53.911 * [progress]: [Phase 1 of 3] Setting up.
0.001 * * * [progress]: [1/2] Preparing points
0.170 * * * [progress]: [2/2] Setting up program.
0.173 * [progress]: [Phase 2 of 3] Improving.
0.173 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.174 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.174 * * [simplify]: iteration 0: 13 enodes
0.177 * * [simplify]: iteration 1: 31 enodes
0.183 * * [simplify]: iteration 2: 62 enodes
0.215 * * [simplify]: iteration 3: 124 enodes
0.250 * * [simplify]: iteration 4: 327 enodes
0.534 * * [simplify]: iteration 5: 929 enodes
0.857 * * [simplify]: iteration complete: 2001 enodes
0.857 * * [simplify]: Extracting #0: cost 1 inf + 0
0.857 * * [simplify]: Extracting #1: cost 89 inf + 0
0.859 * * [simplify]: Extracting #2: cost 318 inf + 1
0.861 * * [simplify]: Extracting #3: cost 464 inf + 46
0.865 * * [simplify]: Extracting #4: cost 447 inf + 3658
0.875 * * [simplify]: Extracting #5: cost 334 inf + 22379
0.899 * * [simplify]: Extracting #6: cost 148 inf + 142462
0.950 * * [simplify]: Extracting #7: cost 5 inf + 279802
1.015 * * [simplify]: Extracting #8: cost 0 inf + 281759
1.092 * * [simplify]: Extracting #9: cost 0 inf + 281496
1.149 * * [simplify]: Extracting #10: cost 0 inf + 280983
1.228 * [simplify]: Simplified to:
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
1.236 * * [progress]: iteration 1 / 4
1.237 * * * [progress]: picking best candidate
1.248 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
1.248 * * * [progress]: localizing error
1.293 * * * [progress]: generating rewritten candidates
1.293 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
1.321 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
1.334 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
1.349 * * * [progress]: generating series expansions
1.349 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
1.350 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
1.350 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
1.350 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
1.350 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
1.350 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
1.350 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.350 * [taylor]: Taking taylor expansion of 1/2 in k
1.350 * [backup-simplify]: Simplify 1/2 into 1/2
1.350 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.350 * [taylor]: Taking taylor expansion of 1/2 in k
1.350 * [backup-simplify]: Simplify 1/2 into 1/2
1.350 * [taylor]: Taking taylor expansion of k in k
1.350 * [backup-simplify]: Simplify 0 into 0
1.350 * [backup-simplify]: Simplify 1 into 1
1.350 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.350 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.350 * [taylor]: Taking taylor expansion of 2 in k
1.350 * [backup-simplify]: Simplify 2 into 2
1.350 * [taylor]: Taking taylor expansion of (* n PI) in k
1.350 * [taylor]: Taking taylor expansion of n in k
1.350 * [backup-simplify]: Simplify n into n
1.350 * [taylor]: Taking taylor expansion of PI in k
1.350 * [backup-simplify]: Simplify PI into PI
1.350 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.350 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.351 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.351 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.352 * [backup-simplify]: Simplify (- 0) into 0
1.352 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.353 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.353 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.353 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.353 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.353 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.353 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.353 * [taylor]: Taking taylor expansion of 1/2 in n
1.353 * [backup-simplify]: Simplify 1/2 into 1/2
1.353 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.353 * [taylor]: Taking taylor expansion of 1/2 in n
1.353 * [backup-simplify]: Simplify 1/2 into 1/2
1.353 * [taylor]: Taking taylor expansion of k in n
1.353 * [backup-simplify]: Simplify k into k
1.353 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.353 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.353 * [taylor]: Taking taylor expansion of 2 in n
1.353 * [backup-simplify]: Simplify 2 into 2
1.353 * [taylor]: Taking taylor expansion of (* n PI) in n
1.353 * [taylor]: Taking taylor expansion of n in n
1.353 * [backup-simplify]: Simplify 0 into 0
1.353 * [backup-simplify]: Simplify 1 into 1
1.353 * [taylor]: Taking taylor expansion of PI in n
1.353 * [backup-simplify]: Simplify PI into PI
1.354 * [backup-simplify]: Simplify (* 0 PI) into 0
1.354 * [backup-simplify]: Simplify (* 2 0) into 0
1.361 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.362 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.364 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.364 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.364 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.364 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.366 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.367 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.368 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
1.368 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.368 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.368 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.368 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.368 * [taylor]: Taking taylor expansion of 1/2 in n
1.368 * [backup-simplify]: Simplify 1/2 into 1/2
1.368 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.369 * [taylor]: Taking taylor expansion of 1/2 in n
1.369 * [backup-simplify]: Simplify 1/2 into 1/2
1.369 * [taylor]: Taking taylor expansion of k in n
1.369 * [backup-simplify]: Simplify k into k
1.369 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.369 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.369 * [taylor]: Taking taylor expansion of 2 in n
1.369 * [backup-simplify]: Simplify 2 into 2
1.369 * [taylor]: Taking taylor expansion of (* n PI) in n
1.369 * [taylor]: Taking taylor expansion of n in n
1.369 * [backup-simplify]: Simplify 0 into 0
1.369 * [backup-simplify]: Simplify 1 into 1
1.369 * [taylor]: Taking taylor expansion of PI in n
1.369 * [backup-simplify]: Simplify PI into PI
1.369 * [backup-simplify]: Simplify (* 0 PI) into 0
1.370 * [backup-simplify]: Simplify (* 2 0) into 0
1.371 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.373 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.374 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.374 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.374 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.374 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.376 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.377 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.378 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
1.379 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
1.379 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
1.379 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.379 * [taylor]: Taking taylor expansion of 1/2 in k
1.379 * [backup-simplify]: Simplify 1/2 into 1/2
1.379 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.379 * [taylor]: Taking taylor expansion of 1/2 in k
1.379 * [backup-simplify]: Simplify 1/2 into 1/2
1.379 * [taylor]: Taking taylor expansion of k in k
1.379 * [backup-simplify]: Simplify 0 into 0
1.379 * [backup-simplify]: Simplify 1 into 1
1.379 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.379 * [taylor]: Taking taylor expansion of (log n) in k
1.379 * [taylor]: Taking taylor expansion of n in k
1.379 * [backup-simplify]: Simplify n into n
1.379 * [backup-simplify]: Simplify (log n) into (log n)
1.379 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.379 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.379 * [taylor]: Taking taylor expansion of 2 in k
1.379 * [backup-simplify]: Simplify 2 into 2
1.379 * [taylor]: Taking taylor expansion of PI in k
1.379 * [backup-simplify]: Simplify PI into PI
1.380 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.381 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.381 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.382 * [backup-simplify]: Simplify (- 0) into 0
1.382 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.384 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.385 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.387 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.388 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.389 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.390 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.393 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.393 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
1.394 * [backup-simplify]: Simplify (- 0) into 0
1.394 * [backup-simplify]: Simplify (+ 0 0) into 0
1.395 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.397 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.399 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.399 * [taylor]: Taking taylor expansion of 0 in k
1.399 * [backup-simplify]: Simplify 0 into 0
1.399 * [backup-simplify]: Simplify 0 into 0
1.400 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.400 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.402 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.403 * [backup-simplify]: Simplify (+ 0 0) into 0
1.403 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
1.404 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.404 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.406 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
1.408 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.410 * [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)))))))
1.411 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.412 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.414 * [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
1.415 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
1.415 * [backup-simplify]: Simplify (- 0) into 0
1.415 * [backup-simplify]: Simplify (+ 0 0) into 0
1.416 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.417 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.419 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.419 * [taylor]: Taking taylor expansion of 0 in k
1.419 * [backup-simplify]: Simplify 0 into 0
1.419 * [backup-simplify]: Simplify 0 into 0
1.419 * [backup-simplify]: Simplify 0 into 0
1.420 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.420 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.422 * [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
1.423 * [backup-simplify]: Simplify (+ 0 0) into 0
1.423 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
1.423 * [backup-simplify]: Simplify (- 0) into 0
1.424 * [backup-simplify]: Simplify (+ 0 0) into 0
1.425 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.427 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
1.430 * [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)))))
1.437 * [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)))))
1.437 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
1.437 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
1.437 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
1.437 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
1.437 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
1.437 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
1.437 * [taylor]: Taking taylor expansion of 1/2 in k
1.437 * [backup-simplify]: Simplify 1/2 into 1/2
1.437 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.437 * [taylor]: Taking taylor expansion of 1/2 in k
1.437 * [backup-simplify]: Simplify 1/2 into 1/2
1.437 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.437 * [taylor]: Taking taylor expansion of k in k
1.437 * [backup-simplify]: Simplify 0 into 0
1.437 * [backup-simplify]: Simplify 1 into 1
1.438 * [backup-simplify]: Simplify (/ 1 1) into 1
1.438 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
1.438 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
1.438 * [taylor]: Taking taylor expansion of 2 in k
1.438 * [backup-simplify]: Simplify 2 into 2
1.438 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.438 * [taylor]: Taking taylor expansion of PI in k
1.438 * [backup-simplify]: Simplify PI into PI
1.438 * [taylor]: Taking taylor expansion of n in k
1.438 * [backup-simplify]: Simplify n into n
1.438 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.438 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
1.438 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
1.438 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.438 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.439 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.439 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
1.439 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
1.439 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
1.439 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.439 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.439 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
1.439 * [taylor]: Taking taylor expansion of 1/2 in n
1.439 * [backup-simplify]: Simplify 1/2 into 1/2
1.439 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.439 * [taylor]: Taking taylor expansion of 1/2 in n
1.439 * [backup-simplify]: Simplify 1/2 into 1/2
1.439 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.439 * [taylor]: Taking taylor expansion of k in n
1.439 * [backup-simplify]: Simplify k into k
1.439 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.439 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.439 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.439 * [taylor]: Taking taylor expansion of 2 in n
1.439 * [backup-simplify]: Simplify 2 into 2
1.439 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.439 * [taylor]: Taking taylor expansion of PI in n
1.439 * [backup-simplify]: Simplify PI into PI
1.439 * [taylor]: Taking taylor expansion of n in n
1.439 * [backup-simplify]: Simplify 0 into 0
1.439 * [backup-simplify]: Simplify 1 into 1
1.440 * [backup-simplify]: Simplify (/ PI 1) into PI
1.440 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.441 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.441 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.441 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
1.441 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
1.442 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.442 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
1.443 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.443 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
1.443 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.443 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.443 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
1.443 * [taylor]: Taking taylor expansion of 1/2 in n
1.443 * [backup-simplify]: Simplify 1/2 into 1/2
1.443 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.443 * [taylor]: Taking taylor expansion of 1/2 in n
1.443 * [backup-simplify]: Simplify 1/2 into 1/2
1.443 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.443 * [taylor]: Taking taylor expansion of k in n
1.443 * [backup-simplify]: Simplify k into k
1.444 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.444 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.444 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.444 * [taylor]: Taking taylor expansion of 2 in n
1.444 * [backup-simplify]: Simplify 2 into 2
1.444 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.444 * [taylor]: Taking taylor expansion of PI in n
1.444 * [backup-simplify]: Simplify PI into PI
1.444 * [taylor]: Taking taylor expansion of n in n
1.444 * [backup-simplify]: Simplify 0 into 0
1.444 * [backup-simplify]: Simplify 1 into 1
1.444 * [backup-simplify]: Simplify (/ PI 1) into PI
1.444 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.445 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.445 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.445 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
1.445 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
1.446 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.447 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
1.448 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.448 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
1.448 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
1.448 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
1.448 * [taylor]: Taking taylor expansion of 1/2 in k
1.448 * [backup-simplify]: Simplify 1/2 into 1/2
1.448 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.448 * [taylor]: Taking taylor expansion of 1/2 in k
1.448 * [backup-simplify]: Simplify 1/2 into 1/2
1.448 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.448 * [taylor]: Taking taylor expansion of k in k
1.448 * [backup-simplify]: Simplify 0 into 0
1.448 * [backup-simplify]: Simplify 1 into 1
1.449 * [backup-simplify]: Simplify (/ 1 1) into 1
1.449 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
1.449 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.449 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.449 * [taylor]: Taking taylor expansion of 2 in k
1.449 * [backup-simplify]: Simplify 2 into 2
1.449 * [taylor]: Taking taylor expansion of PI in k
1.449 * [backup-simplify]: Simplify PI into PI
1.450 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.451 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.451 * [taylor]: Taking taylor expansion of (log n) in k
1.451 * [taylor]: Taking taylor expansion of n in k
1.451 * [backup-simplify]: Simplify n into n
1.451 * [backup-simplify]: Simplify (log n) into (log n)
1.451 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.452 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.452 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.452 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.453 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
1.455 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
1.456 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.457 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.458 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.459 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.461 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.461 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.462 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
1.462 * [backup-simplify]: Simplify (- 0) into 0
1.462 * [backup-simplify]: Simplify (+ 0 0) into 0
1.464 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.465 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
1.468 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
1.468 * [taylor]: Taking taylor expansion of 0 in k
1.468 * [backup-simplify]: Simplify 0 into 0
1.468 * [backup-simplify]: Simplify 0 into 0
1.468 * [backup-simplify]: Simplify 0 into 0
1.469 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.470 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.474 * [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
1.474 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.475 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
1.476 * [backup-simplify]: Simplify (- 0) into 0
1.476 * [backup-simplify]: Simplify (+ 0 0) into 0
1.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.479 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
1.482 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.482 * [taylor]: Taking taylor expansion of 0 in k
1.482 * [backup-simplify]: Simplify 0 into 0
1.482 * [backup-simplify]: Simplify 0 into 0
1.482 * [backup-simplify]: Simplify 0 into 0
1.482 * [backup-simplify]: Simplify 0 into 0
1.487 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.488 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.494 * [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
1.494 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.496 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
1.496 * [backup-simplify]: Simplify (- 0) into 0
1.496 * [backup-simplify]: Simplify (+ 0 0) into 0
1.498 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.500 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
1.503 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.503 * [taylor]: Taking taylor expansion of 0 in k
1.503 * [backup-simplify]: Simplify 0 into 0
1.503 * [backup-simplify]: Simplify 0 into 0
1.504 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
1.505 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
1.505 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
1.505 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
1.505 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
1.505 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
1.505 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
1.505 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.505 * [taylor]: Taking taylor expansion of 1/2 in k
1.505 * [backup-simplify]: Simplify 1/2 into 1/2
1.505 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.505 * [taylor]: Taking taylor expansion of k in k
1.505 * [backup-simplify]: Simplify 0 into 0
1.505 * [backup-simplify]: Simplify 1 into 1
1.505 * [backup-simplify]: Simplify (/ 1 1) into 1
1.505 * [taylor]: Taking taylor expansion of 1/2 in k
1.505 * [backup-simplify]: Simplify 1/2 into 1/2
1.505 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
1.505 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
1.505 * [taylor]: Taking taylor expansion of -2 in k
1.505 * [backup-simplify]: Simplify -2 into -2
1.506 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.506 * [taylor]: Taking taylor expansion of PI in k
1.506 * [backup-simplify]: Simplify PI into PI
1.506 * [taylor]: Taking taylor expansion of n in k
1.506 * [backup-simplify]: Simplify n into n
1.506 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.506 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
1.506 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
1.506 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.507 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.507 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
1.507 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
1.507 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
1.507 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
1.507 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
1.507 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
1.507 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.507 * [taylor]: Taking taylor expansion of 1/2 in n
1.507 * [backup-simplify]: Simplify 1/2 into 1/2
1.507 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.507 * [taylor]: Taking taylor expansion of k in n
1.507 * [backup-simplify]: Simplify k into k
1.507 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.507 * [taylor]: Taking taylor expansion of 1/2 in n
1.508 * [backup-simplify]: Simplify 1/2 into 1/2
1.508 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.508 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.508 * [taylor]: Taking taylor expansion of -2 in n
1.508 * [backup-simplify]: Simplify -2 into -2
1.508 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.508 * [taylor]: Taking taylor expansion of PI in n
1.508 * [backup-simplify]: Simplify PI into PI
1.508 * [taylor]: Taking taylor expansion of n in n
1.508 * [backup-simplify]: Simplify 0 into 0
1.508 * [backup-simplify]: Simplify 1 into 1
1.508 * [backup-simplify]: Simplify (/ PI 1) into PI
1.509 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.510 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.510 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.510 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
1.512 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.513 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
1.515 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.515 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
1.515 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
1.515 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
1.515 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
1.515 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.515 * [taylor]: Taking taylor expansion of 1/2 in n
1.515 * [backup-simplify]: Simplify 1/2 into 1/2
1.515 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.515 * [taylor]: Taking taylor expansion of k in n
1.515 * [backup-simplify]: Simplify k into k
1.515 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.515 * [taylor]: Taking taylor expansion of 1/2 in n
1.515 * [backup-simplify]: Simplify 1/2 into 1/2
1.515 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.515 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.515 * [taylor]: Taking taylor expansion of -2 in n
1.515 * [backup-simplify]: Simplify -2 into -2
1.515 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.515 * [taylor]: Taking taylor expansion of PI in n
1.515 * [backup-simplify]: Simplify PI into PI
1.515 * [taylor]: Taking taylor expansion of n in n
1.515 * [backup-simplify]: Simplify 0 into 0
1.515 * [backup-simplify]: Simplify 1 into 1
1.516 * [backup-simplify]: Simplify (/ PI 1) into PI
1.518 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.519 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.519 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.520 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
1.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.523 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
1.524 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.524 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
1.524 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
1.524 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
1.524 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.524 * [taylor]: Taking taylor expansion of 1/2 in k
1.524 * [backup-simplify]: Simplify 1/2 into 1/2
1.524 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.524 * [taylor]: Taking taylor expansion of k in k
1.524 * [backup-simplify]: Simplify 0 into 0
1.524 * [backup-simplify]: Simplify 1 into 1
1.525 * [backup-simplify]: Simplify (/ 1 1) into 1
1.525 * [taylor]: Taking taylor expansion of 1/2 in k
1.525 * [backup-simplify]: Simplify 1/2 into 1/2
1.525 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
1.525 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
1.525 * [taylor]: Taking taylor expansion of (* -2 PI) in k
1.525 * [taylor]: Taking taylor expansion of -2 in k
1.525 * [backup-simplify]: Simplify -2 into -2
1.525 * [taylor]: Taking taylor expansion of PI in k
1.525 * [backup-simplify]: Simplify PI into PI
1.526 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.527 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.527 * [taylor]: Taking taylor expansion of (log n) in k
1.527 * [taylor]: Taking taylor expansion of n in k
1.527 * [backup-simplify]: Simplify n into n
1.527 * [backup-simplify]: Simplify (log n) into (log n)
1.527 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.528 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.528 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.529 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
1.530 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
1.532 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.533 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.534 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.535 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.537 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
1.537 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.537 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
1.538 * [backup-simplify]: Simplify (+ 0 0) into 0
1.539 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.540 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
1.542 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
1.542 * [taylor]: Taking taylor expansion of 0 in k
1.542 * [backup-simplify]: Simplify 0 into 0
1.542 * [backup-simplify]: Simplify 0 into 0
1.542 * [backup-simplify]: Simplify 0 into 0
1.543 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.545 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.548 * [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
1.548 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.549 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
1.550 * [backup-simplify]: Simplify (+ 0 0) into 0
1.551 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.553 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
1.556 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.556 * [taylor]: Taking taylor expansion of 0 in k
1.556 * [backup-simplify]: Simplify 0 into 0
1.556 * [backup-simplify]: Simplify 0 into 0
1.556 * [backup-simplify]: Simplify 0 into 0
1.556 * [backup-simplify]: Simplify 0 into 0
