansion of 1/2 in n
12.440 * [backup-simplify]: Simplify 1/2 into 1/2
12.440 * [taylor]: Taking taylor expansion of (- 1 k) in n
12.440 * [taylor]: Taking taylor expansion of 1 in n
12.440 * [backup-simplify]: Simplify 1 into 1
12.440 * [taylor]: Taking taylor expansion of k in n
12.440 * [backup-simplify]: Simplify k into k
12.440 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.440 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.440 * [taylor]: Taking taylor expansion of 2 in n
12.440 * [backup-simplify]: Simplify 2 into 2
12.440 * [taylor]: Taking taylor expansion of (* n PI) in n
12.440 * [taylor]: Taking taylor expansion of n in n
12.440 * [backup-simplify]: Simplify 0 into 0
12.440 * [backup-simplify]: Simplify 1 into 1
12.440 * [taylor]: Taking taylor expansion of PI in n
12.441 * [backup-simplify]: Simplify PI into PI
12.441 * [backup-simplify]: Simplify (* 0 PI) into 0
12.441 * [backup-simplify]: Simplify (* 2 0) into 0
12.443 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.445 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.446 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.446 * [backup-simplify]: Simplify (- k) into (- k)
12.446 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
12.446 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
12.447 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.448 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
12.449 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
12.449 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.449 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.449 * [taylor]: Taking taylor expansion of k in n
12.449 * [backup-simplify]: Simplify k into k
12.450 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.450 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.450 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.450 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.450 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
12.450 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
12.450 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
12.450 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
12.450 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
12.450 * [taylor]: Taking taylor expansion of 1/2 in k
12.450 * [backup-simplify]: Simplify 1/2 into 1/2
12.450 * [taylor]: Taking taylor expansion of (- 1 k) in k
12.450 * [taylor]: Taking taylor expansion of 1 in k
12.450 * [backup-simplify]: Simplify 1 into 1
12.450 * [taylor]: Taking taylor expansion of k in k
12.450 * [backup-simplify]: Simplify 0 into 0
12.450 * [backup-simplify]: Simplify 1 into 1
12.450 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.450 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.450 * [taylor]: Taking taylor expansion of 2 in k
12.450 * [backup-simplify]: Simplify 2 into 2
12.450 * [taylor]: Taking taylor expansion of (* n PI) in k
12.450 * [taylor]: Taking taylor expansion of n in k
12.450 * [backup-simplify]: Simplify n into n
12.450 * [taylor]: Taking taylor expansion of PI in k
12.450 * [backup-simplify]: Simplify PI into PI
12.450 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.451 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.451 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.451 * [backup-simplify]: Simplify (- 0) into 0
12.451 * [backup-simplify]: Simplify (+ 1 0) into 1
12.451 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.451 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.452 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.452 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.452 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.452 * [taylor]: Taking taylor expansion of k in k
12.452 * [backup-simplify]: Simplify 0 into 0
12.452 * [backup-simplify]: Simplify 1 into 1
12.452 * [backup-simplify]: Simplify (/ 1 1) into 1
12.452 * [backup-simplify]: Simplify (sqrt 0) into 0
12.453 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.453 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
12.453 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
12.453 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
12.453 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
12.453 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
12.453 * [taylor]: Taking taylor expansion of 1/2 in k
12.453 * [backup-simplify]: Simplify 1/2 into 1/2
12.453 * [taylor]: Taking taylor expansion of (- 1 k) in k
12.453 * [taylor]: Taking taylor expansion of 1 in k
12.453 * [backup-simplify]: Simplify 1 into 1
12.453 * [taylor]: Taking taylor expansion of k in k
12.453 * [backup-simplify]: Simplify 0 into 0
12.453 * [backup-simplify]: Simplify 1 into 1
12.453 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.453 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.453 * [taylor]: Taking taylor expansion of 2 in k
12.453 * [backup-simplify]: Simplify 2 into 2
12.453 * [taylor]: Taking taylor expansion of (* n PI) in k
12.453 * [taylor]: Taking taylor expansion of n in k
12.453 * [backup-simplify]: Simplify n into n
12.453 * [taylor]: Taking taylor expansion of PI in k
12.453 * [backup-simplify]: Simplify PI into PI
12.453 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.454 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.454 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.454 * [backup-simplify]: Simplify (- 0) into 0
12.454 * [backup-simplify]: Simplify (+ 1 0) into 1
12.454 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.454 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.454 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.455 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.455 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.455 * [taylor]: Taking taylor expansion of k in k
12.455 * [backup-simplify]: Simplify 0 into 0
12.455 * [backup-simplify]: Simplify 1 into 1
12.455 * [backup-simplify]: Simplify (/ 1 1) into 1
12.455 * [backup-simplify]: Simplify (sqrt 0) into 0
12.456 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.456 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
12.456 * [taylor]: Taking taylor expansion of 0 in n
12.456 * [backup-simplify]: Simplify 0 into 0
12.456 * [backup-simplify]: Simplify 0 into 0
12.456 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
12.457 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
12.457 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
12.457 * [backup-simplify]: Simplify (- 1) into -1
12.458 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.458 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
12.459 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
12.459 * [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)))))
12.459 * [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)))))
12.459 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
12.459 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
12.459 * [taylor]: Taking taylor expansion of +nan.0 in n
12.459 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.459 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
12.459 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.459 * [taylor]: Taking taylor expansion of 2 in n
12.459 * [backup-simplify]: Simplify 2 into 2
12.459 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.460 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.460 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.460 * [taylor]: Taking taylor expansion of (* n PI) in n
12.460 * [taylor]: Taking taylor expansion of n in n
12.460 * [backup-simplify]: Simplify 0 into 0
12.460 * [backup-simplify]: Simplify 1 into 1
12.460 * [taylor]: Taking taylor expansion of PI in n
12.460 * [backup-simplify]: Simplify PI into PI
12.460 * [backup-simplify]: Simplify (* 0 PI) into 0
12.461 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.461 * [backup-simplify]: Simplify (sqrt 0) into 0
12.462 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.462 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
12.463 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.463 * [backup-simplify]: Simplify (- 0) into 0
12.463 * [backup-simplify]: Simplify 0 into 0
12.463 * [backup-simplify]: Simplify 0 into 0
12.463 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.465 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.466 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
12.466 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
12.467 * [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
12.467 * [backup-simplify]: Simplify (- 0) into 0
12.468 * [backup-simplify]: Simplify (+ 0 0) into 0
12.468 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
12.469 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
12.470 * [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)))
12.470 * [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)))))))
12.470 * [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
12.470 * [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
12.470 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
12.470 * [taylor]: Taking taylor expansion of +nan.0 in n
12.470 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.470 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
12.470 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
12.470 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.470 * [taylor]: Taking taylor expansion of 2 in n
12.470 * [backup-simplify]: Simplify 2 into 2
12.471 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.471 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.471 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.471 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.471 * [taylor]: Taking taylor expansion of 2 in n
12.471 * [backup-simplify]: Simplify 2 into 2
12.471 * [taylor]: Taking taylor expansion of (* n PI) in n
12.471 * [taylor]: Taking taylor expansion of n in n
12.471 * [backup-simplify]: Simplify 0 into 0
12.471 * [backup-simplify]: Simplify 1 into 1
12.471 * [taylor]: Taking taylor expansion of PI in n
12.471 * [backup-simplify]: Simplify PI into PI
12.471 * [backup-simplify]: Simplify (* 0 PI) into 0
12.472 * [backup-simplify]: Simplify (* 2 0) into 0
12.473 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.473 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.474 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.474 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.474 * [taylor]: Taking taylor expansion of (* n PI) in n
12.474 * [taylor]: Taking taylor expansion of n in n
12.474 * [backup-simplify]: Simplify 0 into 0
12.474 * [backup-simplify]: Simplify 1 into 1
12.474 * [taylor]: Taking taylor expansion of PI in n
12.474 * [backup-simplify]: Simplify PI into PI
12.475 * [backup-simplify]: Simplify (* 0 PI) into 0
12.475 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.476 * [backup-simplify]: Simplify (sqrt 0) into 0
12.477 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.477 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
12.477 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
12.477 * [taylor]: Taking taylor expansion of +nan.0 in n
12.477 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.477 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
12.477 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.477 * [taylor]: Taking taylor expansion of 2 in n
12.477 * [backup-simplify]: Simplify 2 into 2
12.477 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.477 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.477 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.477 * [taylor]: Taking taylor expansion of (* n PI) in n
12.477 * [taylor]: Taking taylor expansion of n in n
12.477 * [backup-simplify]: Simplify 0 into 0
12.477 * [backup-simplify]: Simplify 1 into 1
12.477 * [taylor]: Taking taylor expansion of PI in n
12.477 * [backup-simplify]: Simplify PI into PI
12.478 * [backup-simplify]: Simplify (* 0 PI) into 0
12.479 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.479 * [backup-simplify]: Simplify (sqrt 0) into 0
12.480 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.481 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.482 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
12.483 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
12.483 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.483 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
12.483 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.484 * [backup-simplify]: Simplify (- 0) into 0
12.484 * [backup-simplify]: Simplify (+ 0 0) into 0
12.484 * [backup-simplify]: Simplify (- 0) into 0
12.484 * [backup-simplify]: Simplify 0 into 0
12.486 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
12.490 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
12.494 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
12.496 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
12.496 * [backup-simplify]: Simplify 0 into 0
12.497 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.501 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.502 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.503 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
12.506 * [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
12.506 * [backup-simplify]: Simplify (- 0) into 0
12.506 * [backup-simplify]: Simplify (+ 0 0) into 0
12.508 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
12.509 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
12.511 * [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)))
12.512 * [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)))))))))
12.512 * [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
12.512 * [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
12.512 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
12.512 * [taylor]: Taking taylor expansion of +nan.0 in n
12.512 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.512 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
12.512 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
12.512 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.512 * [taylor]: Taking taylor expansion of 2 in n
12.512 * [backup-simplify]: Simplify 2 into 2
12.513 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.513 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.513 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.513 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.513 * [taylor]: Taking taylor expansion of 2 in n
12.513 * [backup-simplify]: Simplify 2 into 2
12.513 * [taylor]: Taking taylor expansion of (* n PI) in n
12.513 * [taylor]: Taking taylor expansion of n in n
12.513 * [backup-simplify]: Simplify 0 into 0
12.514 * [backup-simplify]: Simplify 1 into 1
12.514 * [taylor]: Taking taylor expansion of PI in n
12.514 * [backup-simplify]: Simplify PI into PI
12.514 * [backup-simplify]: Simplify (* 0 PI) into 0
12.514 * [backup-simplify]: Simplify (* 2 0) into 0
12.516 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.517 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.519 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.519 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.519 * [taylor]: Taking taylor expansion of (* n PI) in n
12.519 * [taylor]: Taking taylor expansion of n in n
12.519 * [backup-simplify]: Simplify 0 into 0
12.519 * [backup-simplify]: Simplify 1 into 1
12.519 * [taylor]: Taking taylor expansion of PI in n
12.519 * [backup-simplify]: Simplify PI into PI
12.519 * [backup-simplify]: Simplify (* 0 PI) into 0
12.521 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.521 * [backup-simplify]: Simplify (sqrt 0) into 0
12.523 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.523 * [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
12.523 * [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
12.523 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
12.523 * [taylor]: Taking taylor expansion of +nan.0 in n
12.523 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.523 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
12.523 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.523 * [taylor]: Taking taylor expansion of 2 in n
12.523 * [backup-simplify]: Simplify 2 into 2
12.523 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.524 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.524 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.524 * [taylor]: Taking taylor expansion of (* n PI) in n
12.524 * [taylor]: Taking taylor expansion of n in n
12.524 * [backup-simplify]: Simplify 0 into 0
12.524 * [backup-simplify]: Simplify 1 into 1
12.524 * [taylor]: Taking taylor expansion of PI in n
12.524 * [backup-simplify]: Simplify PI into PI
12.525 * [backup-simplify]: Simplify (* 0 PI) into 0
12.526 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.527 * [backup-simplify]: Simplify (sqrt 0) into 0
12.528 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.528 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
12.528 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
12.528 * [taylor]: Taking taylor expansion of +nan.0 in n
12.528 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.528 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
12.528 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
12.528 * [taylor]: Taking taylor expansion of (sqrt 2) in n
12.528 * [taylor]: Taking taylor expansion of 2 in n
12.528 * [backup-simplify]: Simplify 2 into 2
12.529 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
12.529 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
12.529 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
12.529 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.529 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.529 * [taylor]: Taking taylor expansion of 2 in n
12.529 * [backup-simplify]: Simplify 2 into 2
12.529 * [taylor]: Taking taylor expansion of (* n PI) in n
12.529 * [taylor]: Taking taylor expansion of n in n
12.530 * [backup-simplify]: Simplify 0 into 0
12.530 * [backup-simplify]: Simplify 1 into 1
12.530 * [taylor]: Taking taylor expansion of PI in n
12.530 * [backup-simplify]: Simplify PI into PI
12.530 * [backup-simplify]: Simplify (* 0 PI) into 0
12.530 * [backup-simplify]: Simplify (* 2 0) into 0
12.532 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.533 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.534 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.536 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.536 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
12.536 * [taylor]: Taking taylor expansion of (* n PI) in n
12.536 * [taylor]: Taking taylor expansion of n in n
12.536 * [backup-simplify]: Simplify 0 into 0
12.536 * [backup-simplify]: Simplify 1 into 1
12.536 * [taylor]: Taking taylor expansion of PI in n
12.536 * [backup-simplify]: Simplify PI into PI
12.536 * [backup-simplify]: Simplify (* 0 PI) into 0
12.538 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.539 * [backup-simplify]: Simplify (sqrt 0) into 0
12.541 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
12.542 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.544 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
12.545 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
12.545 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.546 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
12.546 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.548 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.549 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.557 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
12.558 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
12.560 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
12.560 * [backup-simplify]: Simplify (* +nan.0 0) into 0
12.561 * [backup-simplify]: Simplify (- 0) into 0
12.561 * [backup-simplify]: Simplify (+ 0 0) into 0
12.561 * [backup-simplify]: Simplify (- 0) into 0
12.562 * [backup-simplify]: Simplify (+ 0 0) into 0
12.562 * [backup-simplify]: Simplify (- 0) into 0
12.562 * [backup-simplify]: Simplify 0 into 0
12.563 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.564 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.566 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.567 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.569 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.571 * [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))))))))
12.578 * [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))))))))
12.580 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
12.587 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
12.591 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
12.599 * [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))))))))))
12.607 * [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)))))))
12.613 * [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)))))))
12.615 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.619 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
12.620 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
12.625 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
12.634 * [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))))
12.639 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
12.642 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
12.655 * [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)))))))))))))
12.655 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* 2 (* (/ 1 n) PI)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
12.655 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
12.655 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
12.655 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
12.655 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.655 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.655 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
12.655 * [taylor]: Taking taylor expansion of 1/2 in n
12.656 * [backup-simplify]: Simplify 1/2 into 1/2
12.656 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.656 * [taylor]: Taking taylor expansion of 1 in n
12.656 * [backup-simplify]: Simplify 1 into 1
12.656 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.656 * [taylor]: Taking taylor expansion of k in n
12.656 * [backup-simplify]: Simplify k into k
12.656 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.656 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.656 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.656 * [taylor]: Taking taylor expansion of 2 in n
12.656 * [backup-simplify]: Simplify 2 into 2
12.656 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.656 * [taylor]: Taking taylor expansion of PI in n
12.656 * [backup-simplify]: Simplify PI into PI
12.656 * [taylor]: Taking taylor expansion of n in n
12.656 * [backup-simplify]: Simplify 0 into 0
12.656 * [backup-simplify]: Simplify 1 into 1
12.656 * [backup-simplify]: Simplify (/ PI 1) into PI