1.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.558 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.564 * [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
1.565 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.566 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
1.566 * [backup-simplify]: Simplify (+ 0 0) into 0
1.568 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.570 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
1.572 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.572 * [taylor]: Taking taylor expansion of 0 in k
1.572 * [backup-simplify]: Simplify 0 into 0
1.572 * [backup-simplify]: Simplify 0 into 0
1.574 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
1.574 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
1.574 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
1.574 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
1.574 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.574 * [taylor]: Taking taylor expansion of 2 in n
1.574 * [backup-simplify]: Simplify 2 into 2
1.574 * [taylor]: Taking taylor expansion of (* n PI) in n
1.574 * [taylor]: Taking taylor expansion of n in n
1.574 * [backup-simplify]: Simplify 0 into 0
1.574 * [backup-simplify]: Simplify 1 into 1
1.574 * [taylor]: Taking taylor expansion of PI in n
1.574 * [backup-simplify]: Simplify PI into PI
1.574 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.574 * [taylor]: Taking taylor expansion of 2 in n
1.574 * [backup-simplify]: Simplify 2 into 2
1.574 * [taylor]: Taking taylor expansion of (* n PI) in n
1.574 * [taylor]: Taking taylor expansion of n in n
1.574 * [backup-simplify]: Simplify 0 into 0
1.574 * [backup-simplify]: Simplify 1 into 1
1.574 * [taylor]: Taking taylor expansion of PI in n
1.574 * [backup-simplify]: Simplify PI into PI
1.575 * [backup-simplify]: Simplify (* 0 PI) into 0
1.576 * [backup-simplify]: Simplify (* 2 0) into 0
1.576 * [backup-simplify]: Simplify 0 into 0
1.577 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.579 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.579 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.581 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.582 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.582 * [backup-simplify]: Simplify 0 into 0
1.583 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.584 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.584 * [backup-simplify]: Simplify 0 into 0
1.586 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.587 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
1.587 * [backup-simplify]: Simplify 0 into 0
1.589 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.591 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
1.591 * [backup-simplify]: Simplify 0 into 0
1.593 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.594 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
1.595 * [backup-simplify]: Simplify 0 into 0
1.597 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
1.599 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
1.599 * [backup-simplify]: Simplify 0 into 0
1.599 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
1.599 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
1.599 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
1.599 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.600 * [taylor]: Taking taylor expansion of 2 in n
1.600 * [backup-simplify]: Simplify 2 into 2
1.600 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.600 * [taylor]: Taking taylor expansion of PI in n
1.600 * [backup-simplify]: Simplify PI into PI
1.600 * [taylor]: Taking taylor expansion of n in n
1.600 * [backup-simplify]: Simplify 0 into 0
1.600 * [backup-simplify]: Simplify 1 into 1
1.600 * [backup-simplify]: Simplify (/ PI 1) into PI
1.600 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.600 * [taylor]: Taking taylor expansion of 2 in n
1.600 * [backup-simplify]: Simplify 2 into 2
1.600 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.600 * [taylor]: Taking taylor expansion of PI in n
1.600 * [backup-simplify]: Simplify PI into PI
1.600 * [taylor]: Taking taylor expansion of n in n
1.600 * [backup-simplify]: Simplify 0 into 0
1.600 * [backup-simplify]: Simplify 1 into 1
1.601 * [backup-simplify]: Simplify (/ PI 1) into PI
1.602 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.602 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.603 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.604 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.604 * [backup-simplify]: Simplify 0 into 0
1.605 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.606 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.606 * [backup-simplify]: Simplify 0 into 0
1.607 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.609 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.609 * [backup-simplify]: Simplify 0 into 0
1.610 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.611 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.611 * [backup-simplify]: Simplify 0 into 0
1.613 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.614 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.614 * [backup-simplify]: Simplify 0 into 0
1.616 * [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
1.617 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.617 * [backup-simplify]: Simplify 0 into 0
1.618 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
1.618 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
1.618 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
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 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.619 * [taylor]: Taking taylor expansion of -2 in n
1.619 * [backup-simplify]: Simplify -2 into -2
1.619 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.619 * [taylor]: Taking taylor expansion of PI in n
1.619 * [backup-simplify]: Simplify PI into PI
1.619 * [taylor]: Taking taylor expansion of n in n
1.619 * [backup-simplify]: Simplify 0 into 0
1.619 * [backup-simplify]: Simplify 1 into 1
1.620 * [backup-simplify]: Simplify (/ PI 1) into PI
1.620 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.621 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.622 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.622 * [backup-simplify]: Simplify 0 into 0
1.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.625 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.625 * [backup-simplify]: Simplify 0 into 0
1.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.627 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.627 * [backup-simplify]: Simplify 0 into 0
1.629 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.630 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.630 * [backup-simplify]: Simplify 0 into 0
1.631 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.633 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.633 * [backup-simplify]: Simplify 0 into 0
1.634 * [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
1.636 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.636 * [backup-simplify]: Simplify 0 into 0
1.637 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
1.637 * * * * [progress]: [ 3 / 3 ] generating series at (2)
1.637 * [backup-simplify]: Simplify (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
1.637 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
1.637 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
1.637 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.637 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.638 * [taylor]: Taking taylor expansion of k in k
1.638 * [backup-simplify]: Simplify 0 into 0
1.638 * [backup-simplify]: Simplify 1 into 1
1.638 * [backup-simplify]: Simplify (/ 1 1) into 1
1.638 * [backup-simplify]: Simplify (sqrt 0) into 0
1.640 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.640 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
1.640 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
1.640 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
1.640 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.640 * [taylor]: Taking taylor expansion of 1/2 in k
1.640 * [backup-simplify]: Simplify 1/2 into 1/2
1.640 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.640 * [taylor]: Taking taylor expansion of 1/2 in k
1.640 * [backup-simplify]: Simplify 1/2 into 1/2
1.640 * [taylor]: Taking taylor expansion of k in k
1.640 * [backup-simplify]: Simplify 0 into 0
1.640 * [backup-simplify]: Simplify 1 into 1
1.640 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.640 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.640 * [taylor]: Taking taylor expansion of 2 in k
1.640 * [backup-simplify]: Simplify 2 into 2
1.640 * [taylor]: Taking taylor expansion of (* n PI) in k
1.640 * [taylor]: Taking taylor expansion of n in k
1.640 * [backup-simplify]: Simplify n into n
1.641 * [taylor]: Taking taylor expansion of PI in k
1.641 * [backup-simplify]: Simplify PI into PI
1.641 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.641 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.641 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.641 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.642 * [backup-simplify]: Simplify (- 0) into 0
1.645 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.646 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.646 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.646 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
1.646 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
1.646 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.646 * [taylor]: Taking taylor expansion of k in n
1.646 * [backup-simplify]: Simplify k into k
1.646 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.646 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
1.646 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.646 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
1.646 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.646 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.646 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.646 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.646 * [taylor]: Taking taylor expansion of 1/2 in n
1.647 * [backup-simplify]: Simplify 1/2 into 1/2
1.647 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.647 * [taylor]: Taking taylor expansion of 1/2 in n
1.647 * [backup-simplify]: Simplify 1/2 into 1/2
1.647 * [taylor]: Taking taylor expansion of k in n
1.647 * [backup-simplify]: Simplify k into k
1.647 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.647 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.647 * [taylor]: Taking taylor expansion of 2 in n
1.647 * [backup-simplify]: Simplify 2 into 2
1.647 * [taylor]: Taking taylor expansion of (* n PI) in n
1.647 * [taylor]: Taking taylor expansion of n in n
1.647 * [backup-simplify]: Simplify 0 into 0
1.647 * [backup-simplify]: Simplify 1 into 1
1.647 * [taylor]: Taking taylor expansion of PI in n
1.647 * [backup-simplify]: Simplify PI into PI
1.648 * [backup-simplify]: Simplify (* 0 PI) into 0
1.648 * [backup-simplify]: Simplify (* 2 0) into 0
1.650 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.651 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.653 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.653 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.653 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.653 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.654 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.656 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.657 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
1.657 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
1.657 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
1.657 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.657 * [taylor]: Taking taylor expansion of k in n
1.657 * [backup-simplify]: Simplify k into k
1.657 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.657 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
1.657 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.657 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
1.657 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.657 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.658 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.658 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.658 * [taylor]: Taking taylor expansion of 1/2 in n
1.658 * [backup-simplify]: Simplify 1/2 into 1/2
1.658 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.658 * [taylor]: Taking taylor expansion of 1/2 in n
1.658 * [backup-simplify]: Simplify 1/2 into 1/2
1.658 * [taylor]: Taking taylor expansion of k in n
1.658 * [backup-simplify]: Simplify k into k
1.658 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.658 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.658 * [taylor]: Taking taylor expansion of 2 in n
1.658 * [backup-simplify]: Simplify 2 into 2
1.658 * [taylor]: Taking taylor expansion of (* n PI) in n
1.658 * [taylor]: Taking taylor expansion of n in n
1.658 * [backup-simplify]: Simplify 0 into 0
1.658 * [backup-simplify]: Simplify 1 into 1
1.658 * [taylor]: Taking taylor expansion of PI in n
1.658 * [backup-simplify]: Simplify PI into PI
1.658 * [backup-simplify]: Simplify (* 0 PI) into 0
1.659 * [backup-simplify]: Simplify (* 2 0) into 0
1.661 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.662 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.664 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.664 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.664 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.664 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.665 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.667 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.668 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
1.669 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k)))
1.669 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
1.669 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
1.669 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
1.670 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.670 * [taylor]: Taking taylor expansion of 1/2 in k
1.670 * [backup-simplify]: Simplify 1/2 into 1/2
1.670 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.670 * [taylor]: Taking taylor expansion of 1/2 in k
1.670 * [backup-simplify]: Simplify 1/2 into 1/2
1.670 * [taylor]: Taking taylor expansion of k in k
1.670 * [backup-simplify]: Simplify 0 into 0
1.670 * [backup-simplify]: Simplify 1 into 1
1.670 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.670 * [taylor]: Taking taylor expansion of (log n) in k
1.670 * [taylor]: Taking taylor expansion of n in k
1.670 * [backup-simplify]: Simplify n into n
1.670 * [backup-simplify]: Simplify (log n) into (log n)
1.670 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.670 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.670 * [taylor]: Taking taylor expansion of 2 in k
1.670 * [backup-simplify]: Simplify 2 into 2
1.670 * [taylor]: Taking taylor expansion of PI in k
1.670 * [backup-simplify]: Simplify PI into PI
1.671 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.672 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.672 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.673 * [backup-simplify]: Simplify (- 0) into 0
1.673 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.674 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.676 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.677 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.677 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.677 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.677 * [taylor]: Taking taylor expansion of k in k
1.677 * [backup-simplify]: Simplify 0 into 0
1.677 * [backup-simplify]: Simplify 1 into 1
1.678 * [backup-simplify]: Simplify (/ 1 1) into 1
1.678 * [backup-simplify]: Simplify (sqrt 0) into 0
1.679 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.680 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
1.680 * [backup-simplify]: Simplify 0 into 0
1.681 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.681 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.682 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.683 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
1.683 * [backup-simplify]: Simplify (- 0) into 0
1.683 * [backup-simplify]: Simplify (+ 0 0) into 0
1.684 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.685 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.686 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.687 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
1.687 * [taylor]: Taking taylor expansion of 0 in k
1.687 * [backup-simplify]: Simplify 0 into 0
1.687 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.688 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.689 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.689 * [backup-simplify]: Simplify (+ 0 0) into 0
1.690 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
1.690 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.690 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.691 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
1.693 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.696 * [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)))))))
1.697 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.697 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.698 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.700 * [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
1.700 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
1.701 * [backup-simplify]: Simplify (- 0) into 0
1.701 * [backup-simplify]: Simplify (+ 0 0) into 0
1.702 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.703 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.704 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.704 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.705 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
1.706 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
1.706 * [taylor]: Taking taylor expansion of 0 in k
1.706 * [backup-simplify]: Simplify 0 into 0
1.706 * [backup-simplify]: Simplify 0 into 0
1.707 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
1.708 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
1.710 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.710 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.712 * [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
1.713 * [backup-simplify]: Simplify (+ 0 0) into 0
1.713 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
1.713 * [backup-simplify]: Simplify (- 0) into 0
1.714 * [backup-simplify]: Simplify (+ 0 0) into 0
1.715 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.719 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
1.729 * [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))))))))
1.734 * [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))))))))
1.736 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.738 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
1.744 * [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
1.745 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
1.746 * [backup-simplify]: Simplify (- 0) into 0
1.746 * [backup-simplify]: Simplify (+ 0 0) into 0
1.748 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.750 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
1.752 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.753 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.754 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
1.756 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
1.756 * [taylor]: Taking taylor expansion of 0 in k
1.756 * [backup-simplify]: Simplify 0 into 0
1.756 * [backup-simplify]: Simplify 0 into 0
1.756 * [backup-simplify]: Simplify 0 into 0
1.757 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.761 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
1.764 * [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
1.765 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.774 * [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
1.775 * [backup-simplify]: Simplify (+ 0 0) into 0
1.776 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
1.776 * [backup-simplify]: Simplify (- 0) into 0
1.777 * [backup-simplify]: Simplify (+ 0 0) into 0
1.779 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
1.786 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.804 * [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))))))))))))))
1.816 * [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))))))))))))))
1.836 * [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))))))))))))))))))))))
1.837 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
1.837 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
1.837 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
1.837 * [taylor]: Taking taylor expansion of (sqrt k) in k
1.837 * [taylor]: Taking taylor expansion of k in k
1.837 * [backup-simplify]: Simplify 0 into 0
1.837 * [backup-simplify]: Simplify 1 into 1
1.837 * [backup-simplify]: Simplify (sqrt 0) into 0
1.839 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.839 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
1.839 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
1.839 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
1.839 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
1.839 * [taylor]: Taking taylor expansion of 1/2 in k
1.839 * [backup-simplify]: Simplify 1/2 into 1/2
1.839 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.839 * [taylor]: Taking taylor expansion of 1/2 in k
1.839 * [backup-simplify]: Simplify 1/2 into 1/2
1.839 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.839 * [taylor]: Taking taylor expansion of k in k
1.839 * [backup-simplify]: Simplify 0 into 0
1.839 * [backup-simplify]: Simplify 1 into 1
1.840 * [backup-simplify]: Simplify (/ 1 1) into 1
1.840 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
1.840 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
1.840 * [taylor]: Taking taylor expansion of 2 in k
1.840 * [backup-simplify]: Simplify 2 into 2
1.840 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.840 * [taylor]: Taking taylor expansion of PI in k
1.840 * [backup-simplify]: Simplify PI into PI
1.840 * [taylor]: Taking taylor expansion of n in k
1.840 * [backup-simplify]: Simplify n into n
1.840 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.840 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
1.840 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
1.841 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.841 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.842 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.842 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
1.842 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
1.842 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
1.842 * [taylor]: Taking taylor expansion of (sqrt k) in n
1.842 * [taylor]: Taking taylor expansion of k in n
1.842 * [backup-simplify]: Simplify k into k
1.842 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
1.842 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
1.842 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
1.842 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.842 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.842 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
1.842 * [taylor]: Taking taylor expansion of 1/2 in n
1.842 * [backup-simplify]: Simplify 1/2 into 1/2
1.842 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.843 * [taylor]: Taking taylor expansion of 1/2 in n
1.843 * [backup-simplify]: Simplify 1/2 into 1/2
1.843 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.843 * [taylor]: Taking taylor expansion of k in n
1.843 * [backup-simplify]: Simplify k into k
1.843 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.843 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.843 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.843 * [taylor]: Taking taylor expansion of 2 in n
1.843 * [backup-simplify]: Simplify 2 into 2
1.843 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.843 * [taylor]: Taking taylor expansion of PI in n
1.843 * [backup-simplify]: Simplify PI into PI
1.843 * [taylor]: Taking taylor expansion of n in n
1.843 * [backup-simplify]: Simplify 0 into 0
1.843 * [backup-simplify]: Simplify 1 into 1
1.844 * [backup-simplify]: Simplify (/ PI 1) into PI
1.844 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.845 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.845 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.845 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
1.845 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
1.847 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.848 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
1.850 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.850 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
1.850 * [taylor]: Taking taylor expansion of (sqrt k) in n
1.850 * [taylor]: Taking taylor expansion of k in n
1.850 * [backup-simplify]: Simplify k into k
1.850 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
1.850 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
1.850 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
1.850 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.850 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.850 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
1.850 * [taylor]: Taking taylor expansion of 1/2 in n
1.850 * [backup-simplify]: Simplify 1/2 into 1/2
1.850 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.850 * [taylor]: Taking taylor expansion of 1/2 in n
1.850 * [backup-simplify]: Simplify 1/2 into 1/2
1.850 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.850 * [taylor]: Taking taylor expansion of k in n
1.850 * [backup-simplify]: Simplify k into k
1.850 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.851 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.851 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.851 * [taylor]: Taking taylor expansion of 2 in n
1.851 * [backup-simplify]: Simplify 2 into 2
1.851 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.851 * [taylor]: Taking taylor expansion of PI in n
1.851 * [backup-simplify]: Simplify PI into PI
1.851 * [taylor]: Taking taylor expansion of n in n
1.851 * [backup-simplify]: Simplify 0 into 0
1.851 * [backup-simplify]: Simplify 1 into 1
1.851 * [backup-simplify]: Simplify (/ PI 1) into PI
1.852 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.853 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.853 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.853 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
1.853 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
1.855 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.856 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
1.857 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.859 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
1.859 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
1.859 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
1.859 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
1.859 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
1.859 * [taylor]: Taking taylor expansion of 1/2 in k
1.859 * [backup-simplify]: Simplify 1/2 into 1/2
1.859 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.859 * [taylor]: Taking taylor expansion of 1/2 in k
1.859 * [backup-simplify]: Simplify 1/2 into 1/2
1.859 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.859 * [taylor]: Taking taylor expansion of k in k
1.859 * [backup-simplify]: Simplify 0 into 0
1.859 * [backup-simplify]: Simplify 1 into 1
1.860 * [backup-simplify]: Simplify (/ 1 1) into 1
1.860 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
1.860 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.860 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.860 * [taylor]: Taking taylor expansion of 2 in k
1.860 * [backup-simplify]: Simplify 2 into 2
1.860 * [taylor]: Taking taylor expansion of PI in k
1.860 * [backup-simplify]: Simplify PI into PI
1.860 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.861 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.862 * [taylor]: Taking taylor expansion of (log n) in k
1.862 * [taylor]: Taking taylor expansion of n in k
1.862 * [backup-simplify]: Simplify n into n
1.862 * [backup-simplify]: Simplify (log n) into (log n)
1.862 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.862 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.863 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.863 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.864 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
1.865 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
1.866 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.866 * [taylor]: Taking taylor expansion of (sqrt k) in k
1.866 * [taylor]: Taking taylor expansion of k in k