12.657 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.658 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.658 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.658 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.658 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
12.659 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.660 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.662 * [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)))))
12.662 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.662 * [taylor]: Taking taylor expansion of k in n
12.662 * [backup-simplify]: Simplify k into k
12.662 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.662 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.662 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
12.662 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
12.662 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.662 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.662 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
12.662 * [taylor]: Taking taylor expansion of 1/2 in k
12.662 * [backup-simplify]: Simplify 1/2 into 1/2
12.662 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
12.662 * [taylor]: Taking taylor expansion of 1 in k
12.662 * [backup-simplify]: Simplify 1 into 1
12.662 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.662 * [taylor]: Taking taylor expansion of k in k
12.662 * [backup-simplify]: Simplify 0 into 0
12.662 * [backup-simplify]: Simplify 1 into 1
12.662 * [backup-simplify]: Simplify (/ 1 1) into 1
12.663 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.663 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.663 * [taylor]: Taking taylor expansion of 2 in k
12.663 * [backup-simplify]: Simplify 2 into 2
12.663 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.663 * [taylor]: Taking taylor expansion of PI in k
12.663 * [backup-simplify]: Simplify PI into PI
12.663 * [taylor]: Taking taylor expansion of n in k
12.663 * [backup-simplify]: Simplify n into n
12.663 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.663 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.663 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.663 * [backup-simplify]: Simplify (- 1) into -1
12.664 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.664 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
12.664 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.664 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
12.664 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.664 * [taylor]: Taking taylor expansion of k in k
12.665 * [backup-simplify]: Simplify 0 into 0
12.665 * [backup-simplify]: Simplify 1 into 1
12.665 * [backup-simplify]: Simplify (sqrt 0) into 0
12.666 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.666 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
12.666 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
12.666 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.666 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.667 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
12.667 * [taylor]: Taking taylor expansion of 1/2 in k
12.667 * [backup-simplify]: Simplify 1/2 into 1/2
12.667 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
12.667 * [taylor]: Taking taylor expansion of 1 in k
12.667 * [backup-simplify]: Simplify 1 into 1
12.667 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.667 * [taylor]: Taking taylor expansion of k in k
12.667 * [backup-simplify]: Simplify 0 into 0
12.667 * [backup-simplify]: Simplify 1 into 1
12.667 * [backup-simplify]: Simplify (/ 1 1) into 1
12.667 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.667 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.667 * [taylor]: Taking taylor expansion of 2 in k
12.667 * [backup-simplify]: Simplify 2 into 2
12.667 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.667 * [taylor]: Taking taylor expansion of PI in k
12.667 * [backup-simplify]: Simplify PI into PI
12.667 * [taylor]: Taking taylor expansion of n in k
12.667 * [backup-simplify]: Simplify n into n
12.667 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.667 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.668 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.668 * [backup-simplify]: Simplify (- 1) into -1
12.668 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.669 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
12.669 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.669 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
12.669 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.669 * [taylor]: Taking taylor expansion of k in k
12.669 * [backup-simplify]: Simplify 0 into 0
12.669 * [backup-simplify]: Simplify 1 into 1
12.669 * [backup-simplify]: Simplify (sqrt 0) into 0
12.671 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.671 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
12.671 * [taylor]: Taking taylor expansion of 0 in n
12.671 * [backup-simplify]: Simplify 0 into 0
12.671 * [backup-simplify]: Simplify 0 into 0
12.672 * [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))))))))
12.672 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
12.672 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
12.672 * [taylor]: Taking taylor expansion of +nan.0 in n
12.672 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.672 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
12.672 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
12.672 * [taylor]: Taking taylor expansion of 1/2 in n
12.672 * [backup-simplify]: Simplify 1/2 into 1/2
12.672 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
12.672 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.672 * [taylor]: Taking taylor expansion of 1 in n
12.672 * [backup-simplify]: Simplify 1 into 1
12.672 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.672 * [taylor]: Taking taylor expansion of k in n
12.672 * [backup-simplify]: Simplify k into k
12.672 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.672 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.672 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.672 * [taylor]: Taking taylor expansion of 2 in n
12.672 * [backup-simplify]: Simplify 2 into 2
12.672 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.672 * [taylor]: Taking taylor expansion of PI in n
12.672 * [backup-simplify]: Simplify PI into PI
12.672 * [taylor]: Taking taylor expansion of n in n
12.672 * [backup-simplify]: Simplify 0 into 0
12.672 * [backup-simplify]: Simplify 1 into 1
12.673 * [backup-simplify]: Simplify (/ PI 1) into PI
12.673 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.674 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.675 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.675 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.676 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.677 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
12.678 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.679 * [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)))))
12.680 * [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))))))
12.682 * [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)))))))
12.683 * [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)))))))
12.683 * [backup-simplify]: Simplify 0 into 0
12.686 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.687 * [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))))))))
12.687 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
12.687 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
12.687 * [taylor]: Taking taylor expansion of +nan.0 in n
12.687 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.687 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
12.687 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
12.687 * [taylor]: Taking taylor expansion of 1/2 in n
12.687 * [backup-simplify]: Simplify 1/2 into 1/2
12.687 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
12.687 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.687 * [taylor]: Taking taylor expansion of 1 in n
12.687 * [backup-simplify]: Simplify 1 into 1
12.687 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.687 * [taylor]: Taking taylor expansion of k in n
12.687 * [backup-simplify]: Simplify k into k
12.687 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.687 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.687 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.687 * [taylor]: Taking taylor expansion of 2 in n
12.687 * [backup-simplify]: Simplify 2 into 2
12.687 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.687 * [taylor]: Taking taylor expansion of PI in n
12.688 * [backup-simplify]: Simplify PI into PI
12.688 * [taylor]: Taking taylor expansion of n in n
12.688 * [backup-simplify]: Simplify 0 into 0
12.688 * [backup-simplify]: Simplify 1 into 1
12.688 * [backup-simplify]: Simplify (/ PI 1) into PI
12.688 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.689 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.690 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.690 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.698 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.699 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
12.701 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.702 * [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)))))
12.703 * [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))))))
12.704 * [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)))))))
12.705 * [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)))))))
12.706 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.707 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.708 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.709 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.709 * [backup-simplify]: Simplify (- 0) into 0
12.709 * [backup-simplify]: Simplify (+ 0 0) into 0
12.711 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.712 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.713 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
12.715 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.716 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
12.717 * [backup-simplify]: Simplify (- 0) into 0
12.717 * [backup-simplify]: Simplify 0 into 0
12.717 * [backup-simplify]: Simplify 0 into 0
12.721 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.722 * [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))))))))
12.722 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
12.722 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
12.722 * [taylor]: Taking taylor expansion of +nan.0 in n
12.722 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.722 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
12.722 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
12.722 * [taylor]: Taking taylor expansion of 1/2 in n
12.722 * [backup-simplify]: Simplify 1/2 into 1/2
12.722 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
12.722 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
12.722 * [taylor]: Taking taylor expansion of 1 in n
12.722 * [backup-simplify]: Simplify 1 into 1
12.722 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.722 * [taylor]: Taking taylor expansion of k in n
12.722 * [backup-simplify]: Simplify k into k
12.722 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.722 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.722 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.722 * [taylor]: Taking taylor expansion of 2 in n
12.722 * [backup-simplify]: Simplify 2 into 2
12.722 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.722 * [taylor]: Taking taylor expansion of PI in n
12.722 * [backup-simplify]: Simplify PI into PI
12.722 * [taylor]: Taking taylor expansion of n in n
12.722 * [backup-simplify]: Simplify 0 into 0
12.722 * [backup-simplify]: Simplify 1 into 1
12.723 * [backup-simplify]: Simplify (/ PI 1) into PI
12.723 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.724 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.724 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.724 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
12.726 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.727 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
12.728 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
12.729 * [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)))))
12.730 * [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))))))
12.731 * [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)))))))
12.733 * [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)))))))
12.736 * [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))))))))
12.737 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* 2 (* (/ 1 (- n)) PI)) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
12.737 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
12.737 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
12.737 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
12.737 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
12.737 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
12.737 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
12.737 * [taylor]: Taking taylor expansion of 1/2 in n
12.737 * [backup-simplify]: Simplify 1/2 into 1/2
12.737 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.737 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.737 * [taylor]: Taking taylor expansion of k in n
12.737 * [backup-simplify]: Simplify k into k
12.737 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.737 * [taylor]: Taking taylor expansion of 1 in n
12.737 * [backup-simplify]: Simplify 1 into 1
12.737 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.737 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.737 * [taylor]: Taking taylor expansion of -2 in n
12.737 * [backup-simplify]: Simplify -2 into -2
12.737 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.737 * [taylor]: Taking taylor expansion of PI in n
12.737 * [backup-simplify]: Simplify PI into PI
12.737 * [taylor]: Taking taylor expansion of n in n
12.737 * [backup-simplify]: Simplify 0 into 0
12.737 * [backup-simplify]: Simplify 1 into 1
12.738 * [backup-simplify]: Simplify (/ PI 1) into PI
12.738 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.740 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.740 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.740 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
12.741 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.742 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.743 * [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)))))
12.743 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.743 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.743 * [taylor]: Taking taylor expansion of -1 in n
12.743 * [backup-simplify]: Simplify -1 into -1
12.743 * [taylor]: Taking taylor expansion of k in n
12.743 * [backup-simplify]: Simplify k into k
12.743 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.744 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.744 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.744 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.745 * [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)))
12.745 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
12.745 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
12.745 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
12.745 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
12.745 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
12.745 * [taylor]: Taking taylor expansion of 1/2 in k
12.745 * [backup-simplify]: Simplify 1/2 into 1/2
12.745 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.745 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.745 * [taylor]: Taking taylor expansion of k in k
12.745 * [backup-simplify]: Simplify 0 into 0
12.745 * [backup-simplify]: Simplify 1 into 1
12.746 * [backup-simplify]: Simplify (/ 1 1) into 1
12.746 * [taylor]: Taking taylor expansion of 1 in k
12.746 * [backup-simplify]: Simplify 1 into 1
12.746 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.746 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.746 * [taylor]: Taking taylor expansion of -2 in k
12.746 * [backup-simplify]: Simplify -2 into -2
12.746 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.746 * [taylor]: Taking taylor expansion of PI in k
12.746 * [backup-simplify]: Simplify PI into PI
12.746 * [taylor]: Taking taylor expansion of n in k
12.746 * [backup-simplify]: Simplify n into n
12.746 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.746 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.746 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.746 * [backup-simplify]: Simplify (+ 1 0) into 1
12.747 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.747 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.747 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
12.747 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.747 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.747 * [taylor]: Taking taylor expansion of -1 in k
12.747 * [backup-simplify]: Simplify -1 into -1
12.747 * [taylor]: Taking taylor expansion of k in k
12.747 * [backup-simplify]: Simplify 0 into 0
12.747 * [backup-simplify]: Simplify 1 into 1
12.747 * [backup-simplify]: Simplify (/ -1 1) into -1
12.748 * [backup-simplify]: Simplify (sqrt 0) into 0
12.749 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.749 * [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)))))
12.749 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
12.749 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
12.749 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
12.749 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
12.749 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
12.749 * [taylor]: Taking taylor expansion of 1/2 in k
12.749 * [backup-simplify]: Simplify 1/2 into 1/2
12.749 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.749 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.749 * [taylor]: Taking taylor expansion of k in k
12.749 * [backup-simplify]: Simplify 0 into 0
12.749 * [backup-simplify]: Simplify 1 into 1
12.749 * [backup-simplify]: Simplify (/ 1 1) into 1
12.749 * [taylor]: Taking taylor expansion of 1 in k
12.749 * [backup-simplify]: Simplify 1 into 1
12.749 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.749 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.749 * [taylor]: Taking taylor expansion of -2 in k
12.749 * [backup-simplify]: Simplify -2 into -2
12.749 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.749 * [taylor]: Taking taylor expansion of PI in k
12.749 * [backup-simplify]: Simplify PI into PI
12.749 * [taylor]: Taking taylor expansion of n in k
12.749 * [backup-simplify]: Simplify n into n
12.749 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.749 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.750 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.750 * [backup-simplify]: Simplify (+ 1 0) into 1
12.750 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.750 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.750 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
12.750 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.750 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.750 * [taylor]: Taking taylor expansion of -1 in k
12.750 * [backup-simplify]: Simplify -1 into -1
12.750 * [taylor]: Taking taylor expansion of k in k
12.750 * [backup-simplify]: Simplify 0 into 0
12.750 * [backup-simplify]: Simplify 1 into 1
12.751 * [backup-simplify]: Simplify (/ -1 1) into -1
12.751 * [backup-simplify]: Simplify (sqrt 0) into 0
12.752 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.752 * [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)))))
12.752 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
12.752 * [taylor]: Taking taylor expansion of +nan.0 in n
12.752 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.752 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
12.752 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
12.752 * [taylor]: Taking taylor expansion of 1/2 in n
12.752 * [backup-simplify]: Simplify 1/2 into 1/2
12.752 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
12.752 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.752 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.752 * [taylor]: Taking taylor expansion of -2 in n
12.752 * [backup-simplify]: Simplify -2 into -2
12.752 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.752 * [taylor]: Taking taylor expansion of PI in n
12.752 * [backup-simplify]: Simplify PI into PI
12.752 * [taylor]: Taking taylor expansion of n in n
12.752 * [backup-simplify]: Simplify 0 into 0
12.752 * [backup-simplify]: Simplify 1 into 1
12.753 * [backup-simplify]: Simplify (/ PI 1) into PI
12.753 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.754 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.754 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.754 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.754 * [taylor]: Taking taylor expansion of k in n
12.754 * [backup-simplify]: Simplify k into k
12.754 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.754 * [taylor]: Taking taylor expansion of 1 in n
12.754 * [backup-simplify]: Simplify 1 into 1
12.755 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.755 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.755 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
12.756 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.757 * [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)))))
12.757 * [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))))))
12.758 * [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))))))
12.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.760 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.761 * [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))))))
12.761 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
12.761 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
12.761 * [taylor]: Taking taylor expansion of +nan.0 in n
12.761 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.761 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
12.761 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
12.761 * [taylor]: Taking taylor expansion of 1/2 in n
12.761 * [backup-simplify]: Simplify 1/2 into 1/2
12.761 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
12.761 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.761 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.761 * [taylor]: Taking taylor expansion of -2 in n
12.761 * [backup-simplify]: Simplify -2 into -2
12.761 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.761 * [taylor]: Taking taylor expansion of PI in n
12.761 * [backup-simplify]: Simplify PI into PI