1.867 * [backup-simplify]: Simplify 0 into 0
1.867 * [backup-simplify]: Simplify 1 into 1
1.867 * [backup-simplify]: Simplify (sqrt 0) into 0
1.868 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.870 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
1.870 * [backup-simplify]: Simplify 0 into 0
1.871 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.872 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.874 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.874 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.874 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
1.875 * [backup-simplify]: Simplify (- 0) into 0
1.875 * [backup-simplify]: Simplify (+ 0 0) into 0
1.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.878 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
1.880 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
1.881 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
1.881 * [taylor]: Taking taylor expansion of 0 in k
1.881 * [backup-simplify]: Simplify 0 into 0
1.881 * [backup-simplify]: Simplify 0 into 0
1.883 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
1.884 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
1.886 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.887 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.890 * [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
1.891 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.892 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
1.892 * [backup-simplify]: Simplify (- 0) into 0
1.892 * [backup-simplify]: Simplify (+ 0 0) into 0
1.894 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.896 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
1.898 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.899 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
1.901 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
1.901 * [taylor]: Taking taylor expansion of 0 in k
1.901 * [backup-simplify]: Simplify 0 into 0
1.901 * [backup-simplify]: Simplify 0 into 0
1.901 * [backup-simplify]: Simplify 0 into 0
1.904 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
1.906 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
1.908 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
1.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.910 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.916 * [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
1.916 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.921 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
1.922 * [backup-simplify]: Simplify (- 0) into 0
1.922 * [backup-simplify]: Simplify (+ 0 0) into 0
1.924 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.926 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
1.929 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.930 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
1.932 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
1.932 * [taylor]: Taking taylor expansion of 0 in k
1.932 * [backup-simplify]: Simplify 0 into 0
1.932 * [backup-simplify]: Simplify 0 into 0
1.932 * [backup-simplify]: Simplify 0 into 0
1.932 * [backup-simplify]: Simplify 0 into 0
1.936 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
1.938 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
1.939 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
1.943 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
1.944 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
1.944 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
1.944 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
1.944 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
1.944 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
1.944 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
1.944 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
1.944 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.944 * [taylor]: Taking taylor expansion of 1/2 in k
1.944 * [backup-simplify]: Simplify 1/2 into 1/2
1.944 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.944 * [taylor]: Taking taylor expansion of k in k
1.944 * [backup-simplify]: Simplify 0 into 0
1.944 * [backup-simplify]: Simplify 1 into 1
1.945 * [backup-simplify]: Simplify (/ 1 1) into 1
1.945 * [taylor]: Taking taylor expansion of 1/2 in k
1.945 * [backup-simplify]: Simplify 1/2 into 1/2
1.945 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
1.945 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
1.945 * [taylor]: Taking taylor expansion of -2 in k
1.945 * [backup-simplify]: Simplify -2 into -2
1.945 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.945 * [taylor]: Taking taylor expansion of PI in k
1.945 * [backup-simplify]: Simplify PI into PI
1.945 * [taylor]: Taking taylor expansion of n in k
1.945 * [backup-simplify]: Simplify n into n
1.945 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.945 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
1.945 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
1.946 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.946 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.947 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
1.947 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
1.947 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
1.947 * [taylor]: Taking taylor expansion of (/ -1 k) in k
1.947 * [taylor]: Taking taylor expansion of -1 in k
1.947 * [backup-simplify]: Simplify -1 into -1
1.947 * [taylor]: Taking taylor expansion of k in k
1.947 * [backup-simplify]: Simplify 0 into 0
1.947 * [backup-simplify]: Simplify 1 into 1
1.948 * [backup-simplify]: Simplify (/ -1 1) into -1
1.948 * [backup-simplify]: Simplify (sqrt 0) into 0
1.950 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
1.950 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
1.950 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
1.950 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
1.950 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
1.950 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
1.950 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
1.950 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.950 * [taylor]: Taking taylor expansion of 1/2 in n
1.950 * [backup-simplify]: Simplify 1/2 into 1/2
1.950 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.950 * [taylor]: Taking taylor expansion of k in n
1.950 * [backup-simplify]: Simplify k into k
1.950 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.951 * [taylor]: Taking taylor expansion of 1/2 in n
1.951 * [backup-simplify]: Simplify 1/2 into 1/2
1.951 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.951 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.951 * [taylor]: Taking taylor expansion of -2 in n
1.951 * [backup-simplify]: Simplify -2 into -2
1.951 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.951 * [taylor]: Taking taylor expansion of PI in n
1.951 * [backup-simplify]: Simplify PI into PI
1.951 * [taylor]: Taking taylor expansion of n in n
1.951 * [backup-simplify]: Simplify 0 into 0
1.951 * [backup-simplify]: Simplify 1 into 1
1.951 * [backup-simplify]: Simplify (/ PI 1) into PI
1.952 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.953 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.953 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.953 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
1.955 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.956 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
1.957 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.957 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
1.957 * [taylor]: Taking taylor expansion of (/ -1 k) in n
1.957 * [taylor]: Taking taylor expansion of -1 in n
1.957 * [backup-simplify]: Simplify -1 into -1
1.957 * [taylor]: Taking taylor expansion of k in n
1.957 * [backup-simplify]: Simplify k into k
1.957 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
1.958 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
1.958 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
1.958 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
1.959 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
1.959 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
1.959 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
1.959 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
1.959 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
1.959 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
1.959 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.959 * [taylor]: Taking taylor expansion of 1/2 in n
1.959 * [backup-simplify]: Simplify 1/2 into 1/2
1.959 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.959 * [taylor]: Taking taylor expansion of k in n
1.959 * [backup-simplify]: Simplify k into k
1.960 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.960 * [taylor]: Taking taylor expansion of 1/2 in n
1.960 * [backup-simplify]: Simplify 1/2 into 1/2
1.960 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.960 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.960 * [taylor]: Taking taylor expansion of -2 in n
1.960 * [backup-simplify]: Simplify -2 into -2
1.960 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.960 * [taylor]: Taking taylor expansion of PI in n
1.960 * [backup-simplify]: Simplify PI into PI
1.960 * [taylor]: Taking taylor expansion of n in n
1.960 * [backup-simplify]: Simplify 0 into 0
1.960 * [backup-simplify]: Simplify 1 into 1
1.960 * [backup-simplify]: Simplify (/ PI 1) into PI
1.961 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.962 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.962 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.962 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
1.963 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.964 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
1.965 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.965 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
1.965 * [taylor]: Taking taylor expansion of (/ -1 k) in n
1.965 * [taylor]: Taking taylor expansion of -1 in n
1.965 * [backup-simplify]: Simplify -1 into -1
1.965 * [taylor]: Taking taylor expansion of k in n
1.965 * [backup-simplify]: Simplify k into k
1.965 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
1.965 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
1.965 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
1.965 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
1.966 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
1.966 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
1.966 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
1.966 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
1.966 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
1.966 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.966 * [taylor]: Taking taylor expansion of 1/2 in k
1.966 * [backup-simplify]: Simplify 1/2 into 1/2
1.966 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.966 * [taylor]: Taking taylor expansion of k in k
1.966 * [backup-simplify]: Simplify 0 into 0
1.966 * [backup-simplify]: Simplify 1 into 1
1.967 * [backup-simplify]: Simplify (/ 1 1) into 1
1.967 * [taylor]: Taking taylor expansion of 1/2 in k
1.967 * [backup-simplify]: Simplify 1/2 into 1/2
1.967 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
1.967 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
1.967 * [taylor]: Taking taylor expansion of (* -2 PI) in k
1.967 * [taylor]: Taking taylor expansion of -2 in k
1.967 * [backup-simplify]: Simplify -2 into -2
1.967 * [taylor]: Taking taylor expansion of PI in k
1.967 * [backup-simplify]: Simplify PI into PI
1.967 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.968 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.968 * [taylor]: Taking taylor expansion of (log n) in k
1.968 * [taylor]: Taking taylor expansion of n in k
1.968 * [backup-simplify]: Simplify n into n
1.968 * [backup-simplify]: Simplify (log n) into (log n)
1.968 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.968 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.968 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.969 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
1.970 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
1.971 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.971 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
1.971 * [taylor]: Taking taylor expansion of (/ -1 k) in k
1.971 * [taylor]: Taking taylor expansion of -1 in k
1.971 * [backup-simplify]: Simplify -1 into -1
1.971 * [taylor]: Taking taylor expansion of k in k
1.971 * [backup-simplify]: Simplify 0 into 0
1.971 * [backup-simplify]: Simplify 1 into 1
1.971 * [backup-simplify]: Simplify (/ -1 1) into -1
1.971 * [backup-simplify]: Simplify (sqrt 0) into 0
1.972 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
1.973 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
1.974 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
1.974 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.975 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.976 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
1.976 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.976 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
1.976 * [backup-simplify]: Simplify (+ 0 0) into 0
1.977 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.978 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
1.979 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
1.980 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
1.980 * [taylor]: Taking taylor expansion of 0 in k
1.980 * [backup-simplify]: Simplify 0 into 0
1.980 * [backup-simplify]: Simplify 0 into 0
1.981 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
1.983 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
1.984 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
1.985 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
1.985 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.986 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.988 * [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
1.988 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.989 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
1.989 * [backup-simplify]: Simplify (+ 0 0) into 0
1.990 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.991 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
1.994 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.994 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.995 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
1.997 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
1.997 * [taylor]: Taking taylor expansion of 0 in k
1.997 * [backup-simplify]: Simplify 0 into 0
1.997 * [backup-simplify]: Simplify 0 into 0
1.997 * [backup-simplify]: Simplify 0 into 0
1.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.003 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.007 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.008 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.013 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
2.013 * * * [progress]: simplifying candidates
2.013 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.013 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.013 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.013 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.013 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.013 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.013 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.013 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
2.013 * * * * [progress]: [ 9 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.014 * * * * [progress]: [ 10 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.014 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.014 * * * * [progress]: [ 12 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
2.014 * * * * [progress]: [ 13 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
2.014 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.014 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
2.014 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
2.014 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))>
2.014 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.014 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
2.014 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
2.014 * * * * [progress]: [ 21 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
2.014 * * * * [progress]: [ 22 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
2.014 * * * * [progress]: [ 23 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
2.015 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))>
2.015 * * * * [progress]: [ 25 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
2.015 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log (* n 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 34 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 36 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 37 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* (* n 2) PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.015 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.016 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) 1) PI) (- 1/2 (/ k 2))) (sqrt k)))>
2.016 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.016 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.016 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))>
2.016 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) 1))>
2.016 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.016 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.016 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.016 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.016 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
2.016 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
2.016 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
2.016 * * * * [progress]: [ 54 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
2.016 * * * * [progress]: [ 55 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
2.016 * * * * [progress]: [ 56 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
2.016 * * * * [progress]: [ 57 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
2.016 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (- (sqrt k))))>
2.016 * * * * [progress]: [ 59 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))>
2.016 * * * * [progress]: [ 60 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))>
2.016 * * * * [progress]: [ 61 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
2.016 * * * * [progress]: [ 62 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
2.016 * * * * [progress]: [ 63 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
2.017 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
2.017 * * * * [progress]: [ 65 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))>
2.017 * * * * [progress]: [ 66 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))>
2.017 * * * * [progress]: [ 67 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
2.017 * * * * [progress]: [ 68 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
2.017 * * * * [progress]: [ 69 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
2.017 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
2.017 * * * * [progress]: [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.017 * * * * [progress]: [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.017 * * * * [progress]: [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.017 * * * * [progress]: [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
2.017 * * * * [progress]: [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.017 * * * * [progress]: [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
2.017 * * * * [progress]: [ 77 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.017 * * * * [progress]: [ 78 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.017 * * * * [progress]: [ 79 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.017 * * * * [progress]: [ 80 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
2.017 * * * * [progress]: [ 81 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.017 * * * * [progress]: [ 82 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
2.017 * * * * [progress]: [ 83 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.017 * * * * [progress]: [ 84 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.017 * * * * [progress]: [ 85 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.017 * * * * [progress]: [ 86 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
2.018 * * * * [progress]: [ 87 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.018 * * * * [progress]: [ 88 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
2.018 * * * * [progress]: [ 89 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.018 * * * * [progress]: [ 90 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.018 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.018 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.018 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.018 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.018 * * * * [progress]: [ 95 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
2.018 * * * * [progress]: [ 96 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
2.018 * * * * [progress]: [ 97 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.018 * * * * [progress]: [ 98 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.018 * * * * [progress]: [ 99 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.018 * * * * [progress]: [ 100 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.018 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.018 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
2.018 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
2.018 * * * * [progress]: [ 104 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
2.018 * * * * [progress]: [ 105 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
2.018 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.018 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
2.018 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.018 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.018 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
2.018 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
2.019 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))>
2.019 * * * * [progress]: [ 113 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))))>
2.019 * * * * [progress]: [ 114 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))))>
2.019 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
2.019 * * * * [progress]: [ 116 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))))>
2.019 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))>
2.019 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
2.019 * * * * [progress]: [ 119 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
2.019 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
2.019 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
2.019 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.019 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.019 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.019 * * * * [progress]: [ 125 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
2.019 * * * * [progress]: [ 126 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
2.019 * * * * [progress]: [ 127 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
2.021 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (+ (log n) (log 2)) (log PI))
  (+ (log (* n 2)) (log PI))
  (log (* (* n 2) PI))
  (exp (* (* n 2) PI))
  (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))
  (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))
  (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI)))
  (cbrt (* (* n 2) PI))
  (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))
  (sqrt (* (* n 2) PI))
  (sqrt (* (* n 2) PI))
  (* (* n 2) (* (cbrt PI) (cbrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) 1)
  (* 2 PI)
  (real->posit16 (* (* n 2) PI))
  (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) 1)
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) 1)
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) 1)
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1)
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1)
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1)
  (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))
  (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))
  (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))
  (real->posit16 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
2.023 * * [simplify]: iteration 0: 271 enodes
2.095 * * [simplify]: iteration 1: 662 enodes
2.318 * * [simplify]: iteration complete: 2001 enodes
2.318 * * [simplify]: Extracting #0: cost 99 inf + 0
2.320 * * [simplify]: Extracting #1: cost 342 inf + 1
2.323 * * [simplify]: Extracting #2: cost 590 inf + 1931
2.333 * * [simplify]: Extracting #3: cost 627 inf + 25636
2.355 * * [simplify]: Extracting #4: cost 438 inf + 90869
2.405 * * [simplify]: Extracting #5: cost 214 inf + 189941
2.453 * * [simplify]: Extracting #6: cost 112 inf + 249014
2.535 * * [simplify]: Extracting #7: cost 30 inf + 300427
2.611 * * [simplify]: Extracting #8: cost 3 inf + 322021
2.684 * * [simplify]: Extracting #9: cost 0 inf + 324899
2.792 * * [simplify]: Extracting #10: cost 0 inf + 324779
2.876 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* 2 PI) n) (sqrt (- 1/2 (/ k 2))))
  (* (* 2 PI) n)
  (pow (* (* 2 PI) n) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* 2 PI) n) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* 2 PI) n)
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (- (/ k 2)))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (exp (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2)))
  (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2)))
  (real->posit16 (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* (* n (* n n)) 8) PI) (* PI PI))
  (* (* (* (* PI PI) PI) (* n 2)) (* (* n 2) (* n 2)))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* (cbrt PI) (cbrt PI)) (* n 2))
  (* (* (sqrt PI) 2) n)
  (* n 2)
  (* 2 PI)
  (real->posit16 (* (* 2 PI) n))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (exp (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (/ (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) k) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (* (cbrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))
  (/ (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (* (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (fabs (cbrt k)))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- (/ k 2))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- (/ k 2))))
  (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (real->posit16 (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (- (+ (+ (+ (* 1/4 (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* (* k k) (log n)) (log (* 2 PI))))) (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* (* (log n) (log n)) (* k k)) 1/8))) (exp (* (log (* (* 2 PI) n)) 1/2))) (* (* (* 1/8 (* (log (* 2 PI)) (log (* 2 PI)))) (exp (* (log (* (* 2 PI) n)) 1/2))) (* k k))) (* 1/2 (* k (+ (* (exp (* (log (* (* 2 PI) n)) 1/2)) (log n)) (* (log (* 2 PI)) (exp (* (log (* (* 2 PI) n)) 1/2)))))))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* k 1/2))))
  (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (- (+ (- (* (* (log (* 2 PI)) (exp (* (log (* (* 2 PI) n)) 1/2))) (* (* (* k k) (log n)) +nan.0)) (* (log (* 2 PI)) (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* k k) +nan.0)))) (+ (- (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* +nan.0 (* (* (log n) (log n)) (* k k)))) (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* +nan.0 k))) (+ (- (* (exp (* (log (* (* 2 PI) n)) 1/2)) +nan.0) (* (* (log (* 2 PI)) (log (* 2 PI))) (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* k k) +nan.0)))) (+ (+ (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* (* k k) (log n)) +nan.0)) (- (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* k k) +nan.0)))) (- (* +nan.0 (* (* (log (* 2 PI)) k) (exp (* (log (* (* 2 PI) n)) 1/2)))) (* (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* +nan.0 k)) (log n))))))))
  (+ (/ (- (* +nan.0 (exp (* (log (* (* 2 PI) n)) (- 1/2 (* k 1/2)))))) (* (* k k) k)) (* +nan.0 (- (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* k 1/2)))) k) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* k 1/2)))) (* k k)))))
  (+ (* (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) k) (- +nan.0)) (* +nan.0 (- (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))))))
2.889 * * * [progress]: adding candidates to table
3.383 * * [progress]: iteration 2 / 4
3.383 * * * [progress]: picking best candidate
3.426 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.427 * * * [progress]: localizing error
3.456 * * * [progress]: generating rewritten candidates
3.456 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 1 2)
3.457 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2)
3.458 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
3.518 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1)
3.600 * * * [progress]: generating series expansions
3.600 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 1 2)
3.600 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2)
3.600 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
3.601 * [backup-simplify]: Simplify (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
3.602 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
3.602 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
3.602 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
3.602 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
3.602 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.602 * [taylor]: Taking taylor expansion of 1/2 in k
3.602 * [backup-simplify]: Simplify 1/2 into 1/2
3.602 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.602 * [taylor]: Taking taylor expansion of 1/2 in k
3.602 * [backup-simplify]: Simplify 1/2 into 1/2
3.602 * [taylor]: Taking taylor expansion of k in k
3.602 * [backup-simplify]: Simplify 0 into 0
3.602 * [backup-simplify]: Simplify 1 into 1
3.602 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
3.602 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
3.602 * [taylor]: Taking taylor expansion of 2 in k
3.602 * [backup-simplify]: Simplify 2 into 2
3.602 * [taylor]: Taking taylor expansion of (* n PI) in k
3.602 * [taylor]: Taking taylor expansion of n in k
3.602 * [backup-simplify]: Simplify n into n
3.602 * [taylor]: Taking taylor expansion of PI in k
3.602 * [backup-simplify]: Simplify PI into PI
3.602 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.602 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
3.602 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
3.603 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.603 * [backup-simplify]: Simplify (- 0) into 0
3.604 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.604 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
3.604 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
3.604 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.604 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.604 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.604 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.604 * [taylor]: Taking taylor expansion of 1/2 in n
3.604 * [backup-simplify]: Simplify 1/2 into 1/2
3.604 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.604 * [taylor]: Taking taylor expansion of 1/2 in n
3.604 * [backup-simplify]: Simplify 1/2 into 1/2
3.604 * [taylor]: Taking taylor expansion of k in n
3.604 * [backup-simplify]: Simplify k into k
3.604 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.605 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.605 * [taylor]: Taking taylor expansion of 2 in n
3.605 * [backup-simplify]: Simplify 2 into 2
3.605 * [taylor]: Taking taylor expansion of (* n PI) in n
3.605 * [taylor]: Taking taylor expansion of n in n
3.605 * [backup-simplify]: Simplify 0 into 0
3.605 * [backup-simplify]: Simplify 1 into 1
3.605 * [taylor]: Taking taylor expansion of PI in n
3.605 * [backup-simplify]: Simplify PI into PI
3.605 * [backup-simplify]: Simplify (* 0 PI) into 0
3.606 * [backup-simplify]: Simplify (* 2 0) into 0
3.607 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.609 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.610 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.610 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.610 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.610 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.612 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.613 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.614 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.614 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.614 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.614 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.614 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.614 * [taylor]: Taking taylor expansion of 1/2 in n
3.614 * [backup-simplify]: Simplify 1/2 into 1/2
3.614 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.614 * [taylor]: Taking taylor expansion of 1/2 in n
3.614 * [backup-simplify]: Simplify 1/2 into 1/2
3.614 * [taylor]: Taking taylor expansion of k in n
3.615 * [backup-simplify]: Simplify k into k
3.615 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.615 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.615 * [taylor]: Taking taylor expansion of 2 in n
3.615 * [backup-simplify]: Simplify 2 into 2
3.615 * [taylor]: Taking taylor expansion of (* n PI) in n
3.615 * [taylor]: Taking taylor expansion of n in n
3.615 * [backup-simplify]: Simplify 0 into 0
3.615 * [backup-simplify]: Simplify 1 into 1
3.615 * [taylor]: Taking taylor expansion of PI in n
3.615 * [backup-simplify]: Simplify PI into PI
3.615 * [backup-simplify]: Simplify (* 0 PI) into 0
3.616 * [backup-simplify]: Simplify (* 2 0) into 0
3.617 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.619 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.620 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.620 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.621 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.621 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.622 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.623 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.625 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.625 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
3.625 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
3.625 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.625 * [taylor]: Taking taylor expansion of 1/2 in k
3.625 * [backup-simplify]: Simplify 1/2 into 1/2
3.625 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.625 * [taylor]: Taking taylor expansion of 1/2 in k
3.625 * [backup-simplify]: Simplify 1/2 into 1/2
3.625 * [taylor]: Taking taylor expansion of k in k
3.625 * [backup-simplify]: Simplify 0 into 0
3.625 * [backup-simplify]: Simplify 1 into 1
3.625 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
3.625 * [taylor]: Taking taylor expansion of (log n) in k
3.625 * [taylor]: Taking taylor expansion of n in k
3.625 * [backup-simplify]: Simplify n into n
3.625 * [backup-simplify]: Simplify (log n) into (log n)
3.625 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.625 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.625 * [taylor]: Taking taylor expansion of 2 in k
3.625 * [backup-simplify]: Simplify 2 into 2
3.625 * [taylor]: Taking taylor expansion of PI in k
3.625 * [backup-simplify]: Simplify PI into PI
3.626 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.627 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.627 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.628 * [backup-simplify]: Simplify (- 0) into 0
3.628 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.629 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.630 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
3.632 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.633 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.634 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.635 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.638 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.638 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
3.639 * [backup-simplify]: Simplify (- 0) into 0
3.639 * [backup-simplify]: Simplify (+ 0 0) into 0
3.641 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.642 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
3.645 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.645 * [taylor]: Taking taylor expansion of 0 in k
3.645 * [backup-simplify]: Simplify 0 into 0
3.645 * [backup-simplify]: Simplify 0 into 0
3.646 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
3.647 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.649 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.649 * [backup-simplify]: Simplify (+ 0 0) into 0
3.650 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
3.650 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.651 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.652 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
3.656 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.659 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.661 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.665 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.668 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
3.668 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
3.669 * [backup-simplify]: Simplify (- 0) into 0
3.669 * [backup-simplify]: Simplify (+ 0 0) into 0
3.670 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.671 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.672 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.672 * [taylor]: Taking taylor expansion of 0 in k
3.672 * [backup-simplify]: Simplify 0 into 0
3.672 * [backup-simplify]: Simplify 0 into 0
3.672 * [backup-simplify]: Simplify 0 into 0
3.673 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
3.674 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.676 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
3.676 * [backup-simplify]: Simplify (+ 0 0) into 0
3.677 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
3.677 * [backup-simplify]: Simplify (- 0) into 0
3.677 * [backup-simplify]: Simplify (+ 0 0) into 0
3.678 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.681 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
3.684 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
3.690 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
3.690 * [backup-simplify]: Simplify (pow (* (* (* (/ 1 n) 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
3.690 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
3.690 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
3.691 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
3.691 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
3.691 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.691 * [taylor]: Taking taylor expansion of 1/2 in k
3.691 * [backup-simplify]: Simplify 1/2 into 1/2
3.691 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.691 * [taylor]: Taking taylor expansion of 1/2 in k
3.691 * [backup-simplify]: Simplify 1/2 into 1/2
3.691 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.691 * [taylor]: Taking taylor expansion of k in k
3.691 * [backup-simplify]: Simplify 0 into 0
3.691 * [backup-simplify]: Simplify 1 into 1
3.691 * [backup-simplify]: Simplify (/ 1 1) into 1
3.691 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
3.691 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
3.691 * [taylor]: Taking taylor expansion of 2 in k
3.691 * [backup-simplify]: Simplify 2 into 2
3.691 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.691 * [taylor]: Taking taylor expansion of PI in k
3.691 * [backup-simplify]: Simplify PI into PI
3.691 * [taylor]: Taking taylor expansion of n in k
3.691 * [backup-simplify]: Simplify n into n
3.691 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.691 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
3.691 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
3.691 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.692 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.692 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.692 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
3.692 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
3.692 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.692 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.692 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.692 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.692 * [taylor]: Taking taylor expansion of 1/2 in n
3.692 * [backup-simplify]: Simplify 1/2 into 1/2
3.692 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.692 * [taylor]: Taking taylor expansion of 1/2 in n
3.692 * [backup-simplify]: Simplify 1/2 into 1/2
3.692 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.692 * [taylor]: Taking taylor expansion of k in n
3.692 * [backup-simplify]: Simplify k into k
3.692 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.692 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.692 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.692 * [taylor]: Taking taylor expansion of 2 in n
3.692 * [backup-simplify]: Simplify 2 into 2
3.692 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.693 * [taylor]: Taking taylor expansion of PI in n
3.693 * [backup-simplify]: Simplify PI into PI
3.693 * [taylor]: Taking taylor expansion of n in n
3.693 * [backup-simplify]: Simplify 0 into 0
3.693 * [backup-simplify]: Simplify 1 into 1
3.693 * [backup-simplify]: Simplify (/ PI 1) into PI
3.693 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.694 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.694 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.694 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.694 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.695 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.696 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
3.698 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.698 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.698 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.698 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.698 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.698 * [taylor]: Taking taylor expansion of 1/2 in n
3.698 * [backup-simplify]: Simplify 1/2 into 1/2
3.698 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.698 * [taylor]: Taking taylor expansion of 1/2 in n
3.698 * [backup-simplify]: Simplify 1/2 into 1/2
3.698 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.698 * [taylor]: Taking taylor expansion of k in n
3.698 * [backup-simplify]: Simplify k into k
3.698 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.698 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.698 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.698 * [taylor]: Taking taylor expansion of 2 in n
3.698 * [backup-simplify]: Simplify 2 into 2
3.698 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.698 * [taylor]: Taking taylor expansion of PI in n
3.698 * [backup-simplify]: Simplify PI into PI
3.698 * [taylor]: Taking taylor expansion of n in n
3.698 * [backup-simplify]: Simplify 0 into 0
3.698 * [backup-simplify]: Simplify 1 into 1
3.699 * [backup-simplify]: Simplify (/ PI 1) into PI
3.699 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.701 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.701 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.701 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.701 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.702 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.704 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
3.705 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.705 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
3.705 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
3.705 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.705 * [taylor]: Taking taylor expansion of 1/2 in k
3.705 * [backup-simplify]: Simplify 1/2 into 1/2
3.705 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.705 * [taylor]: Taking taylor expansion of 1/2 in k
3.705 * [backup-simplify]: Simplify 1/2 into 1/2
3.705 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.705 * [taylor]: Taking taylor expansion of k in k
3.705 * [backup-simplify]: Simplify 0 into 0
3.705 * [backup-simplify]: Simplify 1 into 1
3.706 * [backup-simplify]: Simplify (/ 1 1) into 1
3.706 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
3.706 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.706 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.706 * [taylor]: Taking taylor expansion of 2 in k
3.706 * [backup-simplify]: Simplify 2 into 2
3.706 * [taylor]: Taking taylor expansion of PI in k
3.706 * [backup-simplify]: Simplify PI into PI
3.706 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.707 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.707 * [taylor]: Taking taylor expansion of (log n) in k
3.707 * [taylor]: Taking taylor expansion of n in k
3.707 * [backup-simplify]: Simplify n into n
3.707 * [backup-simplify]: Simplify (log n) into (log n)
3.708 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.708 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.709 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.709 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.710 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
3.711 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
3.712 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.713 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.714 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.715 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.717 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.717 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.718 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.718 * [backup-simplify]: Simplify (- 0) into 0
3.719 * [backup-simplify]: Simplify (+ 0 0) into 0
3.720 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.721 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
3.723 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.723 * [taylor]: Taking taylor expansion of 0 in k
3.723 * [backup-simplify]: Simplify 0 into 0
3.723 * [backup-simplify]: Simplify 0 into 0
3.723 * [backup-simplify]: Simplify 0 into 0
3.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.726 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.729 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
3.729 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.730 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.731 * [backup-simplify]: Simplify (- 0) into 0
3.731 * [backup-simplify]: Simplify (+ 0 0) into 0
3.733 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.734 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
3.737 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.737 * [taylor]: Taking taylor expansion of 0 in k
3.737 * [backup-simplify]: Simplify 0 into 0
3.737 * [backup-simplify]: Simplify 0 into 0
3.737 * [backup-simplify]: Simplify 0 into 0
3.737 * [backup-simplify]: Simplify 0 into 0
3.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.739 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.745 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
3.746 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.747 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.747 * [backup-simplify]: Simplify (- 0) into 0
3.748 * [backup-simplify]: Simplify (+ 0 0) into 0
3.749 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.751 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
3.754 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
3.754 * [taylor]: Taking taylor expansion of 0 in k
3.754 * [backup-simplify]: Simplify 0 into 0
3.754 * [backup-simplify]: Simplify 0 into 0
3.756 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
3.757 * [backup-simplify]: Simplify (pow (* (* (* (/ 1 (- n)) 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
3.757 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
3.757 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
3.757 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
3.757 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
3.757 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.757 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.757 * [taylor]: Taking taylor expansion of 1/2 in k
3.757 * [backup-simplify]: Simplify 1/2 into 1/2
3.757 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.757 * [taylor]: Taking taylor expansion of k in k
3.757 * [backup-simplify]: Simplify 0 into 0
3.757 * [backup-simplify]: Simplify 1 into 1
3.758 * [backup-simplify]: Simplify (/ 1 1) into 1
3.758 * [taylor]: Taking taylor expansion of 1/2 in k
3.758 * [backup-simplify]: Simplify 1/2 into 1/2
3.758 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
3.758 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
3.758 * [taylor]: Taking taylor expansion of -2 in k
3.758 * [backup-simplify]: Simplify -2 into -2
3.758 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.758 * [taylor]: Taking taylor expansion of PI in k
3.758 * [backup-simplify]: Simplify PI into PI
3.758 * [taylor]: Taking taylor expansion of n in k
3.758 * [backup-simplify]: Simplify n into n
3.758 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.758 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
3.758 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
3.759 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.759 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.759 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
3.759 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
3.759 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.759 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.759 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.759 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.759 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.759 * [taylor]: Taking taylor expansion of 1/2 in n
3.759 * [backup-simplify]: Simplify 1/2 into 1/2
3.760 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.760 * [taylor]: Taking taylor expansion of k in n
3.760 * [backup-simplify]: Simplify k into k
3.760 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.760 * [taylor]: Taking taylor expansion of 1/2 in n
3.760 * [backup-simplify]: Simplify 1/2 into 1/2
3.760 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.760 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.760 * [taylor]: Taking taylor expansion of -2 in n
3.760 * [backup-simplify]: Simplify -2 into -2
3.760 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.760 * [taylor]: Taking taylor expansion of PI in n
3.760 * [backup-simplify]: Simplify PI into PI
3.760 * [taylor]: Taking taylor expansion of n in n
3.760 * [backup-simplify]: Simplify 0 into 0
3.760 * [backup-simplify]: Simplify 1 into 1
3.760 * [backup-simplify]: Simplify (/ PI 1) into PI
3.761 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.762 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.762 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.762 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.764 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.765 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
3.766 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.766 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.766 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.766 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.766 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.766 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.766 * [taylor]: Taking taylor expansion of 1/2 in n
3.766 * [backup-simplify]: Simplify 1/2 into 1/2
3.766 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.766 * [taylor]: Taking taylor expansion of k in n
3.766 * [backup-simplify]: Simplify k into k
3.767 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.767 * [taylor]: Taking taylor expansion of 1/2 in n
3.767 * [backup-simplify]: Simplify 1/2 into 1/2
3.767 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.767 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.767 * [taylor]: Taking taylor expansion of -2 in n
3.767 * [backup-simplify]: Simplify -2 into -2
3.767 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.767 * [taylor]: Taking taylor expansion of PI in n
3.767 * [backup-simplify]: Simplify PI into PI
3.767 * [taylor]: Taking taylor expansion of n in n
3.767 * [backup-simplify]: Simplify 0 into 0
3.767 * [backup-simplify]: Simplify 1 into 1
3.767 * [backup-simplify]: Simplify (/ PI 1) into PI
3.768 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.769 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.769 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.769 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.770 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.772 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
3.773 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.773 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
3.773 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
3.773 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.773 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.773 * [taylor]: Taking taylor expansion of 1/2 in k
3.773 * [backup-simplify]: Simplify 1/2 into 1/2
3.773 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.773 * [taylor]: Taking taylor expansion of k in k
3.773 * [backup-simplify]: Simplify 0 into 0
3.773 * [backup-simplify]: Simplify 1 into 1
3.774 * [backup-simplify]: Simplify (/ 1 1) into 1
3.774 * [taylor]: Taking taylor expansion of 1/2 in k
3.774 * [backup-simplify]: Simplify 1/2 into 1/2
3.774 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
3.774 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
3.774 * [taylor]: Taking taylor expansion of (* -2 PI) in k
3.774 * [taylor]: Taking taylor expansion of -2 in k
3.774 * [backup-simplify]: Simplify -2 into -2
3.774 * [taylor]: Taking taylor expansion of PI in k
3.774 * [backup-simplify]: Simplify PI into PI
3.775 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.776 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.776 * [taylor]: Taking taylor expansion of (log n) in k
3.776 * [taylor]: Taking taylor expansion of n in k
3.776 * [backup-simplify]: Simplify n into n
3.776 * [backup-simplify]: Simplify (log n) into (log n)
3.777 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.777 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.777 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.778 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
3.780 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
3.781 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.782 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.783 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.784 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
3.785 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
3.785 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.785 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.785 * [backup-simplify]: Simplify (+ 0 0) into 0
3.786 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.787 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
3.791 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.791 * [taylor]: Taking taylor expansion of 0 in k
3.791 * [backup-simplify]: Simplify 0 into 0
3.791 * [backup-simplify]: Simplify 0 into 0
3.791 * [backup-simplify]: Simplify 0 into 0
3.792 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.792 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
3.794 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
3.795 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.796 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.796 * [backup-simplify]: Simplify (+ 0 0) into 0
3.797 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.798 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
3.800 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.800 * [taylor]: Taking taylor expansion of 0 in k
3.800 * [backup-simplify]: Simplify 0 into 0
3.800 * [backup-simplify]: Simplify 0 into 0
3.800 * [backup-simplify]: Simplify 0 into 0
3.800 * [backup-simplify]: Simplify 0 into 0
3.801 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.801 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.805 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
3.805 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.806 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.806 * [backup-simplify]: Simplify (+ 0 0) into 0
3.807 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.808 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
3.810 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
3.810 * [taylor]: Taking taylor expansion of 0 in k
3.810 * [backup-simplify]: Simplify 0 into 0
3.810 * [backup-simplify]: Simplify 0 into 0
3.811 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
3.811 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1)
3.812 * [backup-simplify]: Simplify (* (* (* n 2) (sqrt PI)) (sqrt PI)) into (* 2 (* n PI))
3.812 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
3.812 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.812 * [taylor]: Taking taylor expansion of 2 in n
3.812 * [backup-simplify]: Simplify 2 into 2
3.812 * [taylor]: Taking taylor expansion of (* n PI) in n
3.812 * [taylor]: Taking taylor expansion of n in n
3.812 * [backup-simplify]: Simplify 0 into 0
3.812 * [backup-simplify]: Simplify 1 into 1
3.812 * [taylor]: Taking taylor expansion of PI in n