12.761 * [taylor]: Taking taylor expansion of n in n
12.761 * [backup-simplify]: Simplify 0 into 0
12.761 * [backup-simplify]: Simplify 1 into 1
12.762 * [backup-simplify]: Simplify (/ PI 1) into PI
12.762 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.763 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.763 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.763 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.763 * [taylor]: Taking taylor expansion of k in n
12.763 * [backup-simplify]: Simplify k into k
12.763 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.763 * [taylor]: Taking taylor expansion of 1 in n
12.763 * [backup-simplify]: Simplify 1 into 1
12.764 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.764 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.764 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
12.765 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.766 * [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)))))
12.766 * [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))))))
12.767 * [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)))))))
12.768 * [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)))))))
12.769 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.769 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.769 * [backup-simplify]: Simplify (+ 0 0) into 0
12.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.770 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.771 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.772 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
12.772 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
12.774 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.775 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
12.775 * [backup-simplify]: Simplify 0 into 0
12.775 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.778 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.779 * [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))))))
12.779 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
12.779 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
12.779 * [taylor]: Taking taylor expansion of +nan.0 in n
12.779 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.779 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
12.779 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
12.779 * [taylor]: Taking taylor expansion of 1/2 in n
12.779 * [backup-simplify]: Simplify 1/2 into 1/2
12.779 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
12.779 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.779 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.779 * [taylor]: Taking taylor expansion of -2 in n
12.779 * [backup-simplify]: Simplify -2 into -2
12.779 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.779 * [taylor]: Taking taylor expansion of PI in n
12.779 * [backup-simplify]: Simplify PI into PI
12.779 * [taylor]: Taking taylor expansion of n in n
12.779 * [backup-simplify]: Simplify 0 into 0
12.779 * [backup-simplify]: Simplify 1 into 1
12.779 * [backup-simplify]: Simplify (/ PI 1) into PI
12.780 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.780 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.780 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.780 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.780 * [taylor]: Taking taylor expansion of k in n
12.780 * [backup-simplify]: Simplify k into k
12.780 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.780 * [taylor]: Taking taylor expansion of 1 in n
12.780 * [backup-simplify]: Simplify 1 into 1
12.781 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.781 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.782 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
12.783 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.784 * [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)))))
12.785 * [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))))))
12.786 * [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)))))))
12.787 * [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)))))))
12.792 * [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))))))))))))
12.792 * * * [progress]: simplifying candidates
12.792 * * * * [progress]: [ 1 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log1p (expm1 (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.792 * * * * [progress]: [ 2 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (expm1 (log1p (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.793 * * * * [progress]: [ 3 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2)))))>
12.793 * * * * [progress]: [ 4 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2)))))>
12.793 * * * * [progress]: [ 5 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.793 * * * * [progress]: [ 6 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.793 * * * * [progress]: [ 7 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (* 1 (/ (- 1 k) 2)))))>
12.793 * * * * [progress]: [ 8 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (* 1 (/ (- 1 k) 2)))))>
12.793 * * * * [progress]: [ 9 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (* 1 (/ (- 1 k) 2)))))>
12.793 * * * * [progress]: [ 10 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))))>
12.793 * * * * [progress]: [ 11 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
12.793 * * * * [progress]: [ 12 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
12.793 * * * * [progress]: [ 13 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2)))))>
12.793 * * * * [progress]: [ 14 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2)))))>
12.793 * * * * [progress]: [ 15 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2))))>
12.793 * * * * [progress]: [ 16 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2)))))>
12.794 * * * * [progress]: [ 17 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2)))))>
12.794 * * * * [progress]: [ 18 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2))))>
12.794 * * * * [progress]: [ 19 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
12.794 * * * * [progress]: [ 20 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
12.794 * * * * [progress]: [ 21 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ 1 1)) (/ (- 1 k) 2))))>
12.794 * * * * [progress]: [ 22 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2)))))>
12.794 * * * * [progress]: [ 23 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2)))))>
12.794 * * * * [progress]: [ 24 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2))))>
12.794 * * * * [progress]: [ 25 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2)))))>
12.794 * * * * [progress]: [ 26 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2)))))>
12.794 * * * * [progress]: [ 27 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))>
12.794 * * * * [progress]: [ 28 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
12.794 * * * * [progress]: [ 29 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
12.795 * * * * [progress]: [ 30 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ 1 1)) (/ (- 1 k) 2))))>
12.795 * * * * [progress]: [ 31 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) 1) (/ (- 1 k) 2))))>
12.795 * * * * [progress]: [ 32 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (- 1 k)) (/ 1 2))))>
12.795 * * * * [progress]: [ 33 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2)))))>
12.795 * * * * [progress]: [ 34 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* 2 (* n PI)) (/ (- 1 k) 2)) 1)))>
12.795 * * * * [progress]: [ 35 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.795 * * * * [progress]: [ 36 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.795 * * * * [progress]: [ 37 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.795 * * * * [progress]: [ 38 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.795 * * * * [progress]: [ 39 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.795 * * * * [progress]: [ 40 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.795 * * * * [progress]: [ 41 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))))>
12.795 * * * * [progress]: [ 42 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (posit16->real (real->posit16 (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.795 * * * * [progress]: [ 43 / 196 ] simplifiying candidate #<alt (λ (k n) (* (log1p (expm1 (/ 1 (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.795 * * * * [progress]: [ 44 / 196 ] simplifiying candidate #<alt (λ (k n) (* (expm1 (log1p (/ 1 (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 45 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 46 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- 1/2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 47 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 48 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- (/ 1 2))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 49 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 50 / 196 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 51 / 196 ] simplifiying candidate #<alt (λ (k n) (* (exp (- 0 (log (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 52 / 196 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log 1) (log (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 53 / 196 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 54 / 196 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 55 / 196 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 56 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 57 / 196 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 58 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 59 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.796 * * * * [progress]: [ 60 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 61 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 62 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 63 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 64 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 65 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 66 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 67 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 68 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 69 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 70 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 71 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 72 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 73 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.797 * * * * [progress]: [ 74 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 75 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt 1)) (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 76 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 77 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 1) (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 78 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 79 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 80 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 81 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 82 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 83 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 84 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt 1)) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 85 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 86 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.798 * * * * [progress]: [ 87 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 88 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (sqrt 1))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 89 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 90 / 196 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (/ 1 (sqrt k)))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 91 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (log1p (expm1 (* n PI)))) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 92 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (expm1 (log1p (* n PI)))) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 93 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (pow (* n PI) 1)) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 94 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (pow (* n PI) 1)) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 95 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (exp (+ (log n) (log PI)))) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 96 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (exp (log (* n PI)))) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 97 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (log (exp (* n PI)))) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 98 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (cbrt (* (* (* n n) n) (* (* PI PI) PI)))) (/ (- 1 k) 2))))>
12.799 * * * * [progress]: [ 99 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 100 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (cbrt (* (* (* n PI) (* n PI)) (* n PI)))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 101 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* (sqrt (* n PI)) (sqrt (* n PI)))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 102 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* 1 (* n PI))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 103 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 104 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* (* n (* (cbrt PI) (cbrt PI))) (cbrt PI))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 105 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* (* n (sqrt PI)) (sqrt PI))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 106 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* (* n 1) PI)) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 107 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 108 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* (sqrt n) (* (sqrt n) PI))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 109 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* 1 (* n PI))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 110 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (posit16->real (real->posit16 (* n PI)))) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 111 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
12.800 * * * * [progress]: [ 112 / 196 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.800 * * * * [progress]: [ 113 / 196 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.800 * * * * [progress]: [ 114 / 196 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) 1))>
12.801 * * * * [progress]: [ 115 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 116 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 117 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 118 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 119 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (log (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.801 * * * * [progress]: [ 120 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 121 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 122 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 123 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 124 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (log (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.801 * * * * [progress]: [ 125 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 126 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 127 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 128 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.801 * * * * [progress]: [ 129 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (log (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.802 * * * * [progress]: [ 130 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2)))))>
12.802 * * * * [progress]: [ 131 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2)))))>
12.802 * * * * [progress]: [ 132 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.802 * * * * [progress]: [ 133 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))))>
12.802 * * * * [progress]: [ 134 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (log (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.802 * * * * [progress]: [ 135 / 196 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.802 * * * * [progress]: [ 136 / 196 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.802 * * * * [progress]: [ 137 / 196 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.802 * * * * [progress]: [ 138 / 196 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.802 * * * * [progress]: [ 139 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.802 * * * * [progress]: [ 140 / 196 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.802 * * * * [progress]: [ 141 / 196 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.802 * * * * [progress]: [ 142 / 196 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* 2 (* n PI)) (/ 1 2))) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))))>
12.802 * * * * [progress]: [ 143 / 196 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.803 * * * * [progress]: [ 144 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.803 * * * * [progress]: [ 145 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))))>
12.803 * * * * [progress]: [ 146 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.803 * * * * [progress]: [ 147 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))))>
12.803 * * * * [progress]: [ 148 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.803 * * * * [progress]: [ 149 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))))>
12.803 * * * * [progress]: [ 150 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.803 * * * * [progress]: [ 151 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))))>
12.803 * * * * [progress]: [ 152 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.803 * * * * [progress]: [ 153 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))))>
12.803 * * * * [progress]: [ 154 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow 2 (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2))))>
12.803 * * * * [progress]: [ 155 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.803 * * * * [progress]: [ 156 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.803 * * * * [progress]: [ 157 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.804 * * * * [progress]: [ 158 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))))>
12.804 * * * * [progress]: [ 159 / 196 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 160 / 196 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 161 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 162 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 163 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 164 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (* (/ (cbrt 1) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 165 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 166 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (/ (cbrt 1) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 167 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 168 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 169 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 170 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt 1)) (* (/ (sqrt 1) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.804 * * * * [progress]: [ 171 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 172 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (* (/ (sqrt 1) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 173 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ 1 (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 174 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (* (/ 1 (sqrt (cbrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 175 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 176 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 177 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 178 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 179 / 196 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 180 / 196 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
12.805 * * * * [progress]: [ 181 / 196 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2))))>
12.805 * * * * [progress]: [ 182 / 196 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (sqrt k)))>
12.805 * * * * [progress]: [ 183 / 196 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))>
12.805 * * * * [progress]: [ 184 / 196 ] simplifiying candidate #<alt (λ (k n) (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
12.805 * * * * [progress]: [ 185 / 196 ] 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)))))))>
12.806 * * * * [progress]: [ 186 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
12.806 * * * * [progress]: [ 187 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
12.806 * * * * [progress]: [ 188 / 196 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.806 * * * * [progress]: [ 189 / 196 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.806 * * * * [progress]: [ 190 / 196 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.806 * * * * [progress]: [ 191 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.806 * * * * [progress]: [ 192 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.806 * * * * [progress]: [ 193 / 196 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
12.806 * * * * [progress]: [ 194 / 196 ] 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))))))))))))))>
12.806 * * * * [progress]: [ 195 / 196 ] 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)))))))))>
12.806 * * * * [progress]: [ 196 / 196 ] 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)))))))))))))>
12.810 * [simplify]: Simplifying:
  (expm1 (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (log1p (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2))
  (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2))
  (* (log (* 2 (* n PI))) (/ (- 1 k) 2))
  (* (log (* 2 (* n PI))) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* 2 (* n PI)) (/ 1 2))
  (pow (* 2 (* n PI)) (/ k 2))
  (pow (* 2 (* n PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* 2 (* n PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* 2 (* n PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* 2 (* n PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* 2 (* n PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* 2 (* n PI)) (/ (sqrt (- 1 k)) 1))
  (pow (* 2 (* n PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ 1 (sqrt 2)))
  (pow (* 2 (* n PI)) (/ 1 1))
  (pow (* 2 (* n PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* 2 (* n PI)) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* 2 (* n PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* 2 (* n PI)) (/ (+ 1 (sqrt k)) 1))
  (pow (* 2 (* n PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* n PI)) (/ 1 (sqrt 2)))
  (pow (* 2 (* n PI)) (/ 1 1))
  (pow (* 2 (* n PI)) 1)
  (pow (* 2 (* n PI)) (- 1 k))
  (pow 2 (/ (- 1 k) 2))
  (pow (* n PI) (/ (- 1 k) 2))
  (log (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (exp (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))
  (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (expm1 (/ 1 (sqrt k)))
  (log1p (/ 1 (sqrt k)))
  (- 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)))
  (expm1 (* n PI))
  (log1p (* n PI))
  (* n PI)
  (+ (log n) (log PI))
  (log (* n PI))
  (exp (* n PI))
  (* (* (* n n) n) (* (* PI PI) PI))
  (* (cbrt (* n PI)) (cbrt (* n PI)))
  (cbrt (* n PI))
  (* (* (* n PI) (* n PI)) (* n PI))
  (sqrt (* n PI))
  (sqrt (* n PI))
  (* (sqrt n) (sqrt PI))
  (* (sqrt n) (sqrt PI))
  (* n (* (cbrt PI) (cbrt PI)))
  (* n (sqrt PI))
  (* n 1)
  (* (cbrt n) PI)
  (* (sqrt n) PI)
  (* n PI)
  (real->posit16 (* n PI))
  (expm1 (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (log1p (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (+ (- (log (sqrt k))) (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (log (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (+ (- 0 (log (sqrt k))) (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (log (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (+ (- (log 1) (log (sqrt k))) (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (log (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (+ (log (/ 1 (sqrt k))) (* (+ (log 2) (+ (log n) (log PI))) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (+ (log 2) (log (* n PI))) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* 2 (* n PI))) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (log (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (log (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (exp (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (cbrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
  (cbrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* 1 (pow (* 2 (* n PI)) (/ 1 2)))
  (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt k)) (pow 2 (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (* (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
  (* (/ 1 (sqrt k)) (sqrt (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt k)) 1)
  (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)))
  (* (cbrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ 1 (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (cbrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ 1 2)))
  (* 1 (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
  (real->posit16 (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* +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)))))
  (* n PI)
  (* n PI)
  (* 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))))))))))))
12.816 * * [simplify]: iteration 1: (351 enodes)
13.054 * * [simplify]: iteration 2: (1509 enodes)
13.492 * * [simplify]: Extracting #0: cost 105 inf + 0
13.493 * * [simplify]: Extracting #1: cost 530 inf + 4
13.497 * * [simplify]: Extracting #2: cost 850 inf + 14196
13.508 * * [simplify]: Extracting #3: cost 837 inf + 82545
13.557 * * [simplify]: Extracting #4: cost 445 inf + 245340
13.628 * * [simplify]: Extracting #5: cost 132 inf + 354147
13.720 * * [simplify]: Extracting #6: cost 44 inf + 393854
13.810 * * [simplify]: Extracting #7: cost 6 inf + 417808
13.879 * * [simplify]: Extracting #8: cost 0 inf + 421421
13.978 * * [simplify]: Extracting #9: cost 0 inf + 421366
14.054 * [simplify]: Simplified to:
  (expm1 (pow (* (* PI n) 2) (/ (- 1 k) 2)))
  (log1p (pow (* (* PI n) 2) (/ (- 1 k) 2)))
  (/ (* (log (* (* PI n) 2)) (- 1 k)) 2)
  (/ (* (log (* (* PI n) 2)) (- 1 k)) 2)
  (/ (* (log (* (* PI n) 2)) (- 1 k)) 2)
  (/ (* (log (* (* PI n) 2)) (- 1 k)) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* (* PI n) 2))
  (pow (* (* PI n) 2) (/ k 2))
  (pow (* (* PI n) 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI n) 2) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI n) 2) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI n) 2) (* (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt (- 1 k))))
  (pow (* (* PI n) 2) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI n) 2) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI n) 2) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI n) 2) (sqrt (- 1 k)))
  (pow (* (* PI n) 2) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI n) 2) (/ 1 (sqrt 2)))
  (* (* PI n) 2)
  (pow (* (* PI n) 2) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI n) 2) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI n) 2) (+ (sqrt k) 1))
  (pow (* (* PI n) 2) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI n) 2) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI n) 2) (+ (sqrt k) 1))
  (pow (* (* PI n) 2) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI n) 2) (/ 1 (sqrt 2)))
  (* (* PI n) 2)
  (* (* PI n) 2)
  (pow (* (* PI n) 2) (- 1 k))
  (pow 2 (/ (- 1 k) 2))
  (pow (* PI n) (/ (- 1 k) 2))
  (/ (* (log (* (* PI n) 2)) (- 1 k)) 2)
  (exp (pow (* (* PI n) 2) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))
  (pow (pow (* (* PI n) 2) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))
  (pow (* (* PI n) 2) (- 1/4 (/ k 4)))
  (pow (* (* PI n) 2) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* PI n) 2) (/ (- 1 k) 2)))
  (expm1 (/ 1 (sqrt k)))
  (log1p (/ 1 (sqrt k)))
  -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 (sqrt k)) (* (/ 1 (sqrt k)) (/ 1 (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)))
  (expm1 (* PI n))
  (log1p (* PI n))
  (* PI n)
  (log (* PI n))
  (log (* PI n))
  (exp (* PI n))
  (* (* PI n) (* (* PI n) (* PI n)))
  (* (cbrt (* PI n)) (cbrt (* PI n)))
  (cbrt (* PI n))
  (* (* PI n) (* (* PI n) (* PI n)))
  (sqrt (* PI n))
  (sqrt (* PI n))
  (* (sqrt PI) (sqrt n))
  (* (sqrt PI) (sqrt n))
  (* (cbrt PI) (* (cbrt PI) n))
  (* (sqrt PI) n)
  n
  (* (cbrt n) PI)
  (* (sqrt n) PI)
  (* PI n)
  (real->posit16 (* PI n))
  (expm1 (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI n) 2)) (- 1 k)) 2) (log (sqrt k)))
  (exp (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
  (/ (pow (pow (* (* PI n) 2) (/ (- 1 k) 2)) 3) (* k (sqrt k)))
  (* (* (pow (pow (* (* PI n) 2) (/ (- 1 k) 2)) 3) (/ 1 (sqrt k))) (* (/ 1 (sqrt k)) (/ 1 (sqrt k))))
  (* (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
  (* (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) (* (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
  (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (* (* PI n) 2))
  (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))
  (* (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (/ 1 (sqrt k))))
  (* (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (/ 1 (sqrt k))))
  (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
  (/ (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (sqrt k))
  (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (pow (* (* PI n) 2) (- 1/4 (/ k 4))) (sqrt k))
  (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (/ 1 (sqrt k))))
  (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k))))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (sqrt (* (* PI n) 2)) (sqrt k))
  (pow (* (* PI n) 2) (/ (- 1 k) 2))
  (real->posit16 (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
  (fma 1/4 (* (* (log (* 2 PI)) (* (* (log n) k) k)) (exp (* 1/2 (log (* (* PI n) 2))))) (- (fma 1/8 (* (exp (* 1/2 (log (* (* PI n) 2)))) (* (* (log n) k) (* (log n) k))) (fma (* (* (log (* 2 PI)) (log (* 2 PI))) 1/8) (* (exp (* 1/2 (log (* (* PI n) 2)))) (* k k)) (exp (* 1/2 (log (* (* PI n) 2)))))) (* (fma (* (log n) k) (exp (* 1/2 (log (* (* PI n) 2)))) (* (exp (* 1/2 (log (* (* PI n) 2)))) (* k (log (* 2 PI))))) 1/2)))
  (exp (* (* (- 1 k) 1/2) (log (* (* PI n) 2))))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1 k) 1/2)))
  (+ (- (* +nan.0 (* k k))) (- +nan.0 (* +nan.0 k)))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* (* k k) k))))
  (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (* k k))))
  (* PI n)
  (* PI n)
  (* PI n)
  (- (fma (* +nan.0 (sqrt 2)) (* (* PI n) k) (- (fma (* +nan.0 (sqrt 2)) (* PI n) (+ (* (* +nan.0 (sqrt 2)) (- (* (* (* PI n) k) (log n)) (* (* PI n) (* PI n)))) (- (* (* +nan.0 (* (log (* 2 PI)) (sqrt 2))) (* (* PI n) k))))))))
  (- (- (/ +nan.0 (/ k (exp (* (* (- 1 k) 1/2) (log (* (* PI n) 2)))))) (* +nan.0 (- (/ (exp (* (* (- 1 k) 1/2) (log (* (* PI n) 2)))) (* k k)) (/ (exp (* (* (- 1 k) 1/2) (log (* (* PI n) 2)))) (* (* k k) k))))))
  (+ (* (- +nan.0) (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1 k) 1/2))) k)) (* +nan.0 (- (/ (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1 k) 1/2))) k) k) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1 k) 1/2))))))
14.079 * * * [progress]: adding candidates to table
16.347 * * [progress]: iteration 4 / 4
16.347 * * * [progress]: picking best candidate
16.381 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.381 * * * [progress]: localizing error
16.406 * * * [progress]: generating rewritten candidates
16.406 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2)
16.426 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1)
16.441 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1)
16.453 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1)
16.474 * * * [progress]: generating series expansions
16.474 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2)
16.475 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) into (pow (* 2 (* n PI)) (* 1/4 (- 1 k)))
16.475 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in (n k) around 0
16.475 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in k
16.475 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in k
16.475 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in k
16.475 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in k
16.475 * [taylor]: Taking taylor expansion of 1/4 in k
16.475 * [backup-simplify]: Simplify 1/4 into 1/4
16.475 * [taylor]: Taking taylor expansion of (- 1 k) in k
16.475 * [taylor]: Taking taylor expansion of 1 in k
16.475 * [backup-simplify]: Simplify 1 into 1
16.475 * [taylor]: Taking taylor expansion of k in k
16.475 * [backup-simplify]: Simplify 0 into 0
16.475 * [backup-simplify]: Simplify 1 into 1
16.475 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
16.475 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
16.475 * [taylor]: Taking taylor expansion of 2 in k
16.475 * [backup-simplify]: Simplify 2 into 2
16.475 * [taylor]: Taking taylor expansion of (* n PI) in k
16.475 * [taylor]: Taking taylor expansion of n in k
16.475 * [backup-simplify]: Simplify n into n
16.476 * [taylor]: Taking taylor expansion of PI in k
16.476 * [backup-simplify]: Simplify PI into PI
16.476 * [backup-simplify]: Simplify (* n PI) into (* n PI)
16.476 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
16.476 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
16.476 * [backup-simplify]: Simplify (- 0) into 0
16.477 * [backup-simplify]: Simplify (+ 1 0) into 1
16.477 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
16.477 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
16.477 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
16.477 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
16.477 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
16.477 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
16.477 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
16.477 * [taylor]: Taking taylor expansion of 1/4 in n
16.477 * [backup-simplify]: Simplify 1/4 into 1/4
16.477 * [taylor]: Taking taylor expansion of (- 1 k) in n
16.477 * [taylor]: Taking taylor expansion of 1 in n
16.477 * [backup-simplify]: Simplify 1 into 1
16.477 * [taylor]: Taking taylor expansion of k in n
16.477 * [backup-simplify]: Simplify k into k
16.477 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.477 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.477 * [taylor]: Taking taylor expansion of 2 in n
16.477 * [backup-simplify]: Simplify 2 into 2
16.478 * [taylor]: Taking taylor expansion of (* n PI) in n
16.478 * [taylor]: Taking taylor expansion of n in n
16.478 * [backup-simplify]: Simplify 0 into 0
16.478 * [backup-simplify]: Simplify 1 into 1
16.478 * [taylor]: Taking taylor expansion of PI in n
16.478 * [backup-simplify]: Simplify PI into PI
16.478 * [backup-simplify]: Simplify (* 0 PI) into 0
16.478 * [backup-simplify]: Simplify (* 2 0) into 0
16.480 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.481 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.482 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.482 * [backup-simplify]: Simplify (- k) into (- k)
16.482 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
16.482 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
16.484 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.490 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
16.491 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
16.491 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
16.491 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
16.491 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
16.491 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
16.491 * [taylor]: Taking taylor expansion of 1/4 in n
16.491 * [backup-simplify]: Simplify 1/4 into 1/4
16.492 * [taylor]: Taking taylor expansion of (- 1 k) in n
16.492 * [taylor]: Taking taylor expansion of 1 in n
16.492 * [backup-simplify]: Simplify 1 into 1
16.492 * [taylor]: Taking taylor expansion of k in n
16.492 * [backup-simplify]: Simplify k into k
16.492 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.492 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.492 * [taylor]: Taking taylor expansion of 2 in n
16.492 * [backup-simplify]: Simplify 2 into 2
16.492 * [taylor]: Taking taylor expansion of (* n PI) in n
16.492 * [taylor]: Taking taylor expansion of n in n
16.492 * [backup-simplify]: Simplify 0 into 0
16.492 * [backup-simplify]: Simplify 1 into 1
16.492 * [taylor]: Taking taylor expansion of PI in n
16.492 * [backup-simplify]: Simplify PI into PI
16.492 * [backup-simplify]: Simplify (* 0 PI) into 0
16.493 * [backup-simplify]: Simplify (* 2 0) into 0
16.494 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.495 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.496 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.496 * [backup-simplify]: Simplify (- k) into (- k)
16.496 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
16.496 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
16.498 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.499 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
16.500 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
16.500 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
16.500 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
16.500 * [taylor]: Taking taylor expansion of 1/4 in k
16.500 * [backup-simplify]: Simplify 1/4 into 1/4
16.500 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
16.500 * [taylor]: Taking taylor expansion of (- 1 k) in k
16.500 * [taylor]: Taking taylor expansion of 1 in k
16.500 * [backup-simplify]: Simplify 1 into 1
16.501 * [taylor]: Taking taylor expansion of k in k
16.501 * [backup-simplify]: Simplify 0 into 0
16.501 * [backup-simplify]: Simplify 1 into 1
16.501 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
16.501 * [taylor]: Taking taylor expansion of (log n) in k
16.501 * [taylor]: Taking taylor expansion of n in k
16.501 * [backup-simplify]: Simplify n into n
16.501 * [backup-simplify]: Simplify (log n) into (log n)
16.501 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
16.501 * [taylor]: Taking taylor expansion of (* 2 PI) in k
16.501 * [taylor]: Taking taylor expansion of 2 in k
16.501 * [backup-simplify]: Simplify 2 into 2
16.501 * [taylor]: Taking taylor expansion of PI in k
16.501 * [backup-simplify]: Simplify PI into PI
16.501 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.502 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.503 * [backup-simplify]: Simplify (- 0) into 0
16.503 * [backup-simplify]: Simplify (+ 1 0) into 1
16.504 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.505 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
16.506 * [backup-simplify]: Simplify (* 1/4 (+ (log n) (log (* 2 PI)))) into (* 1/4 (+ (log n) (log (* 2 PI))))
16.508 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
16.509 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
16.510 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.511 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
16.512 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.513 * [backup-simplify]: Simplify (- 0) into 0
16.513 * [backup-simplify]: Simplify (+ 0 0) into 0
16.514 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 k))) into 0
16.515 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.516 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
16.518 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.518 * [taylor]: Taking taylor expansion of 0 in k
16.518 * [backup-simplify]: Simplify 0 into 0
16.518 * [backup-simplify]: Simplify 0 into 0
16.519 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
16.520 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.522 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.522 * [backup-simplify]: Simplify (+ 0 0) into 0
16.523 * [backup-simplify]: Simplify (- 1) into -1
16.523 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.525 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
16.527 * [backup-simplify]: Simplify (+ (* 1/4 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
16.528 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
16.530 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
16.531 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.531 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.533 * [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
16.534 * [backup-simplify]: Simplify (- 0) into 0
16.534 * [backup-simplify]: Simplify (+ 0 0) into 0
16.534 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
16.535 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.536 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.537 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.537 * [taylor]: Taking taylor expansion of 0 in k
16.537 * [backup-simplify]: Simplify 0 into 0
16.537 * [backup-simplify]: Simplify 0 into 0
16.537 * [backup-simplify]: Simplify 0 into 0
16.538 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
16.539 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.541 * [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
16.541 * [backup-simplify]: Simplify (+ 0 0) into 0
16.541 * [backup-simplify]: Simplify (- 0) into 0
16.542 * [backup-simplify]: Simplify (+ 0 0) into 0
16.543 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.544 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.546 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
16.549 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
16.555 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
16.555 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (/ (- 1 (/ 1 k)) 2) 2)) into (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k))))
16.555 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in (n k) around 0
16.555 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in k
16.555 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
16.555 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
16.555 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in k
16.555 * [taylor]: Taking taylor expansion of 1/4 in k
16.555 * [backup-simplify]: Simplify 1/4 into 1/4
16.555 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.555 * [taylor]: Taking taylor expansion of 1 in k
16.555 * [backup-simplify]: Simplify 1 into 1
16.555 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.555 * [taylor]: Taking taylor expansion of k in k
16.555 * [backup-simplify]: Simplify 0 into 0
16.555 * [backup-simplify]: Simplify 1 into 1
16.556 * [backup-simplify]: Simplify (/ 1 1) into 1
16.556 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
16.556 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
16.556 * [taylor]: Taking taylor expansion of 2 in k
16.556 * [backup-simplify]: Simplify 2 into 2
16.556 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.556 * [taylor]: Taking taylor expansion of PI in k
16.556 * [backup-simplify]: Simplify PI into PI
16.556 * [taylor]: Taking taylor expansion of n in k
16.556 * [backup-simplify]: Simplify n into n
16.556 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.556 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
16.556 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
16.556 * [backup-simplify]: Simplify (- 1) into -1
16.556 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.557 * [backup-simplify]: Simplify (* 1/4 -1) into -1/4
16.557 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
16.557 * [backup-simplify]: Simplify (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
16.557 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
16.557 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
16.557 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
16.557 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
16.557 * [taylor]: Taking taylor expansion of 1/4 in n
16.557 * [backup-simplify]: Simplify 1/4 into 1/4
16.557 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.557 * [taylor]: Taking taylor expansion of 1 in n
16.557 * [backup-simplify]: Simplify 1 into 1
16.557 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.557 * [taylor]: Taking taylor expansion of k in n
16.557 * [backup-simplify]: Simplify k into k
16.557 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.557 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.557 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.557 * [taylor]: Taking taylor expansion of 2 in n
16.557 * [backup-simplify]: Simplify 2 into 2
16.557 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.557 * [taylor]: Taking taylor expansion of PI in n
16.557 * [backup-simplify]: Simplify PI into PI
16.557 * [taylor]: Taking taylor expansion of n in n
16.557 * [backup-simplify]: Simplify 0 into 0
16.557 * [backup-simplify]: Simplify 1 into 1
16.558 * [backup-simplify]: Simplify (/ PI 1) into PI
16.558 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.558 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.559 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.559 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.559 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
16.560 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.561 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
16.562 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