3.812 * [backup-simplify]: Simplify PI into PI
3.812 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.812 * [taylor]: Taking taylor expansion of 2 in n
3.812 * [backup-simplify]: Simplify 2 into 2
3.812 * [taylor]: Taking taylor expansion of (* n PI) in n
3.812 * [taylor]: Taking taylor expansion of n in n
3.812 * [backup-simplify]: Simplify 0 into 0
3.812 * [backup-simplify]: Simplify 1 into 1
3.812 * [taylor]: Taking taylor expansion of PI in n
3.812 * [backup-simplify]: Simplify PI into PI
3.812 * [backup-simplify]: Simplify (* 0 PI) into 0
3.813 * [backup-simplify]: Simplify (* 2 0) into 0
3.813 * [backup-simplify]: Simplify 0 into 0
3.814 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.815 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.815 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.816 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.817 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.817 * [backup-simplify]: Simplify 0 into 0
3.818 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.820 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.820 * [backup-simplify]: Simplify 0 into 0
3.821 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.823 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
3.823 * [backup-simplify]: Simplify 0 into 0
3.824 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.826 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
3.826 * [backup-simplify]: Simplify 0 into 0
3.828 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.830 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
3.830 * [backup-simplify]: Simplify 0 into 0
3.832 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
3.834 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
3.834 * [backup-simplify]: Simplify 0 into 0
3.835 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
3.836 * [backup-simplify]: Simplify (* (* (* (/ 1 n) 2) (sqrt PI)) (sqrt PI)) into (* 2 (/ PI n))
3.836 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
3.836 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.836 * [taylor]: Taking taylor expansion of 2 in n
3.836 * [backup-simplify]: Simplify 2 into 2
3.836 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.836 * [taylor]: Taking taylor expansion of PI in n
3.836 * [backup-simplify]: Simplify PI into PI
3.836 * [taylor]: Taking taylor expansion of n in n
3.836 * [backup-simplify]: Simplify 0 into 0
3.836 * [backup-simplify]: Simplify 1 into 1
3.837 * [backup-simplify]: Simplify (/ PI 1) into PI
3.837 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.837 * [taylor]: Taking taylor expansion of 2 in n
3.837 * [backup-simplify]: Simplify 2 into 2
3.837 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.837 * [taylor]: Taking taylor expansion of PI in n
3.837 * [backup-simplify]: Simplify PI into PI
3.837 * [taylor]: Taking taylor expansion of n in n
3.837 * [backup-simplify]: Simplify 0 into 0
3.837 * [backup-simplify]: Simplify 1 into 1
3.837 * [backup-simplify]: Simplify (/ PI 1) into PI
3.838 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.838 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.839 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.840 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.840 * [backup-simplify]: Simplify 0 into 0
3.841 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.842 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.842 * [backup-simplify]: Simplify 0 into 0
3.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.845 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.845 * [backup-simplify]: Simplify 0 into 0
3.846 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.847 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.847 * [backup-simplify]: Simplify 0 into 0
3.848 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.849 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.849 * [backup-simplify]: Simplify 0 into 0
3.849 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.850 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.851 * [backup-simplify]: Simplify 0 into 0
3.851 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
3.852 * [backup-simplify]: Simplify (* (* (* (/ 1 (- n)) 2) (sqrt PI)) (sqrt PI)) into (* -2 (/ PI n))
3.852 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
3.852 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.852 * [taylor]: Taking taylor expansion of -2 in n
3.852 * [backup-simplify]: Simplify -2 into -2
3.852 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.852 * [taylor]: Taking taylor expansion of PI in n
3.852 * [backup-simplify]: Simplify PI into PI
3.852 * [taylor]: Taking taylor expansion of n in n
3.852 * [backup-simplify]: Simplify 0 into 0
3.852 * [backup-simplify]: Simplify 1 into 1
3.852 * [backup-simplify]: Simplify (/ PI 1) into PI
3.852 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.852 * [taylor]: Taking taylor expansion of -2 in n
3.852 * [backup-simplify]: Simplify -2 into -2
3.852 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.852 * [taylor]: Taking taylor expansion of PI in n
3.852 * [backup-simplify]: Simplify PI into PI
3.852 * [taylor]: Taking taylor expansion of n in n
3.852 * [backup-simplify]: Simplify 0 into 0
3.852 * [backup-simplify]: Simplify 1 into 1
3.853 * [backup-simplify]: Simplify (/ PI 1) into PI
3.853 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.853 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.854 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.854 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
3.854 * [backup-simplify]: Simplify 0 into 0
3.855 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.856 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
3.856 * [backup-simplify]: Simplify 0 into 0
3.856 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.857 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.857 * [backup-simplify]: Simplify 0 into 0
3.858 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.859 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.859 * [backup-simplify]: Simplify 0 into 0
3.860 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.860 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.860 * [backup-simplify]: Simplify 0 into 0
3.861 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.862 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.862 * [backup-simplify]: Simplify 0 into 0
3.863 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
3.863 * * * [progress]: simplifying candidates
3.863 * * * * [progress]: [ 1 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (pow PI 1/2)) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 2 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (pow (sqrt PI) 1)) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 3 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (exp (log (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 4 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (log (exp (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 5 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (* (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 6 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (cbrt (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 7 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (* (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 8 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 9 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (* (sqrt 1) (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 10 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (pow PI (/ 1 2))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 11 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 12 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (fabs (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 13 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (* 1 (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 14 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (posit16->real (real->posit16 (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 15 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (pow PI 1/2)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 16 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (pow (sqrt PI) 1)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 17 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (exp (log (sqrt PI)))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 18 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (log (exp (sqrt PI)))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 19 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI)))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.863 * * * * [progress]: [ 20 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (cbrt (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 21 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI)))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 22 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 23 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (sqrt 1) (sqrt PI))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 24 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (pow PI (/ 1 2))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 25 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 26 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (fabs (sqrt PI))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 27 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* 1 (sqrt PI))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 28 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (posit16->real (real->posit16 (sqrt PI)))) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 29 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (+ (log n) (log 2)) (log (sqrt PI))) (log (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 30 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (log (* n 2)) (log (sqrt PI))) (log (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 31 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log (* (* n 2) (sqrt PI))) (log (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 32 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* (* n 2) (sqrt PI)) (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 33 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* (* n 2) (sqrt PI)) (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 34 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 35 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 36 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 37 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 38 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1/2) (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 39 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 40 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 41 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 42 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 43 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 44 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.864 * * * * [progress]: [ 45 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1/2) (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- (/ k 2)))) (sqrt k)))>
3.864 * * * * [progress]: [ 46 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1/2) (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- (/ k 2)))) (sqrt k)))>
3.865 * * * * [progress]: [ 47 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
3.865 * * * * [progress]: [ 48 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
3.865 * * * * [progress]: [ 49 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
3.865 * * * * [progress]: [ 50 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
3.865 * * * * [progress]: [ 51 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
3.865 * * * * [progress]: [ 52 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))) (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
3.865 * * * * [progress]: [ 53 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
3.865 * * * * [progress]: [ 54 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
3.865 * * * * [progress]: [ 55 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 56 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
3.865 * * * * [progress]: [ 57 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 58 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 59 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 60 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 61 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (+ (+ (log n) (log 2)) (log (sqrt PI))) (log (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 62 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (+ (log (* n 2)) (log (sqrt PI))) (log (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 63 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log (* (* n 2) (sqrt PI))) (log (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 64 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* (* (* n 2) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 65 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* (* (* n 2) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 66 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 67 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 68 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* (* n 2) (sqrt PI)) (* (* n 2) (sqrt PI))) (* (* n 2) (sqrt PI))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 69 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* (* n 2) (sqrt PI)) (sqrt PI))) (cbrt (* (* (* n 2) (sqrt PI)) (sqrt PI)))) (cbrt (* (* (* n 2) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 70 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* (* n 2) (sqrt PI)) (sqrt PI)) (* (* (* n 2) (sqrt PI)) (sqrt PI))) (* (* (* n 2) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 71 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* (* (* n 2) (sqrt PI)) (sqrt PI))) (sqrt (* (* (* n 2) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.865 * * * * [progress]: [ 72 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* (* (* n 2) (sqrt PI)) (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 73 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))) (cbrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 74 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (* (cbrt PI) (cbrt PI)))) (sqrt (cbrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 75 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 76 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt 1)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 77 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 78 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) 1) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 79 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) (* (sqrt PI) (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 80 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* (* (* n 2) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 81 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt PI) (* (* n 2) (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 82 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 83 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 84 / 89 ] 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)))>
3.866 * * * * [progress]: [ 85 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
3.866 * * * * [progress]: [ 86 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
3.866 * * * * [progress]: [ 87 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 88 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.866 * * * * [progress]: [ 89 / 89 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
3.867 * [simplify]: Simplifying:
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* (* (sqrt PI) (sqrt PI)) (sqrt PI))
  (sqrt (* (cbrt PI) (cbrt PI)))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (sqrt 1)
  (sqrt PI)
  (/ 1 2)
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* (* (sqrt PI) (sqrt PI)) (sqrt PI))
  (sqrt (* (cbrt PI) (cbrt PI)))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (sqrt 1)
  (sqrt PI)
  (/ 1 2)
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (* (+ (+ (+ (log n) (log 2)) (log (sqrt PI))) (log (sqrt PI))) (- 1/2 (/ k 2)))
  (* (+ (+ (log (* n 2)) (log (sqrt PI))) (log (sqrt PI))) (- 1/2 (/ k 2)))
  (* (+ (log (* (* n 2) (sqrt PI))) (log (sqrt PI))) (- 1/2 (/ k 2)))
  (* (log (* (* (* n 2) (sqrt PI)) (sqrt PI))) (- 1/2 (/ k 2)))
  (* (log (* (* (* n 2) (sqrt PI)) (sqrt PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1/2)
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (/ k 2))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1)
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1)
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1/2)
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- (/ k 2)))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) 1/2)
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- (/ k 2)))
  (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
  (pow (sqrt PI) (- 1/2 (/ k 2)))
  (log (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))
  (exp (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2)))) (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))))
  (* (* (* n 2) (sqrt PI)) (sqrt PI))
  (* (* (* n 2) (sqrt PI)) (sqrt PI))
  (* (* (* n 2) (sqrt PI)) (sqrt PI))
  (+ (+ (+ (log n) (log 2)) (log (sqrt PI))) (log (sqrt PI)))
  (+ (+ (log (* n 2)) (log (sqrt PI))) (log (sqrt PI)))
  (+ (log (* (* n 2) (sqrt PI))) (log (sqrt PI)))
  (log (* (* (* n 2) (sqrt PI)) (sqrt PI)))
  (exp (* (* (* n 2) (sqrt PI)) (sqrt PI)))
  (* (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))
  (* (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))
  (* (* (* (* (* n 2) (sqrt PI)) (* (* n 2) (sqrt PI))) (* (* n 2) (sqrt PI))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))
  (* (cbrt (* (* (* n 2) (sqrt PI)) (sqrt PI))) (cbrt (* (* (* n 2) (sqrt PI)) (sqrt PI))))
  (cbrt (* (* (* n 2) (sqrt PI)) (sqrt PI)))
  (* (* (* (* (* n 2) (sqrt PI)) (sqrt PI)) (* (* (* n 2) (sqrt PI)) (sqrt PI))) (* (* (* n 2) (sqrt PI)) (sqrt PI)))
  (sqrt (* (* (* n 2) (sqrt PI)) (sqrt PI)))
  (sqrt (* (* (* n 2) (sqrt PI)) (sqrt PI)))
  (* (* (* n 2) (sqrt PI)) (* (cbrt (sqrt PI)) (cbrt (sqrt PI))))
  (* (* (* n 2) (sqrt PI)) (sqrt (* (cbrt PI) (cbrt PI))))
  (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI)))
  (* (* (* n 2) (sqrt PI)) (sqrt 1))
  (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI)))
  (* (* (* n 2) (sqrt PI)) 1)
  (* (sqrt PI) (sqrt PI))
  (real->posit16 (* (* (* n 2) (sqrt PI)) (sqrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) (sqrt PI))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
3.868 * * [simplify]: iteration 0: 149 enodes
3.938 * * [simplify]: iteration 1: 415 enodes
4.181 * * [simplify]: iteration 2: 1518 enodes
4.505 * * [simplify]: iteration complete: 2001 enodes
4.505 * * [simplify]: Extracting #0: cost 46 inf + 0
4.506 * * [simplify]: Extracting #1: cost 333 inf + 44
4.511 * * [simplify]: Extracting #2: cost 580 inf + 6062
4.525 * * [simplify]: Extracting #3: cost 501 inf + 43204
4.556 * * [simplify]: Extracting #4: cost 252 inf + 98747
4.595 * * [simplify]: Extracting #5: cost 75 inf + 157460
4.627 * * [simplify]: Extracting #6: cost 19 inf + 187690
4.692 * * [simplify]: Extracting #7: cost 0 inf + 198681
4.758 * * [simplify]: Extracting #8: cost 0 inf + 198051
4.805 * [simplify]: Simplified to:
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* PI (sqrt PI))
  (fabs (cbrt PI))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  1
  (sqrt PI)
  1/2
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* PI (sqrt PI))
  (fabs (cbrt PI))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  1
  (sqrt PI)
  1/2
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (/ k 2))
  (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2))))
  (* PI (* n 2))
  (pow (* PI (* n 2)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* PI (* n 2)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* PI (* n 2))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (- (/ k 2)))
  (sqrt (* PI (* n 2)))
  (pow (* PI (* n 2)) (- (/ k 2)))
  (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
  (pow (sqrt PI) (- 1/2 (/ k 2)))
  (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
  (exp (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (pow (* PI (* n 2)) (- 1/4 (/ k 4)))
  (pow (* PI (* n 2)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (log (* PI (* n 2)))
  (exp (+ (* PI n) (* PI n)))
  (* (* (* PI PI) PI) (* (* n n) (* n 8)))
  (* 2 (* (* PI n) (* 4 (* (* PI n) (* PI n)))))
  (* 2 (* (* PI n) (* 4 (* (* PI n) (* PI n)))))
  (* (cbrt (* PI (* n 2))) (cbrt (* PI (* n 2))))
  (cbrt (* PI (* n 2)))
  (* 2 (* (* PI n) (* 4 (* (* PI n) (* PI n)))))
  (sqrt (* PI (* n 2)))
  (sqrt (* PI (* n 2)))
  (* n (* 2 (* (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (sqrt PI))))
  (* n (* (* (sqrt PI) 2) (fabs (cbrt PI))))
  (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI)))
  (* (* n 2) (sqrt PI))
  PI
  (real->posit16 (* PI (* n 2)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) (sqrt PI))
  (+ (+ (+ (* (* (* 1/8 (* (log (* 2 PI)) (log (* 2 PI)))) (* k k)) (sqrt (exp (log (* PI (* n 2)))))) (sqrt (exp (log (* PI (* n 2)))))) (+ (* (* (* (log n) k) (* (log n) k)) (* 1/8 (sqrt (exp (log (* PI (* n 2))))))) (* (* (* (log (* 2 PI)) 1/4) (* (log n) (* k k))) (sqrt (exp (log (* PI (* n 2)))))))) (* -1/2 (* k (+ (* (sqrt (exp (log (* PI (* n 2))))) (log n)) (* (log (* 2 PI)) (sqrt (exp (log (* PI (* n 2))))))))))
  (exp (* (log (* PI (* n 2))) (- 1/2 (* 1/2 k))))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))
  (* PI (* n 2))
  (* PI (* n 2))
  (* PI (* n 2))
4.810 * * * [progress]: adding candidates to table
5.255 * * [progress]: iteration 3 / 4
5.255 * * * [progress]: picking best candidate
5.299 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.299 * * * [progress]: localizing error
5.341 * * * [progress]: generating rewritten candidates
5.341 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2 1)
5.342 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2)
5.343 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1)
5.360 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1)
5.379 * * * [progress]: generating series expansions
5.379 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2 1)
5.379 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2)
5.379 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1)
5.380 * [backup-simplify]: Simplify (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n (sqrt PI))) (- 1/2 (* 1/2 k)))
5.380 * [approximate]: Taking taylor expansion of (pow (* 2 (* n (sqrt PI))) (- 1/2 (* 1/2 k))) in (n k) around 0
5.380 * [taylor]: Taking taylor expansion of (pow (* 2 (* n (sqrt PI))) (- 1/2 (* 1/2 k))) in k
5.380 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n (sqrt PI)))))) in k
5.380 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n (sqrt PI))))) in k
5.380 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
5.380 * [taylor]: Taking taylor expansion of 1/2 in k
5.380 * [backup-simplify]: Simplify 1/2 into 1/2
5.380 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
5.380 * [taylor]: Taking taylor expansion of 1/2 in k
5.380 * [backup-simplify]: Simplify 1/2 into 1/2
5.380 * [taylor]: Taking taylor expansion of k in k
5.380 * [backup-simplify]: Simplify 0 into 0
5.380 * [backup-simplify]: Simplify 1 into 1
5.380 * [taylor]: Taking taylor expansion of (log (* 2 (* n (sqrt PI)))) in k
5.380 * [taylor]: Taking taylor expansion of (* 2 (* n (sqrt PI))) in k
5.380 * [taylor]: Taking taylor expansion of 2 in k
5.380 * [backup-simplify]: Simplify 2 into 2
5.380 * [taylor]: Taking taylor expansion of (* n (sqrt PI)) in k
5.380 * [taylor]: Taking taylor expansion of n in k
5.380 * [backup-simplify]: Simplify n into n
5.380 * [taylor]: Taking taylor expansion of (sqrt PI) in k
5.380 * [taylor]: Taking taylor expansion of PI in k
5.380 * [backup-simplify]: Simplify PI into PI
5.381 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.382 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.382 * [backup-simplify]: Simplify (* n (sqrt PI)) into (* n (sqrt PI))
5.382 * [backup-simplify]: Simplify (* 2 (* n (sqrt PI))) into (* 2 (* n (sqrt PI)))
5.383 * [backup-simplify]: Simplify (log (* 2 (* n (sqrt PI)))) into (log (* 2 (* n (sqrt PI))))
5.383 * [backup-simplify]: Simplify (* 1/2 0) into 0
5.384 * [backup-simplify]: Simplify (- 0) into 0
5.384 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.385 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n (sqrt PI))))) into (* 1/2 (log (* 2 (* n (sqrt PI)))))
5.385 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n (sqrt PI)))))) into (pow (* 2 (* n (sqrt PI))) 1/2)
5.385 * [taylor]: Taking taylor expansion of (pow (* 2 (* n (sqrt PI))) (- 1/2 (* 1/2 k))) in n
5.385 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n (sqrt PI)))))) in n
5.385 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n (sqrt PI))))) in n
5.385 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
5.385 * [taylor]: Taking taylor expansion of 1/2 in n
5.385 * [backup-simplify]: Simplify 1/2 into 1/2
5.385 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
5.385 * [taylor]: Taking taylor expansion of 1/2 in n
5.385 * [backup-simplify]: Simplify 1/2 into 1/2
5.385 * [taylor]: Taking taylor expansion of k in n
5.385 * [backup-simplify]: Simplify k into k
5.385 * [taylor]: Taking taylor expansion of (log (* 2 (* n (sqrt PI)))) in n
5.385 * [taylor]: Taking taylor expansion of (* 2 (* n (sqrt PI))) in n
5.385 * [taylor]: Taking taylor expansion of 2 in n
5.385 * [backup-simplify]: Simplify 2 into 2
5.385 * [taylor]: Taking taylor expansion of (* n (sqrt PI)) in n
5.385 * [taylor]: Taking taylor expansion of n in n
5.385 * [backup-simplify]: Simplify 0 into 0
5.386 * [backup-simplify]: Simplify 1 into 1
5.386 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.386 * [taylor]: Taking taylor expansion of PI in n
5.386 * [backup-simplify]: Simplify PI into PI
5.386 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.387 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.388 * [backup-simplify]: Simplify (* 0 (sqrt PI)) into 0
5.388 * [backup-simplify]: Simplify (* 2 0) into 0
5.390 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (sqrt PI))) into (sqrt PI)
5.393 * [backup-simplify]: Simplify (+ (* 2 (sqrt PI)) (* 0 0)) into (* 2 (sqrt PI))
5.394 * [backup-simplify]: Simplify (log (* 2 (sqrt PI))) into (log (* 2 (sqrt PI)))
5.394 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
5.395 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
5.395 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
5.397 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 (sqrt PI)))) into (+ (log (* 2 (sqrt PI))) (log n))
5.399 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n)))
5.405 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n))))
5.405 * [taylor]: Taking taylor expansion of (pow (* 2 (* n (sqrt PI))) (- 1/2 (* 1/2 k))) in n
5.405 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n (sqrt PI)))))) in n
5.405 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n (sqrt PI))))) in n
5.405 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
5.405 * [taylor]: Taking taylor expansion of 1/2 in n
5.405 * [backup-simplify]: Simplify 1/2 into 1/2
5.405 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
5.406 * [taylor]: Taking taylor expansion of 1/2 in n
5.406 * [backup-simplify]: Simplify 1/2 into 1/2
5.406 * [taylor]: Taking taylor expansion of k in n
5.406 * [backup-simplify]: Simplify k into k
5.406 * [taylor]: Taking taylor expansion of (log (* 2 (* n (sqrt PI)))) in n
5.406 * [taylor]: Taking taylor expansion of (* 2 (* n (sqrt PI))) in n
5.406 * [taylor]: Taking taylor expansion of 2 in n
5.406 * [backup-simplify]: Simplify 2 into 2
5.406 * [taylor]: Taking taylor expansion of (* n (sqrt PI)) in n
5.406 * [taylor]: Taking taylor expansion of n in n
5.406 * [backup-simplify]: Simplify 0 into 0
5.406 * [backup-simplify]: Simplify 1 into 1
5.406 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.406 * [taylor]: Taking taylor expansion of PI in n
5.406 * [backup-simplify]: Simplify PI into PI
5.406 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.407 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.408 * [backup-simplify]: Simplify (* 0 (sqrt PI)) into 0
5.408 * [backup-simplify]: Simplify (* 2 0) into 0
5.411 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (sqrt PI))) into (sqrt PI)
5.413 * [backup-simplify]: Simplify (+ (* 2 (sqrt PI)) (* 0 0)) into (* 2 (sqrt PI))
5.415 * [backup-simplify]: Simplify (log (* 2 (sqrt PI))) into (log (* 2 (sqrt PI)))
5.415 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
5.415 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
5.415 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