16.562 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
16.562 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
16.562 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
16.562 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
16.562 * [taylor]: Taking taylor expansion of 1/4 in n
16.562 * [backup-simplify]: Simplify 1/4 into 1/4
16.562 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.563 * [taylor]: Taking taylor expansion of 1 in n
16.563 * [backup-simplify]: Simplify 1 into 1
16.563 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.563 * [taylor]: Taking taylor expansion of k in n
16.563 * [backup-simplify]: Simplify k into k
16.563 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.563 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.563 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.563 * [taylor]: Taking taylor expansion of 2 in n
16.563 * [backup-simplify]: Simplify 2 into 2
16.563 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.563 * [taylor]: Taking taylor expansion of PI in n
16.563 * [backup-simplify]: Simplify PI into PI
16.563 * [taylor]: Taking taylor expansion of n in n
16.563 * [backup-simplify]: Simplify 0 into 0
16.563 * [backup-simplify]: Simplify 1 into 1
16.563 * [backup-simplify]: Simplify (/ PI 1) into PI
16.563 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.564 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.564 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.564 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.564 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
16.565 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.566 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
16.566 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
16.566 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
16.566 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
16.567 * [taylor]: Taking taylor expansion of 1/4 in k
16.567 * [backup-simplify]: Simplify 1/4 into 1/4
16.567 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
16.567 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.567 * [taylor]: Taking taylor expansion of 1 in k
16.567 * [backup-simplify]: Simplify 1 into 1
16.567 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.567 * [taylor]: Taking taylor expansion of k in k
16.567 * [backup-simplify]: Simplify 0 into 0
16.567 * [backup-simplify]: Simplify 1 into 1
16.567 * [backup-simplify]: Simplify (/ 1 1) into 1
16.567 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
16.567 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
16.567 * [taylor]: Taking taylor expansion of (* 2 PI) in k
16.567 * [taylor]: Taking taylor expansion of 2 in k
16.567 * [backup-simplify]: Simplify 2 into 2
16.567 * [taylor]: Taking taylor expansion of PI in k
16.567 * [backup-simplify]: Simplify PI into PI
16.567 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.568 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.568 * [taylor]: Taking taylor expansion of (log n) in k
16.568 * [taylor]: Taking taylor expansion of n in k
16.568 * [backup-simplify]: Simplify n into n
16.568 * [backup-simplify]: Simplify (log n) into (log n)
16.568 * [backup-simplify]: Simplify (- 1) into -1
16.569 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.569 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.569 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
16.570 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
16.570 * [backup-simplify]: Simplify (* 1/4 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
16.571 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
16.572 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
16.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.573 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.574 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.574 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.574 * [backup-simplify]: Simplify (- 0) into 0
16.575 * [backup-simplify]: Simplify (+ 0 0) into 0
16.575 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 (/ 1 k)))) into 0
16.576 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.577 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
16.578 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.578 * [taylor]: Taking taylor expansion of 0 in k
16.578 * [backup-simplify]: Simplify 0 into 0
16.578 * [backup-simplify]: Simplify 0 into 0
16.578 * [backup-simplify]: Simplify 0 into 0
16.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.579 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.581 * [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
16.581 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.582 * [backup-simplify]: Simplify (- 0) into 0
16.582 * [backup-simplify]: Simplify (+ 0 0) into 0
16.583 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
16.584 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.584 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
16.586 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.586 * [taylor]: Taking taylor expansion of 0 in k
16.586 * [backup-simplify]: Simplify 0 into 0
16.586 * [backup-simplify]: Simplify 0 into 0
16.586 * [backup-simplify]: Simplify 0 into 0
16.586 * [backup-simplify]: Simplify 0 into 0
16.587 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.587 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.595 * [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
16.595 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.596 * [backup-simplify]: Simplify (- 0) into 0
16.596 * [backup-simplify]: Simplify (+ 0 0) into 0
16.597 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
16.598 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.599 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
16.600 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 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
16.600 * [taylor]: Taking taylor expansion of 0 in k
16.600 * [backup-simplify]: Simplify 0 into 0
16.600 * [backup-simplify]: Simplify 0 into 0
16.601 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
16.601 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (/ (- 1 (/ 1 (- k))) 2) 2)) into (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1)))
16.601 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in (n k) around 0
16.601 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in k
16.602 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
16.602 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
16.602 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in k
16.602 * [taylor]: Taking taylor expansion of 1/4 in k
16.602 * [backup-simplify]: Simplify 1/4 into 1/4
16.602 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.602 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.602 * [taylor]: Taking taylor expansion of k in k
16.602 * [backup-simplify]: Simplify 0 into 0
16.602 * [backup-simplify]: Simplify 1 into 1
16.602 * [backup-simplify]: Simplify (/ 1 1) into 1
16.602 * [taylor]: Taking taylor expansion of 1 in k
16.602 * [backup-simplify]: Simplify 1 into 1
16.602 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
16.602 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
16.602 * [taylor]: Taking taylor expansion of -2 in k
16.602 * [backup-simplify]: Simplify -2 into -2
16.602 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.602 * [taylor]: Taking taylor expansion of PI in k
16.602 * [backup-simplify]: Simplify PI into PI
16.602 * [taylor]: Taking taylor expansion of n in k
16.602 * [backup-simplify]: Simplify n into n
16.602 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.602 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
16.602 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
16.602 * [backup-simplify]: Simplify (+ 1 0) into 1
16.603 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
16.603 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
16.603 * [backup-simplify]: Simplify (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/4 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
16.603 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
16.603 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
16.603 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
16.603 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
16.603 * [taylor]: Taking taylor expansion of 1/4 in n
16.603 * [backup-simplify]: Simplify 1/4 into 1/4
16.603 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.603 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.604 * [taylor]: Taking taylor expansion of k in n
16.604 * [backup-simplify]: Simplify k into k
16.604 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.604 * [taylor]: Taking taylor expansion of 1 in n
16.604 * [backup-simplify]: Simplify 1 into 1
16.604 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.604 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.604 * [taylor]: Taking taylor expansion of -2 in n
16.604 * [backup-simplify]: Simplify -2 into -2
16.604 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.604 * [taylor]: Taking taylor expansion of PI in n
16.604 * [backup-simplify]: Simplify PI into PI
16.604 * [taylor]: Taking taylor expansion of n in n
16.604 * [backup-simplify]: Simplify 0 into 0
16.604 * [backup-simplify]: Simplify 1 into 1
16.604 * [backup-simplify]: Simplify (/ PI 1) into PI
16.605 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.606 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.606 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.606 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
16.607 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.608 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
16.610 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
16.610 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
16.610 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
16.610 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
16.610 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
16.610 * [taylor]: Taking taylor expansion of 1/4 in n
16.610 * [backup-simplify]: Simplify 1/4 into 1/4
16.610 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.610 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.610 * [taylor]: Taking taylor expansion of k in n
16.610 * [backup-simplify]: Simplify k into k
16.610 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.610 * [taylor]: Taking taylor expansion of 1 in n
16.610 * [backup-simplify]: Simplify 1 into 1
16.610 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.610 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.610 * [taylor]: Taking taylor expansion of -2 in n
16.610 * [backup-simplify]: Simplify -2 into -2
16.610 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.610 * [taylor]: Taking taylor expansion of PI in n
16.610 * [backup-simplify]: Simplify PI into PI
16.610 * [taylor]: Taking taylor expansion of n in n
16.610 * [backup-simplify]: Simplify 0 into 0
16.610 * [backup-simplify]: Simplify 1 into 1
16.611 * [backup-simplify]: Simplify (/ PI 1) into PI
16.611 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.612 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.612 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.612 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
16.614 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.615 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
16.616 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
16.616 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
16.616 * [taylor]: Taking taylor expansion of (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
16.616 * [taylor]: Taking taylor expansion of 1/4 in k
16.616 * [backup-simplify]: Simplify 1/4 into 1/4
16.616 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
16.616 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.616 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.616 * [taylor]: Taking taylor expansion of k in k
16.616 * [backup-simplify]: Simplify 0 into 0
16.616 * [backup-simplify]: Simplify 1 into 1
16.617 * [backup-simplify]: Simplify (/ 1 1) into 1
16.617 * [taylor]: Taking taylor expansion of 1 in k
16.617 * [backup-simplify]: Simplify 1 into 1
16.617 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
16.617 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
16.617 * [taylor]: Taking taylor expansion of (* -2 PI) in k
16.617 * [taylor]: Taking taylor expansion of -2 in k
16.617 * [backup-simplify]: Simplify -2 into -2
16.617 * [taylor]: Taking taylor expansion of PI in k
16.617 * [backup-simplify]: Simplify PI into PI
16.617 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.619 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.619 * [taylor]: Taking taylor expansion of (log n) in k
16.619 * [taylor]: Taking taylor expansion of n in k
16.619 * [backup-simplify]: Simplify n into n
16.619 * [backup-simplify]: Simplify (log n) into (log n)
16.619 * [backup-simplify]: Simplify (+ 1 0) into 1
16.619 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.620 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
16.621 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
16.622 * [backup-simplify]: Simplify (* 1/4 (- (log (* -2 PI)) (log n))) into (* 1/4 (- (log (* -2 PI)) (log n)))
16.623 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
16.625 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
16.625 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.626 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
16.628 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
16.628 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.629 * [backup-simplify]: Simplify (+ 0 0) into 0
16.629 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (+ (/ 1 k) 1))) into 0
16.630 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.632 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
16.634 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.634 * [taylor]: Taking taylor expansion of 0 in k
16.634 * [backup-simplify]: Simplify 0 into 0
16.634 * [backup-simplify]: Simplify 0 into 0
16.634 * [backup-simplify]: Simplify 0 into 0
16.635 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.635 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
16.637 * [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
16.637 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.638 * [backup-simplify]: Simplify (+ 0 0) into 0
16.638 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
16.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.640 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
16.642 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.642 * [taylor]: Taking taylor expansion of 0 in k
16.642 * [backup-simplify]: Simplify 0 into 0
16.642 * [backup-simplify]: Simplify 0 into 0
16.642 * [backup-simplify]: Simplify 0 into 0
16.642 * [backup-simplify]: Simplify 0 into 0
16.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.643 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.646 * [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
16.646 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.647 * [backup-simplify]: Simplify (+ 0 0) into 0
16.647 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
16.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.649 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
16.651 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 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
16.651 * [taylor]: Taking taylor expansion of 0 in k
16.651 * [backup-simplify]: Simplify 0 into 0
16.651 * [backup-simplify]: Simplify 0 into 0
16.652 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
16.652 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1)
16.652 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) into (pow (* 2 (* n PI)) (* 1/4 (- 1 k)))
16.652 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in (n k) around 0
16.652 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in k
16.652 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in k
16.652 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in k
16.652 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in k
16.652 * [taylor]: Taking taylor expansion of 1/4 in k
16.652 * [backup-simplify]: Simplify 1/4 into 1/4
16.652 * [taylor]: Taking taylor expansion of (- 1 k) in k
16.652 * [taylor]: Taking taylor expansion of 1 in k
16.652 * [backup-simplify]: Simplify 1 into 1
16.653 * [taylor]: Taking taylor expansion of k in k
16.653 * [backup-simplify]: Simplify 0 into 0
16.653 * [backup-simplify]: Simplify 1 into 1
16.653 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
16.653 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
16.653 * [taylor]: Taking taylor expansion of 2 in k
16.653 * [backup-simplify]: Simplify 2 into 2
16.653 * [taylor]: Taking taylor expansion of (* n PI) in k
16.653 * [taylor]: Taking taylor expansion of n in k
16.653 * [backup-simplify]: Simplify n into n
16.653 * [taylor]: Taking taylor expansion of PI in k
16.653 * [backup-simplify]: Simplify PI into PI
16.653 * [backup-simplify]: Simplify (* n PI) into (* n PI)
16.653 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
16.653 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
16.653 * [backup-simplify]: Simplify (- 0) into 0
16.653 * [backup-simplify]: Simplify (+ 1 0) into 1
16.654 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
16.654 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
16.654 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
16.654 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
16.654 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
16.654 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
16.654 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
16.654 * [taylor]: Taking taylor expansion of 1/4 in n
16.654 * [backup-simplify]: Simplify 1/4 into 1/4
16.654 * [taylor]: Taking taylor expansion of (- 1 k) in n
16.654 * [taylor]: Taking taylor expansion of 1 in n
16.654 * [backup-simplify]: Simplify 1 into 1
16.654 * [taylor]: Taking taylor expansion of k in n
16.654 * [backup-simplify]: Simplify k into k
16.654 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.654 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.654 * [taylor]: Taking taylor expansion of 2 in n
16.654 * [backup-simplify]: Simplify 2 into 2
16.654 * [taylor]: Taking taylor expansion of (* n PI) in n
16.654 * [taylor]: Taking taylor expansion of n in n
16.654 * [backup-simplify]: Simplify 0 into 0
16.654 * [backup-simplify]: Simplify 1 into 1
16.654 * [taylor]: Taking taylor expansion of PI in n
16.654 * [backup-simplify]: Simplify PI into PI
16.654 * [backup-simplify]: Simplify (* 0 PI) into 0
16.655 * [backup-simplify]: Simplify (* 2 0) into 0
16.656 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.657 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.657 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.657 * [backup-simplify]: Simplify (- k) into (- k)
16.657 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
16.657 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
16.658 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.659 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
16.659 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
16.660 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
16.660 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
16.660 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
16.660 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
16.660 * [taylor]: Taking taylor expansion of 1/4 in n
16.660 * [backup-simplify]: Simplify 1/4 into 1/4
16.660 * [taylor]: Taking taylor expansion of (- 1 k) in n
16.660 * [taylor]: Taking taylor expansion of 1 in n
16.660 * [backup-simplify]: Simplify 1 into 1
16.660 * [taylor]: Taking taylor expansion of k in n
16.660 * [backup-simplify]: Simplify k into k
16.660 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
16.660 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.660 * [taylor]: Taking taylor expansion of 2 in n
16.660 * [backup-simplify]: Simplify 2 into 2
16.660 * [taylor]: Taking taylor expansion of (* n PI) in n
16.660 * [taylor]: Taking taylor expansion of n in n
16.660 * [backup-simplify]: Simplify 0 into 0
16.660 * [backup-simplify]: Simplify 1 into 1
16.660 * [taylor]: Taking taylor expansion of PI in n
16.660 * [backup-simplify]: Simplify PI into PI
16.660 * [backup-simplify]: Simplify (* 0 PI) into 0
16.660 * [backup-simplify]: Simplify (* 2 0) into 0
16.661 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.662 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.663 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.663 * [backup-simplify]: Simplify (- k) into (- k)
16.663 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
16.663 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
16.664 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.664 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
16.665 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
16.665 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
16.665 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
16.665 * [taylor]: Taking taylor expansion of 1/4 in k
16.665 * [backup-simplify]: Simplify 1/4 into 1/4
16.665 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
16.665 * [taylor]: Taking taylor expansion of (- 1 k) in k
16.665 * [taylor]: Taking taylor expansion of 1 in k
16.665 * [backup-simplify]: Simplify 1 into 1
16.665 * [taylor]: Taking taylor expansion of k in k
16.665 * [backup-simplify]: Simplify 0 into 0
16.665 * [backup-simplify]: Simplify 1 into 1
16.665 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
16.665 * [taylor]: Taking taylor expansion of (log n) in k
16.665 * [taylor]: Taking taylor expansion of n in k
16.665 * [backup-simplify]: Simplify n into n
16.665 * [backup-simplify]: Simplify (log n) into (log n)
16.665 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
16.665 * [taylor]: Taking taylor expansion of (* 2 PI) in k
16.665 * [taylor]: Taking taylor expansion of 2 in k
16.665 * [backup-simplify]: Simplify 2 into 2
16.665 * [taylor]: Taking taylor expansion of PI in k
16.665 * [backup-simplify]: Simplify PI into PI
16.666 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.666 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.667 * [backup-simplify]: Simplify (- 0) into 0
16.667 * [backup-simplify]: Simplify (+ 1 0) into 1
16.668 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.668 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
16.669 * [backup-simplify]: Simplify (* 1/4 (+ (log n) (log (* 2 PI)))) into (* 1/4 (+ (log n) (log (* 2 PI))))
16.669 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
16.670 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
16.671 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.671 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
16.672 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.673 * [backup-simplify]: Simplify (- 0) into 0
16.673 * [backup-simplify]: Simplify (+ 0 0) into 0
16.673 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 k))) into 0
16.674 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.675 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
16.676 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.676 * [taylor]: Taking taylor expansion of 0 in k
16.676 * [backup-simplify]: Simplify 0 into 0
16.676 * [backup-simplify]: Simplify 0 into 0
16.676 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
16.677 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.678 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.678 * [backup-simplify]: Simplify (+ 0 0) into 0
16.678 * [backup-simplify]: Simplify (- 1) into -1
16.679 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.679 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
16.681 * [backup-simplify]: Simplify (+ (* 1/4 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
16.682 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
16.684 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
16.685 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.686 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.687 * [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
16.688 * [backup-simplify]: Simplify (- 0) into 0
16.688 * [backup-simplify]: Simplify (+ 0 0) into 0
16.688 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
16.689 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
16.690 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.696 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.696 * [taylor]: Taking taylor expansion of 0 in k
16.696 * [backup-simplify]: Simplify 0 into 0
16.696 * [backup-simplify]: Simplify 0 into 0
16.696 * [backup-simplify]: Simplify 0 into 0
16.697 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
16.698 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.700 * [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
16.700 * [backup-simplify]: Simplify (+ 0 0) into 0
16.700 * [backup-simplify]: Simplify (- 0) into 0
16.700 * [backup-simplify]: Simplify (+ 0 0) into 0
16.701 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.703 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
16.705 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
16.708 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
16.713 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
16.714 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (/ (- 1 (/ 1 k)) 2) 2)) into (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k))))
16.714 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in (n k) around 0
16.714 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in k
16.714 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
16.714 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
16.714 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in k
16.714 * [taylor]: Taking taylor expansion of 1/4 in k
16.714 * [backup-simplify]: Simplify 1/4 into 1/4
16.714 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.714 * [taylor]: Taking taylor expansion of 1 in k
16.714 * [backup-simplify]: Simplify 1 into 1
16.714 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.714 * [taylor]: Taking taylor expansion of k in k
16.714 * [backup-simplify]: Simplify 0 into 0
16.714 * [backup-simplify]: Simplify 1 into 1
16.714 * [backup-simplify]: Simplify (/ 1 1) into 1
16.714 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
16.714 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
16.714 * [taylor]: Taking taylor expansion of 2 in k
16.714 * [backup-simplify]: Simplify 2 into 2
16.714 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.715 * [taylor]: Taking taylor expansion of PI in k
16.715 * [backup-simplify]: Simplify PI into PI
16.715 * [taylor]: Taking taylor expansion of n in k
16.715 * [backup-simplify]: Simplify n into n
16.715 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.715 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
16.715 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
16.715 * [backup-simplify]: Simplify (- 1) into -1
16.715 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.715 * [backup-simplify]: Simplify (* 1/4 -1) into -1/4
16.716 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
16.716 * [backup-simplify]: Simplify (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
16.716 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
16.716 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
16.716 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
16.716 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
16.716 * [taylor]: Taking taylor expansion of 1/4 in n
16.716 * [backup-simplify]: Simplify 1/4 into 1/4
16.716 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.716 * [taylor]: Taking taylor expansion of 1 in n
16.716 * [backup-simplify]: Simplify 1 into 1
16.716 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.716 * [taylor]: Taking taylor expansion of k in n
16.716 * [backup-simplify]: Simplify k into k
16.716 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.716 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.716 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.716 * [taylor]: Taking taylor expansion of 2 in n
16.716 * [backup-simplify]: Simplify 2 into 2
16.716 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.716 * [taylor]: Taking taylor expansion of PI in n
16.716 * [backup-simplify]: Simplify PI into PI
16.716 * [taylor]: Taking taylor expansion of n in n
16.716 * [backup-simplify]: Simplify 0 into 0
16.716 * [backup-simplify]: Simplify 1 into 1
16.716 * [backup-simplify]: Simplify (/ PI 1) into PI
16.717 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.717 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.717 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.717 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.717 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
16.718 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.719 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
16.720 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
16.720 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
16.720 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
16.720 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
16.720 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
16.720 * [taylor]: Taking taylor expansion of 1/4 in n
16.720 * [backup-simplify]: Simplify 1/4 into 1/4
16.720 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
16.720 * [taylor]: Taking taylor expansion of 1 in n
16.720 * [backup-simplify]: Simplify 1 into 1
16.720 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.720 * [taylor]: Taking taylor expansion of k in n
16.720 * [backup-simplify]: Simplify k into k
16.720 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.720 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
16.720 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.720 * [taylor]: Taking taylor expansion of 2 in n
16.720 * [backup-simplify]: Simplify 2 into 2
16.720 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.720 * [taylor]: Taking taylor expansion of PI in n
16.720 * [backup-simplify]: Simplify PI into PI
16.720 * [taylor]: Taking taylor expansion of n in n
16.720 * [backup-simplify]: Simplify 0 into 0
16.720 * [backup-simplify]: Simplify 1 into 1
16.720 * [backup-simplify]: Simplify (/ PI 1) into PI
16.721 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.721 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.721 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
16.721 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
16.721 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
16.722 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.723 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
16.724 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
16.724 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
16.724 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
16.724 * [taylor]: Taking taylor expansion of 1/4 in k
16.724 * [backup-simplify]: Simplify 1/4 into 1/4
16.724 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
16.724 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
16.724 * [taylor]: Taking taylor expansion of 1 in k
16.724 * [backup-simplify]: Simplify 1 into 1
16.724 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.724 * [taylor]: Taking taylor expansion of k in k
16.724 * [backup-simplify]: Simplify 0 into 0
16.724 * [backup-simplify]: Simplify 1 into 1
16.724 * [backup-simplify]: Simplify (/ 1 1) into 1
16.724 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
16.724 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
16.724 * [taylor]: Taking taylor expansion of (* 2 PI) in k
16.724 * [taylor]: Taking taylor expansion of 2 in k
16.724 * [backup-simplify]: Simplify 2 into 2
16.724 * [taylor]: Taking taylor expansion of PI in k
16.724 * [backup-simplify]: Simplify PI into PI
16.724 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.725 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
16.725 * [taylor]: Taking taylor expansion of (log n) in k
16.725 * [taylor]: Taking taylor expansion of n in k
16.725 * [backup-simplify]: Simplify n into n
16.725 * [backup-simplify]: Simplify (log n) into (log n)
16.725 * [backup-simplify]: Simplify (- 1) into -1
16.726 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.726 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.726 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
16.727 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
16.728 * [backup-simplify]: Simplify (* 1/4 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
16.728 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
16.729 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
16.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.730 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.731 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
16.731 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.732 * [backup-simplify]: Simplify (- 0) into 0
16.732 * [backup-simplify]: Simplify (+ 0 0) into 0
16.733 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 (/ 1 k)))) into 0
16.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.736 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
16.737 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.737 * [taylor]: Taking taylor expansion of 0 in k
16.737 * [backup-simplify]: Simplify 0 into 0
16.737 * [backup-simplify]: Simplify 0 into 0
16.738 * [backup-simplify]: Simplify 0 into 0
16.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.740 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.743 * [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
16.743 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.744 * [backup-simplify]: Simplify (- 0) into 0
16.744 * [backup-simplify]: Simplify (+ 0 0) into 0
16.745 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
16.746 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.748 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
16.750 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.750 * [taylor]: Taking taylor expansion of 0 in k
16.750 * [backup-simplify]: Simplify 0 into 0
16.750 * [backup-simplify]: Simplify 0 into 0
16.750 * [backup-simplify]: Simplify 0 into 0
16.750 * [backup-simplify]: Simplify 0 into 0
16.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.753 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.758 * [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
16.759 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.759 * [backup-simplify]: Simplify (- 0) into 0
16.760 * [backup-simplify]: Simplify (+ 0 0) into 0
16.761 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
16.762 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
16.764 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
16.766 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 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
16.767 * [taylor]: Taking taylor expansion of 0 in k
16.767 * [backup-simplify]: Simplify 0 into 0
16.767 * [backup-simplify]: Simplify 0 into 0
16.768 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
16.768 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (/ (- 1 (/ 1 (- k))) 2) 2)) into (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1)))
16.768 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in (n k) around 0
16.769 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in k
16.769 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
16.769 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
16.769 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in k
16.769 * [taylor]: Taking taylor expansion of 1/4 in k
16.769 * [backup-simplify]: Simplify 1/4 into 1/4
16.769 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.769 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.769 * [taylor]: Taking taylor expansion of k in k
16.769 * [backup-simplify]: Simplify 0 into 0
16.769 * [backup-simplify]: Simplify 1 into 1
16.769 * [backup-simplify]: Simplify (/ 1 1) into 1
16.769 * [taylor]: Taking taylor expansion of 1 in k
16.769 * [backup-simplify]: Simplify 1 into 1
16.769 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
16.769 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
16.769 * [taylor]: Taking taylor expansion of -2 in k
16.769 * [backup-simplify]: Simplify -2 into -2
16.769 * [taylor]: Taking taylor expansion of (/ PI n) in k
16.769 * [taylor]: Taking taylor expansion of PI in k
16.769 * [backup-simplify]: Simplify PI into PI
16.769 * [taylor]: Taking taylor expansion of n in k
16.769 * [backup-simplify]: Simplify n into n
16.770 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
16.770 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
16.770 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
16.770 * [backup-simplify]: Simplify (+ 1 0) into 1
16.771 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
16.771 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
16.771 * [backup-simplify]: Simplify (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/4 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
16.771 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
16.771 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
16.771 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
16.771 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
16.771 * [taylor]: Taking taylor expansion of 1/4 in n
16.771 * [backup-simplify]: Simplify 1/4 into 1/4
16.771 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.771 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.771 * [taylor]: Taking taylor expansion of k in n
16.771 * [backup-simplify]: Simplify k into k
16.771 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.771 * [taylor]: Taking taylor expansion of 1 in n
16.771 * [backup-simplify]: Simplify 1 into 1
16.771 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.771 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.771 * [taylor]: Taking taylor expansion of -2 in n
16.771 * [backup-simplify]: Simplify -2 into -2
16.771 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.771 * [taylor]: Taking taylor expansion of PI in n
16.771 * [backup-simplify]: Simplify PI into PI
16.771 * [taylor]: Taking taylor expansion of n in n
16.771 * [backup-simplify]: Simplify 0 into 0
16.772 * [backup-simplify]: Simplify 1 into 1
16.772 * [backup-simplify]: Simplify (/ PI 1) into PI
16.772 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.774 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.774 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.774 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
16.775 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.776 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
16.777 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
16.777 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
16.777 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
16.777 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
16.777 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
16.777 * [taylor]: Taking taylor expansion of 1/4 in n
16.777 * [backup-simplify]: Simplify 1/4 into 1/4
16.778 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
16.778 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.778 * [taylor]: Taking taylor expansion of k in n
16.778 * [backup-simplify]: Simplify k into k
16.778 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.778 * [taylor]: Taking taylor expansion of 1 in n
16.778 * [backup-simplify]: Simplify 1 into 1
16.778 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
16.778 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.778 * [taylor]: Taking taylor expansion of -2 in n
16.778 * [backup-simplify]: Simplify -2 into -2
16.778 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.778 * [taylor]: Taking taylor expansion of PI in n
16.778 * [backup-simplify]: Simplify PI into PI
16.778 * [taylor]: Taking taylor expansion of n in n
16.778 * [backup-simplify]: Simplify 0 into 0
16.778 * [backup-simplify]: Simplify 1 into 1
16.778 * [backup-simplify]: Simplify (/ PI 1) into PI
16.779 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.780 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.780 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
16.780 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
16.781 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.782 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
16.783 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
16.784 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
16.784 * [taylor]: Taking taylor expansion of (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
16.784 * [taylor]: Taking taylor expansion of 1/4 in k
16.784 * [backup-simplify]: Simplify 1/4 into 1/4
16.784 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
16.784 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
16.784 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.784 * [taylor]: Taking taylor expansion of k in k
16.784 * [backup-simplify]: Simplify 0 into 0
16.784 * [backup-simplify]: Simplify 1 into 1
16.784 * [backup-simplify]: Simplify (/ 1 1) into 1
16.784 * [taylor]: Taking taylor expansion of 1 in k
16.784 * [backup-simplify]: Simplify 1 into 1
16.784 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
16.784 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
16.784 * [taylor]: Taking taylor expansion of (* -2 PI) in k
16.784 * [taylor]: Taking taylor expansion of -2 in k
16.784 * [backup-simplify]: Simplify -2 into -2
16.784 * [taylor]: Taking taylor expansion of PI in k
16.784 * [backup-simplify]: Simplify PI into PI
16.785 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.786 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
16.786 * [taylor]: Taking taylor expansion of (log n) in k
16.786 * [taylor]: Taking taylor expansion of n in k
16.786 * [backup-simplify]: Simplify n into n
16.786 * [backup-simplify]: Simplify (log n) into (log n)
16.786 * [backup-simplify]: Simplify (+ 1 0) into 1
16.786 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
16.787 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
16.788 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
16.789 * [backup-simplify]: Simplify (* 1/4 (- (log (* -2 PI)) (log n))) into (* 1/4 (- (log (* -2 PI)) (log n)))
16.791 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
16.792 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
16.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.793 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
16.795 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
16.795 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.796 * [backup-simplify]: Simplify (+ 0 0) into 0
16.796 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (+ (/ 1 k) 1))) into 0
16.798 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.799 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
16.801 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.801 * [taylor]: Taking taylor expansion of 0 in k
16.801 * [backup-simplify]: Simplify 0 into 0
16.801 * [backup-simplify]: Simplify 0 into 0
16.801 * [backup-simplify]: Simplify 0 into 0
16.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.803 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
16.805 * [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
16.805 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.805 * [backup-simplify]: Simplify (+ 0 0) into 0
16.806 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
16.806 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.811 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
16.813 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
16.813 * [taylor]: Taking taylor expansion of 0 in k
16.813 * [backup-simplify]: Simplify 0 into 0
16.813 * [backup-simplify]: Simplify 0 into 0
16.813 * [backup-simplify]: Simplify 0 into 0
16.813 * [backup-simplify]: Simplify 0 into 0
16.814 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.815 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.818 * [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
16.818 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.818 * [backup-simplify]: Simplify (+ 0 0) into 0
16.819 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
16.820 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
16.821 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
16.823 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 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
16.823 * [taylor]: Taking taylor expansion of 0 in k
16.823 * [backup-simplify]: Simplify 0 into 0
16.823 * [backup-simplify]: Simplify 0 into 0
16.824 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
16.824 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1)
16.824 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
16.824 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
16.824 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.824 * [taylor]: Taking taylor expansion of 2 in n
16.824 * [backup-simplify]: Simplify 2 into 2
16.824 * [taylor]: Taking taylor expansion of (* n PI) in n
16.824 * [taylor]: Taking taylor expansion of n in n
16.824 * [backup-simplify]: Simplify 0 into 0
16.824 * [backup-simplify]: Simplify 1 into 1
16.824 * [taylor]: Taking taylor expansion of PI in n
16.824 * [backup-simplify]: Simplify PI into PI
16.824 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.824 * [taylor]: Taking taylor expansion of 2 in n
16.824 * [backup-simplify]: Simplify 2 into 2
16.824 * [taylor]: Taking taylor expansion of (* n PI) in n
16.824 * [taylor]: Taking taylor expansion of n in n
16.825 * [backup-simplify]: Simplify 0 into 0
16.825 * [backup-simplify]: Simplify 1 into 1