5.417 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 (sqrt PI)))) into (+ (log (* 2 (sqrt PI))) (log n))
5.419 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n)))
5.421 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n))))
5.421 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n)))) in k
5.422 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n))) in k
5.422 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
5.422 * [taylor]: Taking taylor expansion of 1/2 in k
5.422 * [backup-simplify]: Simplify 1/2 into 1/2
5.422 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
5.422 * [taylor]: Taking taylor expansion of 1/2 in k
5.422 * [backup-simplify]: Simplify 1/2 into 1/2
5.422 * [taylor]: Taking taylor expansion of k in k
5.422 * [backup-simplify]: Simplify 0 into 0
5.422 * [backup-simplify]: Simplify 1 into 1
5.422 * [taylor]: Taking taylor expansion of (+ (log (* 2 (sqrt PI))) (log n)) in k
5.422 * [taylor]: Taking taylor expansion of (log (* 2 (sqrt PI))) in k
5.422 * [taylor]: Taking taylor expansion of (* 2 (sqrt PI)) in k
5.422 * [taylor]: Taking taylor expansion of 2 in k
5.422 * [backup-simplify]: Simplify 2 into 2
5.422 * [taylor]: Taking taylor expansion of (sqrt PI) in k
5.422 * [taylor]: Taking taylor expansion of PI in k
5.422 * [backup-simplify]: Simplify PI into PI
5.423 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.423 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.424 * [backup-simplify]: Simplify (* 2 (sqrt PI)) into (* 2 (sqrt PI))
5.426 * [backup-simplify]: Simplify (log (* 2 (sqrt PI))) into (log (* 2 (sqrt PI)))
5.426 * [taylor]: Taking taylor expansion of (log n) in k
5.426 * [taylor]: Taking taylor expansion of n in k
5.426 * [backup-simplify]: Simplify n into n
5.426 * [backup-simplify]: Simplify (log n) into (log n)
5.427 * [backup-simplify]: Simplify (* 1/2 0) into 0
5.427 * [backup-simplify]: Simplify (- 0) into 0
5.428 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.429 * [backup-simplify]: Simplify (+ (log (* 2 (sqrt PI))) (log n)) into (+ (log (* 2 (sqrt PI))) (log n))
5.431 * [backup-simplify]: Simplify (* 1/2 (+ (log (* 2 (sqrt PI))) (log n))) into (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))
5.433 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) into (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n))))
5.435 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) into (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n))))
5.436 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt PI))) into 0
5.438 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (sqrt PI)))) into 0
5.439 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 (sqrt PI)) (* 0 0))) into 0
5.441 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (sqrt PI)) 1)))) 1) into 0
5.442 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
5.442 * [backup-simplify]: Simplify (- 0) into 0
5.443 * [backup-simplify]: Simplify (+ 0 0) into 0
5.445 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 (sqrt PI)))) into (+ (log (* 2 (sqrt PI))) (log n))
5.447 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log (* 2 (sqrt PI))) (log n)))) into 0
5.450 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
5.450 * [taylor]: Taking taylor expansion of 0 in k
5.450 * [backup-simplify]: Simplify 0 into 0
5.450 * [backup-simplify]: Simplify 0 into 0
5.451 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (sqrt PI))) into 0
5.453 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (sqrt PI)) 1)))) 1) into 0
5.454 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.454 * [backup-simplify]: Simplify (+ 0 0) into 0
5.455 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
5.456 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.456 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.458 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log (* 2 (sqrt PI))) (log n)))) into (- (+ (* 1/2 (log (* 2 (sqrt PI)))) (* 1/2 (log n))))
5.463 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 (sqrt PI)))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log (* 2 (sqrt PI)))) (* 1/2 (log n))) (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n))))))
5.467 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log (* 2 (sqrt PI)))) (* 1/2 (log n))) (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))))) into (* -1 (* (+ (* 1/2 (log (* 2 (sqrt PI)))) (* 1/2 (log n))) (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n))))))
5.469 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.470 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.472 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 (sqrt PI)) (* 0 0)))) into 0
5.476 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (sqrt PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (sqrt PI)) 1)))) 2) into 0
5.477 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
5.477 * [backup-simplify]: Simplify (- 0) into 0
5.478 * [backup-simplify]: Simplify (+ 0 0) into 0
5.480 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 (sqrt PI)))) into (+ (log (* 2 (sqrt PI))) (log n))
5.482 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 (sqrt PI))) (log n))))) into 0
5.484 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log (* 2 (sqrt PI))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.484 * [taylor]: Taking taylor expansion of 0 in k
5.484 * [backup-simplify]: Simplify 0 into 0
5.484 * [backup-simplify]: Simplify 0 into 0
5.484 * [backup-simplify]: Simplify 0 into 0
5.485 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt PI))) into 0
5.486 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0
5.488 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (sqrt PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (sqrt PI)) 1)))) 2) into 0
5.489 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.489 * [backup-simplify]: Simplify (+ 0 0) into 0
5.490 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
5.490 * [backup-simplify]: Simplify (- 0) into 0
5.490 * [backup-simplify]: Simplify (+ 0 0) into 0
5.492 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log (* 2 (sqrt PI))) (log n))))) into 0
5.495 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 (sqrt PI)))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log (* 2 (sqrt PI))) 2)) (* 1/4 (* (log (* 2 (sqrt PI))) (log n))))))
5.499 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log (* 2 (sqrt PI))) 2)) (* 1/4 (* (log (* 2 (sqrt PI))) (log n)))))) into (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log (* 2 (sqrt PI))) 2)) (* 1/4 (* (log (* 2 (sqrt PI))) (log n))))))
5.508 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log (* 2 (sqrt PI))) 2)) (* 1/4 (* (log (* 2 (sqrt PI))) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log (* 2 (sqrt PI)))) (* 1/2 (log n))) (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))))) into (- (+ (* 1/4 (* (log n) (* (log (* 2 (sqrt PI))) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2))))) (+ (* 1/8 (* (pow (log n) 2) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2)))) (+ (* 1/8 (* (pow (log (* 2 (sqrt PI))) 2) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2)))) (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (* (log n) k))) (* 1/2 (* (log (* 2 (sqrt PI))) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) k)))))
5.509 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) (sqrt PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (* (/ 1 n) (sqrt PI))) (- 1/2 (* 1/2 (/ 1 k))))
5.509 * [approximate]: Taking taylor expansion of (pow (* 2 (* (/ 1 n) (sqrt PI))) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
5.509 * [taylor]: Taking taylor expansion of (pow (* 2 (* (/ 1 n) (sqrt PI))) (- 1/2 (* 1/2 (/ 1 k)))) in k
5.509 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (* (/ 1 n) (sqrt PI)))))) in k
5.509 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (* (/ 1 n) (sqrt PI))))) in k
5.509 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
5.509 * [taylor]: Taking taylor expansion of 1/2 in k
5.509 * [backup-simplify]: Simplify 1/2 into 1/2
5.509 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.509 * [taylor]: Taking taylor expansion of 1/2 in k
5.509 * [backup-simplify]: Simplify 1/2 into 1/2
5.509 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.509 * [taylor]: Taking taylor expansion of k in k
5.509 * [backup-simplify]: Simplify 0 into 0
5.509 * [backup-simplify]: Simplify 1 into 1
5.509 * [backup-simplify]: Simplify (/ 1 1) into 1
5.509 * [taylor]: Taking taylor expansion of (log (* 2 (* (/ 1 n) (sqrt PI)))) in k
5.509 * [taylor]: Taking taylor expansion of (* 2 (* (/ 1 n) (sqrt PI))) in k
5.509 * [taylor]: Taking taylor expansion of 2 in k
5.509 * [backup-simplify]: Simplify 2 into 2
5.509 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in k
5.509 * [taylor]: Taking taylor expansion of (/ 1 n) in k
5.509 * [taylor]: Taking taylor expansion of n in k
5.509 * [backup-simplify]: Simplify n into n
5.509 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
5.509 * [taylor]: Taking taylor expansion of (sqrt PI) in k
5.509 * [taylor]: Taking taylor expansion of PI in k
5.509 * [backup-simplify]: Simplify PI into PI
5.510 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.510 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.510 * [backup-simplify]: Simplify (* (/ 1 n) (sqrt PI)) into (* (/ 1 n) (sqrt PI))
5.511 * [backup-simplify]: Simplify (* 2 (* (/ 1 n) (sqrt PI))) into (* 2 (* (/ 1 n) (sqrt PI)))
5.511 * [backup-simplify]: Simplify (log (* 2 (* (/ 1 n) (sqrt PI)))) into (log (* 2 (* (/ 1 n) (sqrt PI))))
5.511 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.512 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.512 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.512 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (* (/ 1 n) (sqrt PI))))) into (* -1/2 (log (* 2 (* (/ 1 n) (sqrt PI)))))
5.513 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (* (/ 1 n) (sqrt PI)))))) into (exp (* (log (* 2 (* (/ 1 n) (sqrt PI)))) (- 1/2 (* 1/2 (/ 1 k)))))
5.513 * [taylor]: Taking taylor expansion of (pow (* 2 (* (/ 1 n) (sqrt PI))) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.513 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (* (/ 1 n) (sqrt PI)))))) in n
5.513 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (* (/ 1 n) (sqrt PI))))) in n
5.513 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.513 * [taylor]: Taking taylor expansion of 1/2 in n
5.513 * [backup-simplify]: Simplify 1/2 into 1/2
5.513 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.513 * [taylor]: Taking taylor expansion of 1/2 in n
5.513 * [backup-simplify]: Simplify 1/2 into 1/2
5.513 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.513 * [taylor]: Taking taylor expansion of k in n
5.513 * [backup-simplify]: Simplify k into k
5.513 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.513 * [taylor]: Taking taylor expansion of (log (* 2 (* (/ 1 n) (sqrt PI)))) in n
5.513 * [taylor]: Taking taylor expansion of (* 2 (* (/ 1 n) (sqrt PI))) in n
5.513 * [taylor]: Taking taylor expansion of 2 in n
5.513 * [backup-simplify]: Simplify 2 into 2
5.513 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in n
5.513 * [taylor]: Taking taylor expansion of (/ 1 n) in n
5.513 * [taylor]: Taking taylor expansion of n in n
5.513 * [backup-simplify]: Simplify 0 into 0
5.513 * [backup-simplify]: Simplify 1 into 1
5.513 * [backup-simplify]: Simplify (/ 1 1) into 1
5.513 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.513 * [taylor]: Taking taylor expansion of PI in n
5.513 * [backup-simplify]: Simplify PI into PI
5.514 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.514 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.515 * [backup-simplify]: Simplify (* 1 (sqrt PI)) into (sqrt PI)
5.515 * [backup-simplify]: Simplify (* 2 (sqrt PI)) into (* 2 (sqrt PI))
5.517 * [backup-simplify]: Simplify (log (* 2 (sqrt PI))) into (log (* 2 (sqrt PI)))
5.517 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.517 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.517 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 (sqrt PI)))) into (- (log (* 2 (sqrt PI))) (log n))
5.521 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))
5.523 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n))))
5.523 * [taylor]: Taking taylor expansion of (pow (* 2 (* (/ 1 n) (sqrt PI))) (- 1/2 (* 1/2 (/ 1 k)))) in n
5.523 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (* (/ 1 n) (sqrt PI)))))) in n
5.523 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (* (/ 1 n) (sqrt PI))))) in n
5.523 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
5.523 * [taylor]: Taking taylor expansion of 1/2 in n
5.523 * [backup-simplify]: Simplify 1/2 into 1/2
5.523 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.523 * [taylor]: Taking taylor expansion of 1/2 in n
5.523 * [backup-simplify]: Simplify 1/2 into 1/2
5.523 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.523 * [taylor]: Taking taylor expansion of k in n
5.523 * [backup-simplify]: Simplify k into k
5.523 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.523 * [taylor]: Taking taylor expansion of (log (* 2 (* (/ 1 n) (sqrt PI)))) in n
5.523 * [taylor]: Taking taylor expansion of (* 2 (* (/ 1 n) (sqrt PI))) in n
5.523 * [taylor]: Taking taylor expansion of 2 in n
5.523 * [backup-simplify]: Simplify 2 into 2
5.523 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in n
5.524 * [taylor]: Taking taylor expansion of (/ 1 n) in n
5.524 * [taylor]: Taking taylor expansion of n in n
5.524 * [backup-simplify]: Simplify 0 into 0
5.524 * [backup-simplify]: Simplify 1 into 1
5.524 * [backup-simplify]: Simplify (/ 1 1) into 1
5.524 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.524 * [taylor]: Taking taylor expansion of PI in n
5.524 * [backup-simplify]: Simplify PI into PI
5.524 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.525 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.526 * [backup-simplify]: Simplify (* 1 (sqrt PI)) into (sqrt PI)
5.527 * [backup-simplify]: Simplify (* 2 (sqrt PI)) into (* 2 (sqrt PI))
5.529 * [backup-simplify]: Simplify (log (* 2 (sqrt PI))) into (log (* 2 (sqrt PI)))
5.529 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.529 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
5.529 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
5.534 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 (sqrt PI)))) into (- (log (* 2 (sqrt PI))) (log n))
5.536 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))
5.538 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n))))
5.538 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))) in k
5.538 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n))) in k
5.538 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
5.539 * [taylor]: Taking taylor expansion of 1/2 in k
5.539 * [backup-simplify]: Simplify 1/2 into 1/2
5.539 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.539 * [taylor]: Taking taylor expansion of 1/2 in k
5.539 * [backup-simplify]: Simplify 1/2 into 1/2
5.539 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.539 * [taylor]: Taking taylor expansion of k in k
5.539 * [backup-simplify]: Simplify 0 into 0
5.539 * [backup-simplify]: Simplify 1 into 1
5.539 * [backup-simplify]: Simplify (/ 1 1) into 1
5.539 * [taylor]: Taking taylor expansion of (- (log (* 2 (sqrt PI))) (log n)) in k
5.539 * [taylor]: Taking taylor expansion of (log (* 2 (sqrt PI))) in k
5.539 * [taylor]: Taking taylor expansion of (* 2 (sqrt PI)) in k
5.539 * [taylor]: Taking taylor expansion of 2 in k
5.539 * [backup-simplify]: Simplify 2 into 2
5.539 * [taylor]: Taking taylor expansion of (sqrt PI) in k
5.539 * [taylor]: Taking taylor expansion of PI in k
5.539 * [backup-simplify]: Simplify PI into PI
5.539 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.540 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.541 * [backup-simplify]: Simplify (* 2 (sqrt PI)) into (* 2 (sqrt PI))
5.542 * [backup-simplify]: Simplify (log (* 2 (sqrt PI))) into (log (* 2 (sqrt PI)))
5.542 * [taylor]: Taking taylor expansion of (log n) in k
5.542 * [taylor]: Taking taylor expansion of n in k
5.542 * [backup-simplify]: Simplify n into n
5.542 * [backup-simplify]: Simplify (log n) into (log n)
5.542 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.542 * [backup-simplify]: Simplify (- 1/2) into -1/2
5.542 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
5.543 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.544 * [backup-simplify]: Simplify (+ (log (* 2 (sqrt PI))) (- (log n))) into (- (log (* 2 (sqrt PI))) (log n))
5.545 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 (sqrt PI))) (log n))) into (* -1/2 (- (log (* 2 (sqrt PI))) (log n)))
5.546 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n))))
5.547 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n))))
5.547 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.548 * [backup-simplify]: Simplify (+ (* 1 0) (* 0 (sqrt PI))) into 0
5.548 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (sqrt PI))) into 0
5.550 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (sqrt PI)) 1)))) 1) into 0
5.550 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.550 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
5.550 * [backup-simplify]: Simplify (- 0) into 0
5.551 * [backup-simplify]: Simplify (+ 0 0) into 0
5.552 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 (sqrt PI)))) into (- (log (* 2 (sqrt PI))) (log n))
5.553 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 (sqrt PI))) (log n)))) into 0
5.554 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
5.555 * [taylor]: Taking taylor expansion of 0 in k
5.555 * [backup-simplify]: Simplify 0 into 0
5.555 * [backup-simplify]: Simplify 0 into 0
5.555 * [backup-simplify]: Simplify 0 into 0
5.555 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt PI))) into 0
5.556 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.557 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0
5.557 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0
5.560 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (sqrt PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (sqrt PI)) 1)))) 2) into 0
5.560 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.560 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
5.561 * [backup-simplify]: Simplify (- 0) into 0
5.561 * [backup-simplify]: Simplify (+ 0 0) into 0
5.562 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 (sqrt PI)))) into (- (log (* 2 (sqrt PI))) (log n))
5.563 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 (sqrt PI))) (log n))))) into 0
5.565 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.565 * [taylor]: Taking taylor expansion of 0 in k
5.565 * [backup-simplify]: Simplify 0 into 0
5.565 * [backup-simplify]: Simplify 0 into 0
5.565 * [backup-simplify]: Simplify 0 into 0
5.565 * [backup-simplify]: Simplify 0 into 0
5.566 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.567 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.568 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.569 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.575 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (sqrt PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (sqrt PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (sqrt PI)) 1)))) 6) into 0
5.575 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.577 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
5.577 * [backup-simplify]: Simplify (- 0) into 0
5.577 * [backup-simplify]: Simplify (+ 0 0) into 0
5.579 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 (sqrt PI)))) into (- (log (* 2 (sqrt PI))) (log n))
5.582 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 (sqrt PI))) (log n)))))) into 0
5.586 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 (sqrt PI))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.586 * [taylor]: Taking taylor expansion of 0 in k
5.586 * [backup-simplify]: Simplify 0 into 0
5.586 * [backup-simplify]: Simplify 0 into 0
5.588 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 (sqrt PI))) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 (sqrt PI))) (log (/ 1 n)))))
5.589 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) (sqrt PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (* (/ 1 n) (sqrt PI))) (+ (* 1/2 (/ 1 k)) 1/2))
5.589 * [approximate]: Taking taylor expansion of (pow (* -2 (* (/ 1 n) (sqrt PI))) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
5.589 * [taylor]: Taking taylor expansion of (pow (* -2 (* (/ 1 n) (sqrt PI))) (+ (* 1/2 (/ 1 k)) 1/2)) in k
5.589 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (* (/ 1 n) (sqrt PI)))))) in k
5.589 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (* (/ 1 n) (sqrt PI))))) in k
5.589 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
5.589 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.589 * [taylor]: Taking taylor expansion of 1/2 in k
5.589 * [backup-simplify]: Simplify 1/2 into 1/2
5.589 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.589 * [taylor]: Taking taylor expansion of k in k
5.589 * [backup-simplify]: Simplify 0 into 0
5.589 * [backup-simplify]: Simplify 1 into 1
5.590 * [backup-simplify]: Simplify (/ 1 1) into 1
5.590 * [taylor]: Taking taylor expansion of 1/2 in k
5.590 * [backup-simplify]: Simplify 1/2 into 1/2
5.590 * [taylor]: Taking taylor expansion of (log (* -2 (* (/ 1 n) (sqrt PI)))) in k
5.590 * [taylor]: Taking taylor expansion of (* -2 (* (/ 1 n) (sqrt PI))) in k
5.590 * [taylor]: Taking taylor expansion of -2 in k
5.590 * [backup-simplify]: Simplify -2 into -2
5.590 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in k
5.590 * [taylor]: Taking taylor expansion of (/ 1 n) in k
5.590 * [taylor]: Taking taylor expansion of n in k
5.590 * [backup-simplify]: Simplify n into n
5.590 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
5.590 * [taylor]: Taking taylor expansion of (sqrt PI) in k
5.590 * [taylor]: Taking taylor expansion of PI in k
5.590 * [backup-simplify]: Simplify PI into PI
5.590 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.591 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.591 * [backup-simplify]: Simplify (* (/ 1 n) (sqrt PI)) into (* (/ 1 n) (sqrt PI))
5.592 * [backup-simplify]: Simplify (* -2 (* (/ 1 n) (sqrt PI))) into (* -2 (* (/ 1 n) (sqrt PI)))
5.592 * [backup-simplify]: Simplify (log (* -2 (* (/ 1 n) (sqrt PI)))) into (log (* -2 (* (/ 1 n) (sqrt PI))))
5.592 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.593 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.593 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (* (/ 1 n) (sqrt PI))))) into (* 1/2 (log (* -2 (* (/ 1 n) (sqrt PI)))))
5.593 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (* (/ 1 n) (sqrt PI)))))) into (pow (* -2 (* (/ 1 n) (sqrt PI))) (+ (* 1/2 (/ 1 k)) 1/2))
5.593 * [taylor]: Taking taylor expansion of (pow (* -2 (* (/ 1 n) (sqrt PI))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.593 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (* (/ 1 n) (sqrt PI)))))) in n
5.593 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (* (/ 1 n) (sqrt PI))))) in n
5.593 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.593 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.593 * [taylor]: Taking taylor expansion of 1/2 in n
5.593 * [backup-simplify]: Simplify 1/2 into 1/2
5.593 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.594 * [taylor]: Taking taylor expansion of k in n
5.594 * [backup-simplify]: Simplify k into k
5.594 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.594 * [taylor]: Taking taylor expansion of 1/2 in n
5.594 * [backup-simplify]: Simplify 1/2 into 1/2
5.594 * [taylor]: Taking taylor expansion of (log (* -2 (* (/ 1 n) (sqrt PI)))) in n
5.594 * [taylor]: Taking taylor expansion of (* -2 (* (/ 1 n) (sqrt PI))) in n
5.594 * [taylor]: Taking taylor expansion of -2 in n
5.594 * [backup-simplify]: Simplify -2 into -2
5.594 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in n
5.594 * [taylor]: Taking taylor expansion of (/ 1 n) in n
5.594 * [taylor]: Taking taylor expansion of n in n
5.594 * [backup-simplify]: Simplify 0 into 0
5.594 * [backup-simplify]: Simplify 1 into 1
5.594 * [backup-simplify]: Simplify (/ 1 1) into 1
5.594 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.594 * [taylor]: Taking taylor expansion of PI in n
5.594 * [backup-simplify]: Simplify PI into PI
5.594 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.595 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.595 * [backup-simplify]: Simplify (* 1 (sqrt PI)) into (sqrt PI)
5.596 * [backup-simplify]: Simplify (* -2 (sqrt PI)) into (* -2 (sqrt PI))
5.597 * [backup-simplify]: Simplify (log (* -2 (sqrt PI))) into (log (* -2 (sqrt PI)))
5.597 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.597 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.598 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 (sqrt PI)))) into (- (log (* -2 (sqrt PI))) (log n))
5.600 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))
5.601 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n))))
5.601 * [taylor]: Taking taylor expansion of (pow (* -2 (* (/ 1 n) (sqrt PI))) (+ (* 1/2 (/ 1 k)) 1/2)) in n
5.601 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (* (/ 1 n) (sqrt PI)))))) in n
5.601 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (* (/ 1 n) (sqrt PI))))) in n
5.601 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
5.601 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
5.601 * [taylor]: Taking taylor expansion of 1/2 in n
5.601 * [backup-simplify]: Simplify 1/2 into 1/2
5.601 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.601 * [taylor]: Taking taylor expansion of k in n
5.601 * [backup-simplify]: Simplify k into k
5.601 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.601 * [taylor]: Taking taylor expansion of 1/2 in n
5.601 * [backup-simplify]: Simplify 1/2 into 1/2
5.601 * [taylor]: Taking taylor expansion of (log (* -2 (* (/ 1 n) (sqrt PI)))) in n
5.601 * [taylor]: Taking taylor expansion of (* -2 (* (/ 1 n) (sqrt PI))) in n
5.601 * [taylor]: Taking taylor expansion of -2 in n
5.601 * [backup-simplify]: Simplify -2 into -2
5.601 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in n
5.601 * [taylor]: Taking taylor expansion of (/ 1 n) in n
5.601 * [taylor]: Taking taylor expansion of n in n
5.601 * [backup-simplify]: Simplify 0 into 0
5.601 * [backup-simplify]: Simplify 1 into 1
5.601 * [backup-simplify]: Simplify (/ 1 1) into 1
5.601 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.601 * [taylor]: Taking taylor expansion of PI in n
5.601 * [backup-simplify]: Simplify PI into PI
5.602 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.602 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.603 * [backup-simplify]: Simplify (* 1 (sqrt PI)) into (sqrt PI)
5.603 * [backup-simplify]: Simplify (* -2 (sqrt PI)) into (* -2 (sqrt PI))
5.604 * [backup-simplify]: Simplify (log (* -2 (sqrt PI))) into (log (* -2 (sqrt PI)))
5.604 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
5.604 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
5.606 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 (sqrt PI)))) into (- (log (* -2 (sqrt PI))) (log n))
5.607 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))
5.608 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n))))
5.609 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))) in k
5.609 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n))) in k
5.609 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
5.609 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
5.609 * [taylor]: Taking taylor expansion of 1/2 in k
5.609 * [backup-simplify]: Simplify 1/2 into 1/2
5.609 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.609 * [taylor]: Taking taylor expansion of k in k
5.609 * [backup-simplify]: Simplify 0 into 0
5.609 * [backup-simplify]: Simplify 1 into 1
5.609 * [backup-simplify]: Simplify (/ 1 1) into 1
5.609 * [taylor]: Taking taylor expansion of 1/2 in k
5.609 * [backup-simplify]: Simplify 1/2 into 1/2
5.609 * [taylor]: Taking taylor expansion of (- (log (* -2 (sqrt PI))) (log n)) in k
5.609 * [taylor]: Taking taylor expansion of (log (* -2 (sqrt PI))) in k
5.609 * [taylor]: Taking taylor expansion of (* -2 (sqrt PI)) in k
5.609 * [taylor]: Taking taylor expansion of -2 in k
5.609 * [backup-simplify]: Simplify -2 into -2
5.609 * [taylor]: Taking taylor expansion of (sqrt PI) in k
5.609 * [taylor]: Taking taylor expansion of PI in k
5.609 * [backup-simplify]: Simplify PI into PI
5.609 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.610 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.611 * [backup-simplify]: Simplify (* -2 (sqrt PI)) into (* -2 (sqrt PI))
5.612 * [backup-simplify]: Simplify (log (* -2 (sqrt PI))) into (log (* -2 (sqrt PI)))
5.612 * [taylor]: Taking taylor expansion of (log n) in k
5.612 * [taylor]: Taking taylor expansion of n in k
5.612 * [backup-simplify]: Simplify n into n
5.612 * [backup-simplify]: Simplify (log n) into (log n)
5.612 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.612 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