16.825 * [taylor]: Taking taylor expansion of PI in n
16.825 * [backup-simplify]: Simplify PI into PI
16.825 * [backup-simplify]: Simplify (* 0 PI) into 0
16.825 * [backup-simplify]: Simplify (* 2 0) into 0
16.825 * [backup-simplify]: Simplify 0 into 0
16.826 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.827 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.827 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.828 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.828 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
16.828 * [backup-simplify]: Simplify 0 into 0
16.829 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.830 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.830 * [backup-simplify]: Simplify 0 into 0
16.831 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.832 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
16.832 * [backup-simplify]: Simplify 0 into 0
16.833 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.835 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
16.835 * [backup-simplify]: Simplify 0 into 0
16.837 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.838 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
16.838 * [backup-simplify]: Simplify 0 into 0
16.840 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
16.842 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
16.842 * [backup-simplify]: Simplify 0 into 0
16.843 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
16.843 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
16.843 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
16.843 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.843 * [taylor]: Taking taylor expansion of 2 in n
16.843 * [backup-simplify]: Simplify 2 into 2
16.843 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.843 * [taylor]: Taking taylor expansion of PI in n
16.843 * [backup-simplify]: Simplify PI into PI
16.843 * [taylor]: Taking taylor expansion of n in n
16.843 * [backup-simplify]: Simplify 0 into 0
16.843 * [backup-simplify]: Simplify 1 into 1
16.844 * [backup-simplify]: Simplify (/ PI 1) into PI
16.844 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.844 * [taylor]: Taking taylor expansion of 2 in n
16.844 * [backup-simplify]: Simplify 2 into 2
16.844 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.844 * [taylor]: Taking taylor expansion of PI in n
16.844 * [backup-simplify]: Simplify PI into PI
16.844 * [taylor]: Taking taylor expansion of n in n
16.844 * [backup-simplify]: Simplify 0 into 0
16.844 * [backup-simplify]: Simplify 1 into 1
16.844 * [backup-simplify]: Simplify (/ PI 1) into PI
16.845 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.845 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.846 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.847 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.847 * [backup-simplify]: Simplify 0 into 0
16.848 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.849 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.849 * [backup-simplify]: Simplify 0 into 0
16.850 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.851 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.851 * [backup-simplify]: Simplify 0 into 0
16.853 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.854 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.854 * [backup-simplify]: Simplify 0 into 0
16.855 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.857 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.857 * [backup-simplify]: Simplify 0 into 0
16.858 * [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
16.859 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.860 * [backup-simplify]: Simplify 0 into 0
16.860 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
16.861 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
16.861 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
16.861 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.861 * [taylor]: Taking taylor expansion of -2 in n
16.861 * [backup-simplify]: Simplify -2 into -2
16.861 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.861 * [taylor]: Taking taylor expansion of PI in n
16.861 * [backup-simplify]: Simplify PI into PI
16.861 * [taylor]: Taking taylor expansion of n in n
16.861 * [backup-simplify]: Simplify 0 into 0
16.861 * [backup-simplify]: Simplify 1 into 1
16.862 * [backup-simplify]: Simplify (/ PI 1) into PI
16.862 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.862 * [taylor]: Taking taylor expansion of -2 in n
16.862 * [backup-simplify]: Simplify -2 into -2
16.862 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.862 * [taylor]: Taking taylor expansion of PI in n
16.862 * [backup-simplify]: Simplify PI into PI
16.862 * [taylor]: Taking taylor expansion of n in n
16.862 * [backup-simplify]: Simplify 0 into 0
16.862 * [backup-simplify]: Simplify 1 into 1
16.862 * [backup-simplify]: Simplify (/ PI 1) into PI
16.863 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.864 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.865 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.866 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
16.866 * [backup-simplify]: Simplify 0 into 0
16.867 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.868 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
16.868 * [backup-simplify]: Simplify 0 into 0
16.869 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.870 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.870 * [backup-simplify]: Simplify 0 into 0
16.871 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.873 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.873 * [backup-simplify]: Simplify 0 into 0
16.874 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.876 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.876 * [backup-simplify]: Simplify 0 into 0
16.877 * [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
16.878 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.879 * [backup-simplify]: Simplify 0 into 0
16.879 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
16.879 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1)
16.880 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
16.880 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
16.880 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.880 * [taylor]: Taking taylor expansion of 2 in n
16.880 * [backup-simplify]: Simplify 2 into 2
16.880 * [taylor]: Taking taylor expansion of (* n PI) in n
16.880 * [taylor]: Taking taylor expansion of n in n
16.880 * [backup-simplify]: Simplify 0 into 0
16.880 * [backup-simplify]: Simplify 1 into 1
16.880 * [taylor]: Taking taylor expansion of PI in n
16.880 * [backup-simplify]: Simplify PI into PI
16.880 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
16.880 * [taylor]: Taking taylor expansion of 2 in n
16.880 * [backup-simplify]: Simplify 2 into 2
16.880 * [taylor]: Taking taylor expansion of (* n PI) in n
16.880 * [taylor]: Taking taylor expansion of n in n
16.880 * [backup-simplify]: Simplify 0 into 0
16.880 * [backup-simplify]: Simplify 1 into 1
16.880 * [taylor]: Taking taylor expansion of PI in n
16.880 * [backup-simplify]: Simplify PI into PI
16.881 * [backup-simplify]: Simplify (* 0 PI) into 0
16.881 * [backup-simplify]: Simplify (* 2 0) into 0
16.881 * [backup-simplify]: Simplify 0 into 0
16.882 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.883 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
16.884 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.884 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.885 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
16.885 * [backup-simplify]: Simplify 0 into 0
16.886 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.886 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.886 * [backup-simplify]: Simplify 0 into 0
16.887 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.888 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
16.888 * [backup-simplify]: Simplify 0 into 0
16.889 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.889 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
16.889 * [backup-simplify]: Simplify 0 into 0
16.890 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.891 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
16.891 * [backup-simplify]: Simplify 0 into 0
16.892 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
16.893 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
16.893 * [backup-simplify]: Simplify 0 into 0
16.894 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
16.894 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
16.894 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
16.894 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.894 * [taylor]: Taking taylor expansion of 2 in n
16.894 * [backup-simplify]: Simplify 2 into 2
16.894 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.894 * [taylor]: Taking taylor expansion of PI in n
16.894 * [backup-simplify]: Simplify PI into PI
16.894 * [taylor]: Taking taylor expansion of n in n
16.894 * [backup-simplify]: Simplify 0 into 0
16.894 * [backup-simplify]: Simplify 1 into 1
16.895 * [backup-simplify]: Simplify (/ PI 1) into PI
16.895 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
16.895 * [taylor]: Taking taylor expansion of 2 in n
16.895 * [backup-simplify]: Simplify 2 into 2
16.895 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.895 * [taylor]: Taking taylor expansion of PI in n
16.895 * [backup-simplify]: Simplify PI into PI
16.895 * [taylor]: Taking taylor expansion of n in n
16.895 * [backup-simplify]: Simplify 0 into 0
16.895 * [backup-simplify]: Simplify 1 into 1
16.895 * [backup-simplify]: Simplify (/ PI 1) into PI
16.895 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.896 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
16.896 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.897 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
16.897 * [backup-simplify]: Simplify 0 into 0
16.897 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.898 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
16.898 * [backup-simplify]: Simplify 0 into 0
16.898 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.899 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.899 * [backup-simplify]: Simplify 0 into 0
16.900 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.900 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.901 * [backup-simplify]: Simplify 0 into 0
16.901 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.902 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.902 * [backup-simplify]: Simplify 0 into 0
16.903 * [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
16.904 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.904 * [backup-simplify]: Simplify 0 into 0
16.904 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
16.904 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
16.904 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
16.904 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.904 * [taylor]: Taking taylor expansion of -2 in n
16.904 * [backup-simplify]: Simplify -2 into -2
16.904 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.904 * [taylor]: Taking taylor expansion of PI in n
16.904 * [backup-simplify]: Simplify PI into PI
16.904 * [taylor]: Taking taylor expansion of n in n
16.904 * [backup-simplify]: Simplify 0 into 0
16.904 * [backup-simplify]: Simplify 1 into 1
16.905 * [backup-simplify]: Simplify (/ PI 1) into PI
16.905 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
16.905 * [taylor]: Taking taylor expansion of -2 in n
16.905 * [backup-simplify]: Simplify -2 into -2
16.905 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.905 * [taylor]: Taking taylor expansion of PI in n
16.905 * [backup-simplify]: Simplify PI into PI
16.905 * [taylor]: Taking taylor expansion of n in n
16.905 * [backup-simplify]: Simplify 0 into 0
16.905 * [backup-simplify]: Simplify 1 into 1
16.905 * [backup-simplify]: Simplify (/ PI 1) into PI
16.906 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.906 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
16.906 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.907 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
16.907 * [backup-simplify]: Simplify 0 into 0
16.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.908 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
16.908 * [backup-simplify]: Simplify 0 into 0
16.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.909 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.909 * [backup-simplify]: Simplify 0 into 0
16.910 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.911 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.911 * [backup-simplify]: Simplify 0 into 0
16.911 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.912 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.912 * [backup-simplify]: Simplify 0 into 0
16.913 * [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
16.914 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.914 * [backup-simplify]: Simplify 0 into 0
16.914 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
16.914 * * * [progress]: simplifying candidates
16.914 * * * * [progress]: [ 1 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (log1p (expm1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
16.915 * * * * [progress]: [ 2 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (expm1 (log1p (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
16.915 * * * * [progress]: [ 3 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 4 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 5 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 6 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 7 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 8 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 9 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 10 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (pow (* n (* 2 PI)) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 11 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2)))) (cbrt (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 12 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (sqrt (/ (/ (- 1 k) 2) 2))) (sqrt (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 13 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 14 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2))) (/ (cbrt (/ (- 1 k) 2)) (sqrt 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 15 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1)) (/ (cbrt (/ (- 1 k) 2)) 2))) (sqrt k)))>
16.915 * * * * [progress]: [ 16 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (/ (- 1 k) 2)) (cbrt 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 17 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 18 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) 1)) (/ (sqrt (/ (- 1 k) 2)) 2))) (sqrt k)))>
16.915 * * * * [progress]: [ 19 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 20 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
16.915 * * * * [progress]: [ 21 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) 2))) (sqrt k)))>
16.915 * * * * [progress]: [ 22 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 23 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 24 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) 1)) (/ (/ (cbrt (- 1 k)) (sqrt 2)) 2))) (sqrt k)))>
16.916 * * * * [progress]: [ 25 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) 2) (cbrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 26 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (sqrt 2))) (/ (/ (cbrt (- 1 k)) 2) (sqrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 27 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1)) (/ (/ (cbrt (- 1 k)) 2) 2))) (sqrt k)))>
16.916 * * * * [progress]: [ 28 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 29 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 30 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) 2))) (sqrt k)))>
16.916 * * * * [progress]: [ 31 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 32 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 33 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 1)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 2))) (sqrt k)))>
16.916 * * * * [progress]: [ 34 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) 2) (cbrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 35 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2))) (/ (/ (sqrt (- 1 k)) 2) (sqrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 36 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) 1)) (/ (/ (sqrt (- 1 k)) 2) 2))) (sqrt k)))>
16.916 * * * * [progress]: [ 37 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 38 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 39 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2))) (sqrt k)))>
16.916 * * * * [progress]: [ 40 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 41 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 42 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2))) (sqrt k)))>
16.916 * * * * [progress]: [ 43 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2)))) (sqrt k)))>
16.916 * * * * [progress]: [ 44 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 45 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.917 * * * * [progress]: [ 46 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 47 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 48 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) 2))) (sqrt k)))>
16.917 * * * * [progress]: [ 49 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 50 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 51 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) 2))) (sqrt k)))>
16.917 * * * * [progress]: [ 52 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (cbrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 53 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (sqrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 54 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) 1)) (/ (/ (- (sqrt 1) (sqrt k)) 2) 2))) (sqrt k)))>
16.917 * * * * [progress]: [ 55 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 56 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 57 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 (sqrt k)) (cbrt 2)) 2))) (sqrt k)))>
16.917 * * * * [progress]: [ 58 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 59 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 60 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) 1)) (/ (/ (- 1 (sqrt k)) (sqrt 2)) 2))) (sqrt k)))>
16.917 * * * * [progress]: [ 61 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) 2) (cbrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 62 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (sqrt 2))) (/ (/ (- 1 (sqrt k)) 2) (sqrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 63 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) 1)) (/ (/ (- 1 (sqrt k)) 2) 2))) (sqrt k)))>
16.917 * * * * [progress]: [ 64 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
16.917 * * * * [progress]: [ 65 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 66 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2))) (sqrt k)))>
16.918 * * * * [progress]: [ 67 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 68 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 69 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2))) (sqrt k)))>
16.918 * * * * [progress]: [ 70 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 71 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 72 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.918 * * * * [progress]: [ 73 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 74 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 75 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.918 * * * * [progress]: [ 76 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (- 1 k) (* (cbrt 2) (cbrt 2)))) (/ (/ 1 2) (cbrt 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 77 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (- 1 k) (sqrt 2))) (/ (/ 1 2) (sqrt 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 78 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (- 1 k) 1)) (/ (/ 1 2) 2))) (sqrt k)))>
16.918 * * * * [progress]: [ 79 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.918 * * * * [progress]: [ 80 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 2))) (sqrt k)))>
16.918 * * * * [progress]: [ 81 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (pow n (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 82 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)) (sqrt k)))>
16.918 * * * * [progress]: [ 83 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
16.918 * * * * [progress]: [ 84 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (log (exp (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
16.918 * * * * [progress]: [ 85 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
16.918 * * * * [progress]: [ 86 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
16.918 * * * * [progress]: [ 87 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
16.918 * * * * [progress]: [ 88 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
16.918 * * * * [progress]: [ 89 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))) (sqrt k)))>
16.919 * * * * [progress]: [ 90 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
16.919 * * * * [progress]: [ 91 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (log1p (expm1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 92 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (expm1 (log1p (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 93 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 94 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 95 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 96 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 97 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 98 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 99 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 100 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ (pow (* n (* 2 PI)) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 101 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2)))) (cbrt (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 102 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (sqrt (/ (/ (- 1 k) 2) 2))) (sqrt (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.919 * * * * [progress]: [ 103 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 104 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2))) (/ (cbrt (/ (- 1 k) 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 105 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1)) (/ (cbrt (/ (- 1 k) 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 106 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (/ (- 1 k) 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 107 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 108 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) 1)) (/ (sqrt (/ (- 1 k) 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 109 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 110 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 111 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 112 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 113 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 114 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) 1)) (/ (/ (cbrt (- 1 k)) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 115 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.920 * * * * [progress]: [ 116 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (sqrt 2))) (/ (/ (cbrt (- 1 k)) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 117 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1)) (/ (/ (cbrt (- 1 k)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 118 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 119 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 120 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 121 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 122 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 123 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 1)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 124 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 125 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2))) (/ (/ (sqrt (- 1 k)) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 126 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) 1)) (/ (/ (sqrt (- 1 k)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 127 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 128 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 129 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.921 * * * * [progress]: [ 130 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 131 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 132 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 133 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 134 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 135 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 136 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 137 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 138 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 139 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 140 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.922 * * * * [progress]: [ 141 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 142 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 143 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 144 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) 1)) (/ (/ (- (sqrt 1) (sqrt k)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 145 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 146 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 147 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 (sqrt k)) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 148 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 149 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 150 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) 1)) (/ (/ (- 1 (sqrt k)) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 151 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.923 * * * * [progress]: [ 152 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (sqrt 2))) (/ (/ (- 1 (sqrt k)) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 153 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) 1)) (/ (/ (- 1 (sqrt k)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 154 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 155 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 156 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 157 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 158 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 159 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 160 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 161 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 162 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 163 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 164 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.924 * * * * [progress]: [ 165 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 166 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) (* (cbrt 2) (cbrt 2)))) (/ (/ 1 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 167 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) (sqrt 2))) (/ (/ 1 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 168 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) 1)) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 169 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 170 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 171 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow n (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 172 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 173 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 174 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (log (exp (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 175 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 176 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 177 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 178 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (* 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 179 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.925 * * * * [progress]: [ 180 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 181 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (log1p (expm1 (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 182 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (expm1 (log1p (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 183 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 184 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 185 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 186 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 187 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (exp (+ (log n) (log (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 188 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (exp (log (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 189 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (log (exp (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 190 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 191 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 192 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 193 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.926 * * * * [progress]: [ 194 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 195 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 1 (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 196 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (* n 2) PI) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 197 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 198 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 199 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 1 (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 200 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 201 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 202 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (log1p (expm1 (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 203 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (expm1 (log1p (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 204 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 205 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 206 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 207 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 208 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (exp (+ (log n) (log (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.927 * * * * [progress]: [ 209 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (exp (log (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 210 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (log (exp (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 211 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 212 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 213 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 214 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 215 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 216 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 1 (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 217 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 218 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 219 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 220 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 1 (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 221 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 222 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.928 * * * * [progress]: [ 223 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))) (sqrt k)))>
16.928 * * * * [progress]: [ 224 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (sqrt k)))>
16.929 * * * * [progress]: [ 225 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (sqrt k)))>
16.929 * * * * [progress]: [ 226 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.929 * * * * [progress]: [ 227 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.929 * * * * [progress]: [ 228 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.929 * * * * [progress]: [ 229 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.929 * * * * [progress]: [ 230 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.929 * * * * [progress]: [ 231 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.929 * * * * [progress]: [ 232 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.929 * * * * [progress]: [ 233 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.929 * * * * [progress]: [ 234 / 234 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
16.940 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))
  (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))
  (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))
  (* 1 (/ (/ (- 1 k) 2) 2))
  (* 1 (/ (/ (- 1 k) 2) 2))
  (* 1 (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ 1 2) 2))
  (pow (* n (* 2 PI)) (/ (/ k 2) 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (/ (- 1 k) 2) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 1) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 1) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (- 1 k) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (- 1 k) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (- 1 k) 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (/ (- 1 k) 2))
  (pow n (/ (/ (- 1 k) 2) 2))
  (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))
  (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (exp (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (expm1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))
  (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))
  (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))
  (* 1 (/ (/ (- 1 k) 2) 2))
  (* 1 (/ (/ (- 1 k) 2) 2))
  (* 1 (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ 1 2) 2))
  (pow (* n (* 2 PI)) (/ (/ k 2) 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (/ (- 1 k) 2) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 1) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (/ 1 1) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (- 1 k) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (- 1 k) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (- 1 k) 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (/ (- 1 k) 2))
  (pow n (/ (/ (- 1 k) 2) 2))
  (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))
  (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (exp (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
16.946 * * [simplify]: iteration 1: (261 enodes)
17.099 * * [simplify]: iteration 2: (1219 enodes)
17.671 * * [simplify]: Extracting #0: cost 66 inf + 0
17.672 * * [simplify]: Extracting #1: cost 490 inf + 0
17.684 * * [simplify]: Extracting #2: cost 939 inf + 4800
17.698 * * [simplify]: Extracting #3: cost 979 inf + 31275
17.737 * * [simplify]: Extracting #4: cost 635 inf + 138498
17.795 * * [simplify]: Extracting #5: cost 176 inf + 317038
17.875 * * [simplify]: Extracting #6: cost 34 inf + 392035
17.986 * * [simplify]: Extracting #7: cost 14 inf + 399074
18.051 * * [simplify]: Extracting #8: cost 1 inf + 403261
18.125 * * [simplify]: Extracting #9: cost 0 inf + 403929
18.199 * [simplify]: Simplified to:
  (expm1 (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (log1p (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (/ (- 1 k) 4)
  (/ (- 1 k) 4)
  (/ (- 1 k) 4)
  (exp (* 1/4 (log (* PI (* n 2)))))
  (pow (* PI (* n 2)) (/ k 4))
  (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 4)) (cbrt (/ (- 1 k) 4))))
  (pow (* PI (* n 2)) (sqrt (/ (- 1 k) 4)))
  (pow (* PI (* n 2)) (* (/ (cbrt (/ (- 1 k) 2)) (cbrt 2)) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (cbrt (/ (- 1 k) 2)) (/ (sqrt 2) (cbrt (/ (- 1 k) 2)))))
  (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* PI (* n 2)) (/ (/ (sqrt (/ (- 1 k) 2)) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* n 2)) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2)))
  (pow (* PI (* n 2)) (sqrt (/ (- 1 k) 2)))
  (pow (* PI (* n 2)) (* (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 2))
  (pow (* PI (* n 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* PI (* n 2)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* PI (* n 2)) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (* (* (sqrt 2) (cbrt 2)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (* (* (sqrt 2) (cbrt 2)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) 2))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* PI (* n 2)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* PI (* n 2)) (sqrt (- 1 k)))
  (pow (* PI (* n 2)) (/ 1 (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* PI (* n 2)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (* (sqrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (* (sqrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) 2))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* n 2)) (+ (sqrt k) 1))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (* (sqrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (* (sqrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) 2))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* n 2)) (+ (sqrt k) 1))
  (pow (* PI (* n 2)) (/ 1 (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* PI (* n 2)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (/ (- 1 k) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (- 1 k) (sqrt 2)))
  (pow (* PI (* n 2)) (- 1 k))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 4))
  (pow (* PI 2) (/ (- 1 k) 4))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (exp (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 4))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 4))))
  (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (pow (pow (* PI (* n 2)) (/ (- 1 k) 4)) 3)
  (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (pow (* PI (* n 2)) (/ (/ (- 1 k) 2) 4))
  (pow (* PI (* n 2)) (/ (/ (- 1 k) 2) 4))
  (real->posit16 (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (expm1 (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (log1p (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (/ (- 1 k) 4)
  (/ (- 1 k) 4)
  (/ (- 1 k) 4)
  (exp (* 1/4 (log (* PI (* n 2)))))
  (pow (* PI (* n 2)) (/ k 4))
  (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 4)) (cbrt (/ (- 1 k) 4))))
  (pow (* PI (* n 2)) (sqrt (/ (- 1 k) 4)))
  (pow (* PI (* n 2)) (* (/ (cbrt (/ (- 1 k) 2)) (cbrt 2)) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (cbrt (/ (- 1 k) 2)) (/ (sqrt 2) (cbrt (/ (- 1 k) 2)))))
  (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* PI (* n 2)) (/ (/ (sqrt (/ (- 1 k) 2)) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* n 2)) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2)))
  (pow (* PI (* n 2)) (sqrt (/ (- 1 k) 2)))
  (pow (* PI (* n 2)) (* (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 2))
  (pow (* PI (* n 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* PI (* n 2)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* PI (* n 2)) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (* (* (sqrt 2) (cbrt 2)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (* (* (sqrt 2) (cbrt 2)) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) 2))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* PI (* n 2)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* PI (* n 2)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* PI (* n 2)) (sqrt (- 1 k)))
  (pow (* PI (* n 2)) (/ 1 (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* PI (* n 2)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (* (sqrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (* (sqrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) 2))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* n 2)) (+ (sqrt k) 1))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (* (sqrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (* (sqrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) 2))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* PI (* n 2)) (+ (sqrt k) 1))
  (pow (* PI (* n 2)) (/ 1 (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* PI (* n 2)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2)))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ 1 (sqrt 2)))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (/ (- 1 k) (* (cbrt 2) (cbrt 2))))
  (pow (* PI (* n 2)) (/ (- 1 k) (sqrt 2)))
  (pow (* PI (* n 2)) (- 1 k))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 4))
  (pow (* PI 2) (/ (- 1 k) 4))
  (* (/ (- 1 k) 4) (log (* PI (* n 2))))
  (exp (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 4))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 4))))
  (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (pow (pow (* PI (* n 2)) (/ (- 1 k) 4)) 3)
  (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (pow (* PI (* n 2)) (/ (/ (- 1 k) 2) 4))
  (pow (* PI (* n 2)) (/ (/ (- 1 k) 2) 4))
  (real->posit16 (pow (* PI (* n 2)) (/ (- 1 k) 4)))
  (expm1 (* PI (* n 2)))
  (log1p (* PI (* n 2)))
  (* PI (* n 2))
  (* PI (* n 2))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* (* n (* n n)) (* (* PI PI) PI)) 8)
  (* (* (* PI (* n 2)) (* PI (* n 2))) (* PI (* n 2)))
  (* (cbrt (* PI (* n 2))) (cbrt (* PI (* n 2))))
  (cbrt (* PI (* n 2)))
  (* (* (* PI (* n 2)) (* PI (* n 2))) (* PI (* n 2)))
  (sqrt (* PI (* n 2)))
  (sqrt (* PI (* n 2)))
  (* n 2)
  (* (* 2 (cbrt n)) PI)
  (* 2 (* PI (sqrt n)))
  (* PI (* n 2))
  (real->posit16 (* PI (* n 2)))
  (expm1 (* PI (* n 2)))
  (log1p (* PI (* n 2)))
  (* PI (* n 2))
  (* PI (* n 2))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* (* n (* n n)) (* (* PI PI) PI)) 8)
  (* (* (* PI (* n 2)) (* PI (* n 2))) (* PI (* n 2)))
  (* (cbrt (* PI (* n 2))) (cbrt (* PI (* n 2))))
  (cbrt (* PI (* n 2)))
  (* (* (* PI (* n 2)) (* PI (* n 2))) (* PI (* n 2)))
  (sqrt (* PI (* n 2)))
  (sqrt (* PI (* n 2)))
  (* n 2)
  (* (* 2 (cbrt n)) PI)
  (* 2 (* PI (sqrt n)))
  (* PI (* n 2))
  (real->posit16 (* PI (* n 2)))
  (- (fma (* (* (* (log (* PI 2)) (exp (* 1/4 (log (* PI (* n 2)))))) (log n)) (* k k)) 1/16 (fma 1/32 (* (* k k) (+ (* (exp (* 1/4 (log (* PI (* n 2))))) (* (log n) (log n))) (* (log (* PI 2)) (* (log (* PI 2)) (exp (* 1/4 (log (* PI (* n 2))))))))) (exp (* 1/4 (log (* PI (* n 2))))))) (* (* k (+ (* (exp (* 1/4 (log (* PI (* n 2))))) (log n)) (* (log (* PI 2)) (exp (* 1/4 (log (* PI (* n 2)))))))) 1/4))
  (exp (* (* (- 1 k) 1/4) (log (* PI (* n 2)))))
  (exp (* (* 1/4 (- 1 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (- (fma (* (* (* (log (* PI 2)) (exp (* 1/4 (log (* PI (* n 2)))))) (log n)) (* k k)) 1/16 (fma 1/32 (* (* k k) (+ (* (exp (* 1/4 (log (* PI (* n 2))))) (* (log n) (log n))) (* (log (* PI 2)) (* (log (* PI 2)) (exp (* 1/4 (log (* PI (* n 2))))))))) (exp (* 1/4 (log (* PI (* n 2))))))) (* (* k (+ (* (exp (* 1/4 (log (* PI (* n 2))))) (log n)) (* (log (* PI 2)) (exp (* 1/4 (log (* PI (* n 2)))))))) 1/4))
  (exp (* (* (- 1 k) 1/4) (log (* PI (* n 2)))))
  (exp (* (* 1/4 (- 1 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
18.230 * * * [progress]: adding candidates to table
21.547 * [progress]: [Phase 3 of 3] Extracting.
21.547 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))> #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2)))))> #<alt (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))))> #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>)
21.548 * * * [regime-changes]: Trying 2 branch expressions: (n k)
21.548 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))> #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2)))))> #<alt (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))))> #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>)
21.601 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))) (/ 1 (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))> #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2)))))> #<alt (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))))> #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>)
21.643 * * * [regime]: Found split indices: #<option (#s(si 5 255))>
21.643 * [simplify]: Simplifying:
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
21.643 * * [simplify]: iteration 1: (13 enodes)
21.644 * * [simplify]: iteration 2: (17 enodes)
21.645 * * [simplify]: Extracting #0: cost 1 inf + 0
21.646 * * [simplify]: Extracting #1: cost 3 inf + 0
21.646 * * [simplify]: Extracting #2: cost 4 inf + 1
21.646 * * [simplify]: Extracting #3: cost 7 inf + 1
21.646 * * [simplify]: Extracting #4: cost 9 inf + 43
21.646 * * [simplify]: Extracting #5: cost 6 inf + 170
21.646 * * [simplify]: Extracting #6: cost 5 inf + 171
21.646 * * [simplify]: Extracting #7: cost 3 inf + 296
21.646 * * [simplify]: Extracting #8: cost 1 inf + 1126
21.646 * * [simplify]: Extracting #9: cost 0 inf + 1621
21.646 * [simplify]: Simplified to:
  (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
30.033 * [regime-testing]: Baseline error score: 0.3970616448389685
30.035 * [regime-testing]: Oracle error score: 0.036577896062179996
30.039 * [regime-testing]: End program error score: 0.3970616448389685