5.612 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.613 * [backup-simplify]: Simplify (+ (log (* -2 (sqrt PI))) (- (log n))) into (- (log (* -2 (sqrt PI))) (log n))
5.614 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 (sqrt PI))) (log n))) into (* 1/2 (- (log (* -2 (sqrt PI))) (log n)))
5.615 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n))))
5.617 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n))))
5.617 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.618 * [backup-simplify]: Simplify (+ (* 1 0) (* 0 (sqrt PI))) into 0
5.618 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 (sqrt PI))) into 0
5.620 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 (sqrt PI)) 1)))) 1) into 0
5.620 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.621 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
5.621 * [backup-simplify]: Simplify (+ 0 0) into 0
5.623 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 (sqrt PI)))) into (- (log (* -2 (sqrt PI))) (log n))
5.625 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 (sqrt PI))) (log n)))) into 0
5.628 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
5.628 * [taylor]: Taking taylor expansion of 0 in k
5.628 * [backup-simplify]: Simplify 0 into 0
5.628 * [backup-simplify]: Simplify 0 into 0
5.628 * [backup-simplify]: Simplify 0 into 0
5.629 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt PI))) into 0
5.630 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.631 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0
5.632 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0
5.636 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 (sqrt PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 (sqrt PI)) 1)))) 2) into 0
5.637 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.637 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
5.638 * [backup-simplify]: Simplify (+ 0 0) into 0
5.640 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 (sqrt PI)))) into (- (log (* -2 (sqrt PI))) (log n))
5.645 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 (sqrt PI))) (log n))))) into 0
5.649 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.649 * [taylor]: Taking taylor expansion of 0 in k
5.649 * [backup-simplify]: Simplify 0 into 0
5.649 * [backup-simplify]: Simplify 0 into 0
5.649 * [backup-simplify]: Simplify 0 into 0
5.649 * [backup-simplify]: Simplify 0 into 0
5.650 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.651 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.653 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.654 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.661 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 (sqrt PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 (sqrt PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 (sqrt PI)) 1)))) 6) into 0
5.662 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.663 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
5.663 * [backup-simplify]: Simplify (+ 0 0) into 0
5.666 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 (sqrt PI)))) into (- (log (* -2 (sqrt PI))) (log n))
5.668 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 (sqrt PI))) (log n)))))) into 0
5.672 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 (sqrt PI))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.672 * [taylor]: Taking taylor expansion of 0 in k
5.672 * [backup-simplify]: Simplify 0 into 0
5.672 * [backup-simplify]: Simplify 0 into 0
5.674 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 (sqrt PI))) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 (sqrt PI))) (log (/ -1 n)))))
5.674 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1)
5.675 * [backup-simplify]: Simplify (* (* n 2) (sqrt PI)) into (* 2 (* n (sqrt PI)))
5.675 * [approximate]: Taking taylor expansion of (* 2 (* n (sqrt PI))) in (n) around 0
5.675 * [taylor]: Taking taylor expansion of (* 2 (* n (sqrt PI))) in n
5.675 * [taylor]: Taking taylor expansion of 2 in n
5.675 * [backup-simplify]: Simplify 2 into 2
5.675 * [taylor]: Taking taylor expansion of (* n (sqrt PI)) in n
5.675 * [taylor]: Taking taylor expansion of n in n
5.675 * [backup-simplify]: Simplify 0 into 0
5.675 * [backup-simplify]: Simplify 1 into 1
5.675 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.675 * [taylor]: Taking taylor expansion of PI in n
5.675 * [backup-simplify]: Simplify PI into PI
5.676 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.676 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.677 * [taylor]: Taking taylor expansion of (* 2 (* n (sqrt PI))) in n
5.677 * [taylor]: Taking taylor expansion of 2 in n
5.677 * [backup-simplify]: Simplify 2 into 2
5.677 * [taylor]: Taking taylor expansion of (* n (sqrt PI)) in n
5.677 * [taylor]: Taking taylor expansion of n in n
5.677 * [backup-simplify]: Simplify 0 into 0
5.677 * [backup-simplify]: Simplify 1 into 1
5.677 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.677 * [taylor]: Taking taylor expansion of PI in n
5.677 * [backup-simplify]: Simplify PI into PI
5.677 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.678 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.679 * [backup-simplify]: Simplify (* 0 (sqrt PI)) into 0
5.679 * [backup-simplify]: Simplify (* 2 0) into 0
5.679 * [backup-simplify]: Simplify 0 into 0
5.682 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (sqrt PI))) into (sqrt PI)
5.684 * [backup-simplify]: Simplify (+ (* 2 (sqrt PI)) (* 0 0)) into (* 2 (sqrt PI))
5.685 * [backup-simplify]: Simplify (* 2 (sqrt PI)) into (* 2 (sqrt PI))
5.686 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt PI))) into 0
5.688 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (sqrt PI)))) into 0
5.689 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 (sqrt PI)) (* 0 0))) into 0
5.689 * [backup-simplify]: Simplify 0 into 0
5.690 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.693 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 (sqrt PI)) (* 0 0)))) into 0
5.693 * [backup-simplify]: Simplify 0 into 0
5.695 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.697 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))) into 0
5.698 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (sqrt PI)) (* 0 0))))) into 0
5.698 * [backup-simplify]: Simplify 0 into 0
5.700 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))))) into 0
5.703 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (sqrt PI)) (* 0 0)))))) into 0
5.703 * [backup-simplify]: Simplify 0 into 0
5.705 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.707 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))))) into 0
5.709 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (sqrt PI)) (* 0 0))))))) into 0
5.709 * [backup-simplify]: Simplify 0 into 0
5.710 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.712 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))))))) into 0
5.713 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (sqrt PI)) (* 0 0)))))))) into 0
5.713 * [backup-simplify]: Simplify 0 into 0
5.714 * [backup-simplify]: Simplify (* (* 2 (sqrt PI)) n) into (* 2 (* n (sqrt PI)))
5.714 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) (sqrt PI)) into (* 2 (* (/ 1 n) (sqrt PI)))
5.714 * [approximate]: Taking taylor expansion of (* 2 (* (/ 1 n) (sqrt PI))) in (n) around 0
5.714 * [taylor]: Taking taylor expansion of (* 2 (* (/ 1 n) (sqrt PI))) in n
5.714 * [taylor]: Taking taylor expansion of 2 in n
5.714 * [backup-simplify]: Simplify 2 into 2
5.714 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in n
5.714 * [taylor]: Taking taylor expansion of (/ 1 n) in n
5.714 * [taylor]: Taking taylor expansion of n in n
5.714 * [backup-simplify]: Simplify 0 into 0
5.714 * [backup-simplify]: Simplify 1 into 1
5.715 * [backup-simplify]: Simplify (/ 1 1) into 1
5.715 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.715 * [taylor]: Taking taylor expansion of PI in n
5.715 * [backup-simplify]: Simplify PI into PI
5.715 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.715 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.715 * [taylor]: Taking taylor expansion of (* 2 (* (/ 1 n) (sqrt PI))) in n
5.715 * [taylor]: Taking taylor expansion of 2 in n
5.715 * [backup-simplify]: Simplify 2 into 2
5.715 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in n
5.715 * [taylor]: Taking taylor expansion of (/ 1 n) in n
5.715 * [taylor]: Taking taylor expansion of n in n
5.715 * [backup-simplify]: Simplify 0 into 0
5.715 * [backup-simplify]: Simplify 1 into 1
5.716 * [backup-simplify]: Simplify (/ 1 1) into 1
5.716 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.716 * [taylor]: Taking taylor expansion of PI in n
5.716 * [backup-simplify]: Simplify PI into PI
5.716 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.716 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.717 * [backup-simplify]: Simplify (* 1 (sqrt PI)) into (sqrt PI)
5.718 * [backup-simplify]: Simplify (* 2 (sqrt PI)) into (* 2 (sqrt PI))
5.718 * [backup-simplify]: Simplify (* 2 (sqrt PI)) into (* 2 (sqrt PI))
5.719 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.720 * [backup-simplify]: Simplify (+ (* 1 0) (* 0 (sqrt PI))) into 0
5.720 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (sqrt PI))) into 0
5.720 * [backup-simplify]: Simplify 0 into 0
5.721 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt PI))) into 0
5.721 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.722 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0
5.723 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0
5.723 * [backup-simplify]: Simplify 0 into 0
5.724 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.724 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.725 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.726 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.726 * [backup-simplify]: Simplify 0 into 0
5.727 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.727 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.728 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))) into 0
5.730 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))) into 0
5.730 * [backup-simplify]: Simplify 0 into 0
5.731 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.731 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.732 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))))) into 0
5.733 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))))) into 0
5.733 * [backup-simplify]: Simplify 0 into 0
5.734 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.735 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.736 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))))) into 0
5.737 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))))) into 0
5.737 * [backup-simplify]: Simplify 0 into 0
5.738 * [backup-simplify]: Simplify (* (* 2 (sqrt PI)) (/ 1 (/ 1 n))) into (* 2 (* n (sqrt PI)))
5.738 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) (sqrt PI)) into (* -2 (* (/ 1 n) (sqrt PI)))
5.738 * [approximate]: Taking taylor expansion of (* -2 (* (/ 1 n) (sqrt PI))) in (n) around 0
5.738 * [taylor]: Taking taylor expansion of (* -2 (* (/ 1 n) (sqrt PI))) in n
5.738 * [taylor]: Taking taylor expansion of -2 in n
5.738 * [backup-simplify]: Simplify -2 into -2
5.738 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in n
5.738 * [taylor]: Taking taylor expansion of (/ 1 n) in n
5.738 * [taylor]: Taking taylor expansion of n in n
5.738 * [backup-simplify]: Simplify 0 into 0
5.739 * [backup-simplify]: Simplify 1 into 1
5.739 * [backup-simplify]: Simplify (/ 1 1) into 1
5.739 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.739 * [taylor]: Taking taylor expansion of PI in n
5.739 * [backup-simplify]: Simplify PI into PI
5.739 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.740 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.740 * [taylor]: Taking taylor expansion of (* -2 (* (/ 1 n) (sqrt PI))) in n
5.740 * [taylor]: Taking taylor expansion of -2 in n
5.740 * [backup-simplify]: Simplify -2 into -2
5.740 * [taylor]: Taking taylor expansion of (* (/ 1 n) (sqrt PI)) in n
5.740 * [taylor]: Taking taylor expansion of (/ 1 n) in n
5.740 * [taylor]: Taking taylor expansion of n in n
5.740 * [backup-simplify]: Simplify 0 into 0
5.740 * [backup-simplify]: Simplify 1 into 1
5.740 * [backup-simplify]: Simplify (/ 1 1) into 1
5.740 * [taylor]: Taking taylor expansion of (sqrt PI) in n
5.740 * [taylor]: Taking taylor expansion of PI in n
5.740 * [backup-simplify]: Simplify PI into PI
5.740 * [backup-simplify]: Simplify (sqrt PI) into (sqrt PI)
5.741 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt PI))) into 0
5.742 * [backup-simplify]: Simplify (* 1 (sqrt PI)) into (sqrt PI)
5.742 * [backup-simplify]: Simplify (* -2 (sqrt PI)) into (* -2 (sqrt PI))
5.743 * [backup-simplify]: Simplify (* -2 (sqrt PI)) into (* -2 (sqrt PI))
5.744 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.745 * [backup-simplify]: Simplify (+ (* 1 0) (* 0 (sqrt PI))) into 0
5.746 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 (sqrt PI))) into 0
5.746 * [backup-simplify]: Simplify 0 into 0
5.747 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt PI))) into 0
5.748 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.750 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0
5.751 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 (sqrt PI)))) into 0
5.751 * [backup-simplify]: Simplify 0 into 0
5.752 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.753 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.755 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.756 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))) into 0
5.756 * [backup-simplify]: Simplify 0 into 0
5.758 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.759 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.760 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))) into 0
5.762 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))) into 0
5.762 * [backup-simplify]: Simplify 0 into 0
5.764 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.765 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.766 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))))) into 0
5.768 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI))))))) into 0
5.768 * [backup-simplify]: Simplify 0 into 0
5.770 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt PI))) into 0
5.771 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.773 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))))) into 0
5.778 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt PI)))))))) into 0
5.779 * [backup-simplify]: Simplify 0 into 0
5.780 * [backup-simplify]: Simplify (* (* -2 (sqrt PI)) (/ 1 (/ 1 (- n)))) into (* 2 (* n (sqrt PI)))
5.780 * * * [progress]: simplifying candidates
5.780 * * * * [progress]: [ 1 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (pow PI 1/2) (- 1/2 (/ k 2)))) (sqrt k)))>
5.780 * * * * [progress]: [ 2 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (pow (sqrt PI) 1) (- 1/2 (/ k 2)))) (sqrt k)))>
5.780 * * * * [progress]: [ 3 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (exp (log (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
5.780 * * * * [progress]: [ 4 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (log (exp (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
5.780 * * * * [progress]: [ 5 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 6 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (cbrt (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 7 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 8 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 9 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* (sqrt 1) (sqrt PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 10 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (pow PI (/ 1 2)) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 11 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 12 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (fabs (sqrt PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 13 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* 1 (sqrt PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 14 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (posit16->real (real->posit16 (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 15 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (pow PI 1/2)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 16 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (pow (sqrt PI) 1)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 17 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (exp (log (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 18 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (log (exp (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.781 * * * * [progress]: [ 19 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (* (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 20 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (cbrt (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 21 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (* (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 22 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 23 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (* (sqrt 1) (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 24 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (pow PI (/ 1 2))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 25 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 26 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (fabs (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 27 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (* 1 (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 28 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (posit16->real (real->posit16 (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 29 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (+ (+ (log n) (log 2)) (log (sqrt PI))) (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 30 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (+ (log (* n 2)) (log (sqrt PI))) (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 31 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (log (* (* n 2) (sqrt PI))) (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.782 * * * * [progress]: [ 32 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (log (* (* n 2) (sqrt PI))) (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 33 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (* 1 (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 34 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (* 1 (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 35 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (* 1 (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 36 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ (pow (* (* n 2) (sqrt PI)) 1/2) (pow (* (* n 2) (sqrt PI)) (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 37 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 38 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 39 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) 1) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 40 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 41 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 42 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) 1) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.783 * * * * [progress]: [ 43 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* (* n 2) (sqrt PI)) 1/2) (pow (* (* n 2) (sqrt PI)) (- (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 44 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* (* n 2) (sqrt PI)) 1/2) (pow (* (* n 2) (sqrt PI)) (- (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 45 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n 2) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 46 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) 1) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 47 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (log (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 48 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (log (exp (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 49 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (* (cbrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 50 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (* (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))) (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 51 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (sqrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 52 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (* 1 (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 53 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* (* n 2) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 54 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (posit16->real (real->posit16 (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 55 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) 1) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 56 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) 1) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.784 * * * * [progress]: [ 57 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* (* n 2) (sqrt PI)) 1) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 58 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (exp (+ (+ (log n) (log 2)) (log (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 59 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (exp (+ (log (* n 2)) (log (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 60 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (exp (log (* (* n 2) (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 61 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (log (exp (* (* n 2) (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 62 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 63 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 64 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (cbrt (* (* n 2) (sqrt PI))) (cbrt (* (* n 2) (sqrt PI)))) (cbrt (* (* n 2) (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 65 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (cbrt (* (* (* (* n 2) (sqrt PI)) (* (* n 2) (sqrt PI))) (* (* n 2) (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 66 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (sqrt (* (* n 2) (sqrt PI))) (sqrt (* (* n 2) (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 67 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 1 (* (* n 2) (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 68 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))) (cbrt (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 69 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) (sqrt (* (cbrt PI) (cbrt PI)))) (sqrt (cbrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.785 * * * * [progress]: [ 70 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 71 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) (sqrt 1)) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 72 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 73 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) 1) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 74 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 75 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (posit16->real (real->posit16 (* (* n 2) (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 76 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (sqrt PI) (* n 2)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 77 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 78 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 79 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (- (+ (* 1/4 (* (log n) (* (log (* 2 (sqrt PI))) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2))))) (+ (* 1/8 (* (pow (log n) 2) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2)))) (+ (* 1/8 (* (pow (log (* 2 (sqrt PI))) 2) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2)))) (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (* (log n) k))) (* 1/2 (* (log (* 2 (sqrt PI))) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) k))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 80 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 (sqrt PI))) (log (/ 1 n))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 81 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 (sqrt PI))) (log (/ -1 n))))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 82 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 83 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.786 * * * * [progress]: [ 84 / 84 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))>
5.788 * [simplify]: Simplifying:
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* (* (sqrt PI) (sqrt PI)) (sqrt PI))
  (sqrt (* (cbrt PI) (cbrt PI)))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (sqrt 1)
  (sqrt PI)
  (/ 1 2)
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* (* (sqrt PI) (sqrt PI)) (sqrt PI))
  (sqrt (* (cbrt PI) (cbrt PI)))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (sqrt 1)
  (sqrt PI)
  (/ 1 2)
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (* (+ (+ (log n) (log 2)) (log (sqrt PI))) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log (sqrt PI))) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) (sqrt PI))) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) (sqrt PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) (sqrt PI)) 1/2)
  (pow (* (* n 2) (sqrt PI)) (/ k 2))
  (pow (* (* n 2) (sqrt PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) (sqrt PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) (sqrt PI)) 1)
  (pow (* (* n 2) (sqrt PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) (sqrt PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) (sqrt PI)) 1)
  (pow (* (* n 2) (sqrt PI)) 1/2)
  (pow (* (* n 2) (sqrt PI)) (- (/ k 2)))
  (pow (* (* n 2) (sqrt PI)) 1/2)
  (pow (* (* n 2) (sqrt PI)) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow (sqrt PI) (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))) (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))
  (pow (* (* n 2) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))))
  (* (* n 2) (sqrt PI))
  (* (* n 2) (sqrt PI))
  (+ (+ (log n) (log 2)) (log (sqrt PI)))
  (+ (log (* n 2)) (log (sqrt PI)))
  (log (* (* n 2) (sqrt PI)))
  (exp (* (* n 2) (sqrt PI)))
  (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))
  (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))
  (* (cbrt (* (* n 2) (sqrt PI))) (cbrt (* (* n 2) (sqrt PI))))
  (cbrt (* (* n 2) (sqrt PI)))
  (* (* (* (* n 2) (sqrt PI)) (* (* n 2) (sqrt PI))) (* (* n 2) (sqrt PI)))
  (sqrt (* (* n 2) (sqrt PI)))
  (sqrt (* (* n 2) (sqrt PI)))
  (* (* n 2) (* (cbrt (sqrt PI)) (cbrt (sqrt PI))))
  (* (* n 2) (sqrt (* (cbrt PI) (cbrt PI))))
  (* (* n 2) (sqrt (sqrt PI)))
  (* (* n 2) (sqrt 1))
  (* (* n 2) (sqrt (sqrt PI)))
  (* (* n 2) 1)
  (* 2 (sqrt PI))
  (real->posit16 (* (* n 2) (sqrt PI)))
  (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
  (pow (sqrt PI) (- 1/2 (/ k 2)))
  (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2)))
  (pow (sqrt PI) (- 1/2 (/ k 2)))
  (- (+ (* 1/4 (* (log n) (* (log (* 2 (sqrt PI))) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2))))) (+ (* 1/8 (* (pow (log n) 2) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2)))) (+ (* 1/8 (* (pow (log (* 2 (sqrt PI))) 2) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2)))) (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (* (log n) k))) (* 1/2 (* (log (* 2 (sqrt PI))) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 (sqrt PI))) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 (sqrt PI))) (log (/ -1 n)))))
  (* 2 (* n (sqrt PI)))
  (* 2 (* n (sqrt PI)))
  (* 2 (* n (sqrt PI)))
5.791 * * [simplify]: iteration 0: 136 enodes
5.845 * * [simplify]: iteration 1: 366 enodes
6.012 * * [simplify]: iteration 2: 1301 enodes
6.396 * * [simplify]: iteration complete: 2003 enodes
6.396 * * [simplify]: Extracting #0: cost 46 inf + 0
6.397 * * [simplify]: Extracting #1: cost 248 inf + 2
6.399 * * [simplify]: Extracting #2: cost 454 inf + 638
6.408 * * [simplify]: Extracting #3: cost 558 inf + 19305
6.425 * * [simplify]: Extracting #4: cost 290 inf + 90001
6.451 * * [simplify]: Extracting #5: cost 105 inf + 148199
6.504 * * [simplify]: Extracting #6: cost 20 inf + 183199
6.543 * * [simplify]: Extracting #7: cost 1 inf + 187741
6.587 * * [simplify]: Extracting #8: cost 0 inf + 187234
6.647 * * [simplify]: Extracting #9: cost 0 inf + 187194
6.709 * [simplify]: Simplified to:
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* PI (sqrt PI))
  (fabs (cbrt PI))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  1
  (sqrt PI)
  1/2
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* PI (sqrt PI))
  (fabs (cbrt PI))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  1
  (sqrt PI)
  1/2
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (* (- 1/2 (/ k 2)) (log (* n (* (sqrt PI) 2))))
  (* (- 1/2 (/ k 2)) (log (* n (* (sqrt PI) 2))))
  (* (- 1/2 (/ k 2)) (log (* n (* (sqrt PI) 2))))
  (* (- 1/2 (/ k 2)) (log (* n (* (sqrt PI) 2))))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* n (* (sqrt PI) 2)))
  (pow (* n (* (sqrt PI) 2)) (/ k 2))
  (pow (* n (* (sqrt PI) 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* (sqrt PI) 2)) (sqrt (- 1/2 (/ k 2))))
  (* n (* (sqrt PI) 2))
  (pow (* n (* (sqrt PI) 2)) (+ (sqrt (/ k 2)) (sqrt 1/2)))
  (pow (* n (* (sqrt PI) 2)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* n (* (sqrt PI) 2))
  (sqrt (* n (* (sqrt PI) 2)))
  (pow (* n (* (sqrt PI) 2)) (- (/ k 2)))
  (sqrt (* n (* (sqrt PI) 2)))
  (pow (* n (* (sqrt PI) 2)) (- (/ k 2)))
  (pow (* 2 n) (- 1/2 (/ k 2)))
  (pow (sqrt PI) (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* n (* (sqrt PI) 2))))
  (exp (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2))) (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2)))) (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2))))
  (pow (* n (* (sqrt PI) 2)) (- 1/4 (/ k 4)))
  (pow (* n (* (sqrt PI) 2)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2))))
  (* n (* (sqrt PI) 2))
  (* n (* (sqrt PI) 2))
  (log (* n (* (sqrt PI) 2)))
  (log (* n (* (sqrt PI) 2)))
  (log (* n (* (sqrt PI) 2)))
  (exp (+ (* (sqrt PI) n) (* (sqrt PI) n)))
  (* (sqrt PI) (* (* n (* n n)) (* 8 PI)))
  (* (sqrt PI) (* (* n (* n n)) (* 8 PI)))
  (* (cbrt (* n (* (sqrt PI) 2))) (cbrt (* n (* (sqrt PI) 2))))
  (cbrt (* n (* (sqrt PI) 2)))
  (* (sqrt PI) (* (* n (* n n)) (* 8 PI)))
  (sqrt (* n (* (sqrt PI) 2)))
  (sqrt (* n (* (sqrt PI) 2)))
  (* (* (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) n) 2)
  (* (fabs (cbrt PI)) (* 2 n))
  (* (sqrt (sqrt PI)) (* 2 n))
  (* 2 n)
  (* (sqrt (sqrt PI)) (* 2 n))
  (* 2 n)
  (* (sqrt PI) 2)
  (real->posit16 (* n (* (sqrt PI) 2)))
  (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2)))
  (pow (sqrt PI) (- 1/2 (/ k 2)))
  (pow (* n (* (sqrt PI) 2)) (- 1/2 (/ k 2)))
  (pow (sqrt PI) (- 1/2 (/ k 2)))
  (- (+ (* (* (* k k) (exp (/ (log (* n (* (sqrt PI) 2))) 2))) (+ (* (* (log n) (log n)) 1/8) (* (* (log (* (sqrt PI) 2)) (log (* (sqrt PI) 2))) 1/8))) (+ (exp (/ (log (* n (* (sqrt PI) 2))) 2)) (* (* 1/4 (* (log (* (sqrt PI) 2)) (log n))) (* (* k k) (exp (/ (log (* n (* (sqrt PI) 2))) 2)))))) (/ (* k (+ (* (exp (/ (log (* n (* (sqrt PI) 2))) 2)) (log n)) (* (log (* (sqrt PI) 2)) (exp (/ (log (* n (* (sqrt PI) 2))) 2))))) 2))
  (exp (* (- 1/2 (* k 1/2)) (log (* n (* (sqrt PI) 2)))))
  (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 (sqrt PI))) (log (/ -1 n)))))
  (* n (* (sqrt PI) 2))
  (* n (* (sqrt PI) 2))
  (* n (* (sqrt PI) 2))
6.721 * * * [progress]: adding candidates to table
7.237 * * [progress]: iteration 4 / 4
7.237 * * * [progress]: picking best candidate
7.293 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.293 * * * [progress]: localizing error
7.343 * * * [progress]: generating rewritten candidates
7.343 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 1 2 1)
7.344 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2 1)
7.346 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1 1 2)
7.348 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1)
7.585 * * * [progress]: generating series expansions
7.585 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 1 2 1)
7.585 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2 1)
7.585 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1 1 2)
7.585 * * * * [progress]: [ 4 / 4 ] generating series at (2 1)
7.587 * [backup-simplify]: Simplify (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
7.587 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
7.587 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
7.587 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
7.587 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
7.587 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
7.587 * [taylor]: Taking taylor expansion of 1/2 in k
7.587 * [backup-simplify]: Simplify 1/2 into 1/2
7.587 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
7.587 * [taylor]: Taking taylor expansion of 1/2 in k
7.587 * [backup-simplify]: Simplify 1/2 into 1/2
7.587 * [taylor]: Taking taylor expansion of k in k
7.587 * [backup-simplify]: Simplify 0 into 0
7.587 * [backup-simplify]: Simplify 1 into 1
7.587 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
7.587 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
7.587 * [taylor]: Taking taylor expansion of 2 in k
7.587 * [backup-simplify]: Simplify 2 into 2
7.587 * [taylor]: Taking taylor expansion of (* n PI) in k
7.588 * [taylor]: Taking taylor expansion of n in k
7.588 * [backup-simplify]: Simplify n into n
7.588 * [taylor]: Taking taylor expansion of PI in k
7.588 * [backup-simplify]: Simplify PI into PI
7.588 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.588 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
7.588 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
7.588 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.588 * [backup-simplify]: Simplify (- 0) into 0
7.589 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.589 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
7.589 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
7.589 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
7.589 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
7.589 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
7.589 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.589 * [taylor]: Taking taylor expansion of 1/2 in n
7.589 * [backup-simplify]: Simplify 1/2 into 1/2
7.589 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.589 * [taylor]: Taking taylor expansion of 1/2 in n
7.589 * [backup-simplify]: Simplify 1/2 into 1/2
7.589 * [taylor]: Taking taylor expansion of k in n
7.589 * [backup-simplify]: Simplify k into k
7.589 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.589 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.589 * [taylor]: Taking taylor expansion of 2 in n
7.589 * [backup-simplify]: Simplify 2 into 2
7.589 * [taylor]: Taking taylor expansion of (* n PI) in n
7.589 * [taylor]: Taking taylor expansion of n in n
7.589 * [backup-simplify]: Simplify 0 into 0
7.589 * [backup-simplify]: Simplify 1 into 1
7.589 * [taylor]: Taking taylor expansion of PI in n
7.589 * [backup-simplify]: Simplify PI into PI
7.590 * [backup-simplify]: Simplify (* 0 PI) into 0
7.590 * [backup-simplify]: Simplify (* 2 0) into 0
7.591 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.592 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.593 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.593 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.593 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.593 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.594 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.595 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
7.596 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
7.596 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
7.596 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
7.596 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
7.596 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.596 * [taylor]: Taking taylor expansion of 1/2 in n
7.596 * [backup-simplify]: Simplify 1/2 into 1/2
7.596 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.596 * [taylor]: Taking taylor expansion of 1/2 in n
7.596 * [backup-simplify]: Simplify 1/2 into 1/2
7.596 * [taylor]: Taking taylor expansion of k in n
7.596 * [backup-simplify]: Simplify k into k
7.596 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.596 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.596 * [taylor]: Taking taylor expansion of 2 in n
7.596 * [backup-simplify]: Simplify 2 into 2
7.596 * [taylor]: Taking taylor expansion of (* n PI) in n
7.596 * [taylor]: Taking taylor expansion of n in n
7.596 * [backup-simplify]: Simplify 0 into 0
7.596 * [backup-simplify]: Simplify 1 into 1
7.596 * [taylor]: Taking taylor expansion of PI in n
7.596 * [backup-simplify]: Simplify PI into PI
7.597 * [backup-simplify]: Simplify (* 0 PI) into 0
7.597 * [backup-simplify]: Simplify (* 2 0) into 0
7.598 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.599 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.600 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.600 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.600 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.600 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.602 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.603 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
7.604 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
7.604 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
7.604 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
7.604 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
7.604 * [taylor]: Taking taylor expansion of 1/2 in k
7.604 * [backup-simplify]: Simplify 1/2 into 1/2
7.604 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
7.604 * [taylor]: Taking taylor expansion of 1/2 in k
7.604 * [backup-simplify]: Simplify 1/2 into 1/2
7.604 * [taylor]: Taking taylor expansion of k in k
7.604 * [backup-simplify]: Simplify 0 into 0
7.605 * [backup-simplify]: Simplify 1 into 1
7.605 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
7.605 * [taylor]: Taking taylor expansion of (log n) in k
7.605 * [taylor]: Taking taylor expansion of n in k
7.605 * [backup-simplify]: Simplify n into n
7.605 * [backup-simplify]: Simplify (log n) into (log n)
7.605 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.605 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.605 * [taylor]: Taking taylor expansion of 2 in k
7.605 * [backup-simplify]: Simplify 2 into 2
7.605 * [taylor]: Taking taylor expansion of PI in k
7.605 * [backup-simplify]: Simplify PI into PI
7.605 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.606 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.607 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.607 * [backup-simplify]: Simplify (- 0) into 0
7.607 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.608 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.609 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
7.610 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
7.611 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
7.613 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.614 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
7.616 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.616 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
7.617 * [backup-simplify]: Simplify (- 0) into 0
7.617 * [backup-simplify]: Simplify (+ 0 0) into 0
7.618 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.619 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
7.621 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.621 * [taylor]: Taking taylor expansion of 0 in k
7.621 * [backup-simplify]: Simplify 0 into 0
7.621 * [backup-simplify]: Simplify 0 into 0
7.622 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.623 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.624 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.625 * [backup-simplify]: Simplify (+ 0 0) into 0
7.625 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
7.626 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.627 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.628 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
7.632 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
7.635 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
7.637 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.638 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.641 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
7.642 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
7.643 * [backup-simplify]: Simplify (- 0) into 0
7.643 * [backup-simplify]: Simplify (+ 0 0) into 0
7.645 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.646 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.649 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.649 * [taylor]: Taking taylor expansion of 0 in k
7.649 * [backup-simplify]: Simplify 0 into 0
7.649 * [backup-simplify]: Simplify 0 into 0
7.649 * [backup-simplify]: Simplify 0 into 0
7.651 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.652 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.656 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
7.656 * [backup-simplify]: Simplify (+ 0 0) into 0
7.657 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
7.658 * [backup-simplify]: Simplify (- 0) into 0
7.658 * [backup-simplify]: Simplify (+ 0 0) into 0
7.660 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.665 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
7.669 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
7.676 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
7.678 * [backup-simplify]: Simplify (pow (* (* (* (* (/ 1 n) 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
7.678 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
7.678 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
7.678 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
7.678 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
7.678 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
7.678 * [taylor]: Taking taylor expansion of 1/2 in k
7.678 * [backup-simplify]: Simplify 1/2 into 1/2
7.678 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.678 * [taylor]: Taking taylor expansion of 1/2 in k
7.678 * [backup-simplify]: Simplify 1/2 into 1/2
7.678 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.678 * [taylor]: Taking taylor expansion of k in k
7.678 * [backup-simplify]: Simplify 0 into 0
7.678 * [backup-simplify]: Simplify 1 into 1
7.678 * [backup-simplify]: Simplify (/ 1 1) into 1
7.678 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
7.678 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
7.678 * [taylor]: Taking taylor expansion of 2 in k
7.678 * [backup-simplify]: Simplify 2 into 2
7.678 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.678 * [taylor]: Taking taylor expansion of PI in k
7.678 * [backup-simplify]: Simplify PI into PI
7.678 * [taylor]: Taking taylor expansion of n in k
7.678 * [backup-simplify]: Simplify n into n
7.678 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.678 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
7.678 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
7.679 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.679 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.679 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.679 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
7.679 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
7.679 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
7.679 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.679 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.679 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
7.679 * [taylor]: Taking taylor expansion of 1/2 in n
7.679 * [backup-simplify]: Simplify 1/2 into 1/2
7.680 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.680 * [taylor]: Taking taylor expansion of 1/2 in n
7.680 * [backup-simplify]: Simplify 1/2 into 1/2
7.680 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.680 * [taylor]: Taking taylor expansion of k in n
7.680 * [backup-simplify]: Simplify k into k
7.680 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.680 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.680 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.680 * [taylor]: Taking taylor expansion of 2 in n
7.680 * [backup-simplify]: Simplify 2 into 2
7.680 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.680 * [taylor]: Taking taylor expansion of PI in n
7.680 * [backup-simplify]: Simplify PI into PI
7.680 * [taylor]: Taking taylor expansion of n in n
7.680 * [backup-simplify]: Simplify 0 into 0
7.680 * [backup-simplify]: Simplify 1 into 1
7.680 * [backup-simplify]: Simplify (/ PI 1) into PI
7.680 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.681 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.681 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.681 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
7.681 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
7.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.683 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
7.684 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
7.684 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
7.684 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.684 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.684 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
7.684 * [taylor]: Taking taylor expansion of 1/2 in n
7.684 * [backup-simplify]: Simplify 1/2 into 1/2
7.684 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.684 * [taylor]: Taking taylor expansion of 1/2 in n
7.684 * [backup-simplify]: Simplify 1/2 into 1/2
7.684 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.684 * [taylor]: Taking taylor expansion of k in n
7.684 * [backup-simplify]: Simplify k into k
7.684 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.684 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.684 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.684 * [taylor]: Taking taylor expansion of 2 in n
7.684 * [backup-simplify]: Simplify 2 into 2
7.684 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.684 * [taylor]: Taking taylor expansion of PI in n
7.684 * [backup-simplify]: Simplify PI into PI
7.684 * [taylor]: Taking taylor expansion of n in n
7.684 * [backup-simplify]: Simplify 0 into 0
7.684 * [backup-simplify]: Simplify 1 into 1
7.684 * [backup-simplify]: Simplify (/ PI 1) into PI
7.685 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.685 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.685 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.686 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
7.686 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
7.687 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.687 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
7.688 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
7.688 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
7.688 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
7.688 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
7.688 * [taylor]: Taking taylor expansion of 1/2 in k
7.688 * [backup-simplify]: Simplify 1/2 into 1/2
7.688 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.688 * [taylor]: Taking taylor expansion of 1/2 in k
7.688 * [backup-simplify]: Simplify 1/2 into 1/2
7.688 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.688 * [taylor]: Taking taylor expansion of k in k
7.688 * [backup-simplify]: Simplify 0 into 0
7.688 * [backup-simplify]: Simplify 1 into 1
7.689 * [backup-simplify]: Simplify (/ 1 1) into 1
7.689 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
7.689 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.689 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.689 * [taylor]: Taking taylor expansion of 2 in k
7.689 * [backup-simplify]: Simplify 2 into 2
7.689 * [taylor]: Taking taylor expansion of PI in k
7.689 * [backup-simplify]: Simplify PI into PI
7.689 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.690 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.690 * [taylor]: Taking taylor expansion of (log n) in k
7.690 * [taylor]: Taking taylor expansion of n in k
7.690 * [backup-simplify]: Simplify n into n
7.690 * [backup-simplify]: Simplify (log n) into (log n)
7.690 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.690 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.691 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.691 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.691 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
7.692 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
7.693 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
7.694 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
7.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.695 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.697 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.697 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.697 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
7.698 * [backup-simplify]: Simplify (- 0) into 0
7.698 * [backup-simplify]: Simplify (+ 0 0) into 0
7.700 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.701 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
7.703 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.703 * [taylor]: Taking taylor expansion of 0 in k
7.703 * [backup-simplify]: Simplify 0 into 0
7.703 * [backup-simplify]: Simplify 0 into 0
7.703 * [backup-simplify]: Simplify 0 into 0
7.704 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.706 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.709 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
7.709 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.710 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
7.710 * [backup-simplify]: Simplify (- 0) into 0
7.711 * [backup-simplify]: Simplify (+ 0 0) into 0
7.712 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.714 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
7.717 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.717 * [taylor]: Taking taylor expansion of 0 in k
7.717 * [backup-simplify]: Simplify 0 into 0
7.717 * [backup-simplify]: Simplify 0 into 0
7.717 * [backup-simplify]: Simplify 0 into 0
7.717 * [backup-simplify]: Simplify 0 into 0
7.718 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.720 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.724 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
7.725 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.725 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
7.726 * [backup-simplify]: Simplify (- 0) into 0
7.726 * [backup-simplify]: Simplify (+ 0 0) into 0
7.727 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.731 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
7.732 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
7.732 * [taylor]: Taking taylor expansion of 0 in k
7.732 * [backup-simplify]: Simplify 0 into 0
7.732 * [backup-simplify]: Simplify 0 into 0
7.733 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
7.735 * [backup-simplify]: Simplify (pow (* (* (* (* (/ 1 (- n)) 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
7.735 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
7.735 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
7.735 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
7.735 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
7.735 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
7.735 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.735 * [taylor]: Taking taylor expansion of 1/2 in k
7.735 * [backup-simplify]: Simplify 1/2 into 1/2
7.735 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.735 * [taylor]: Taking taylor expansion of k in k
7.735 * [backup-simplify]: Simplify 0 into 0
7.735 * [backup-simplify]: Simplify 1 into 1
7.735 * [backup-simplify]: Simplify (/ 1 1) into 1
7.735 * [taylor]: Taking taylor expansion of 1/2 in k
7.735 * [backup-simplify]: Simplify 1/2 into 1/2
7.735 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
7.735 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
7.735 * [taylor]: Taking taylor expansion of -2 in k
7.735 * [backup-simplify]: Simplify -2 into -2
7.735 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.735 * [taylor]: Taking taylor expansion of PI in k
7.736 * [backup-simplify]: Simplify PI into PI
7.736 * [taylor]: Taking taylor expansion of n in k
7.736 * [backup-simplify]: Simplify n into n
7.736 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.736 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
7.736 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
7.736 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.736 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.736 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
7.736 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
7.736 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
7.736 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
7.737 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
7.737 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
7.737 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.737 * [taylor]: Taking taylor expansion of 1/2 in n
7.737 * [backup-simplify]: Simplify 1/2 into 1/2
7.737 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.737 * [taylor]: Taking taylor expansion of k in n
7.737 * [backup-simplify]: Simplify k into k
7.737 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.737 * [taylor]: Taking taylor expansion of 1/2 in n
7.737 * [backup-simplify]: Simplify 1/2 into 1/2
7.737 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.737 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.737 * [taylor]: Taking taylor expansion of -2 in n
7.737 * [backup-simplify]: Simplify -2 into -2
7.737 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.737 * [taylor]: Taking taylor expansion of PI in n
7.737 * [backup-simplify]: Simplify PI into PI
7.737 * [taylor]: Taking taylor expansion of n in n
7.737 * [backup-simplify]: Simplify 0 into 0
7.737 * [backup-simplify]: Simplify 1 into 1
7.737 * [backup-simplify]: Simplify (/ PI 1) into PI
7.737 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.738 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.738 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.738 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
7.739 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.740 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
7.741 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
7.741 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
7.741 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
7.741 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
7.741 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
7.741 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.741 * [taylor]: Taking taylor expansion of 1/2 in n
7.741 * [backup-simplify]: Simplify 1/2 into 1/2
7.741 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.741 * [taylor]: Taking taylor expansion of k in n
7.741 * [backup-simplify]: Simplify k into k
7.741 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.741 * [taylor]: Taking taylor expansion of 1/2 in n
7.741 * [backup-simplify]: Simplify 1/2 into 1/2
7.741 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.741 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.741 * [taylor]: Taking taylor expansion of -2 in n
7.741 * [backup-simplify]: Simplify -2 into -2
7.741 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.741 * [taylor]: Taking taylor expansion of PI in n
7.741 * [backup-simplify]: Simplify PI into PI
7.741 * [taylor]: Taking taylor expansion of n in n
7.741 * [backup-simplify]: Simplify 0 into 0
7.741 * [backup-simplify]: Simplify 1 into 1
7.741 * [backup-simplify]: Simplify (/ PI 1) into PI
7.742 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.742 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.742 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.743 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
7.743 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.744 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
7.745 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
7.745 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
7.745 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
7.745 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
7.745 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.745 * [taylor]: Taking taylor expansion of 1/2 in k
7.745 * [backup-simplify]: Simplify 1/2 into 1/2
7.745 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.745 * [taylor]: Taking taylor expansion of k in k
7.745 * [backup-simplify]: Simplify 0 into 0
7.745 * [backup-simplify]: Simplify 1 into 1
7.745 * [backup-simplify]: Simplify (/ 1 1) into 1
7.745 * [taylor]: Taking taylor expansion of 1/2 in k
7.746 * [backup-simplify]: Simplify 1/2 into 1/2
7.746 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
7.746 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
7.746 * [taylor]: Taking taylor expansion of (* -2 PI) in k
7.746 * [taylor]: Taking taylor expansion of -2 in k
7.746 * [backup-simplify]: Simplify -2 into -2
7.746 * [taylor]: Taking taylor expansion of PI in k
7.746 * [backup-simplify]: Simplify PI into PI
7.746 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.747 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.747 * [taylor]: Taking taylor expansion of (log n) in k
7.747 * [taylor]: Taking taylor expansion of n in k
7.747 * [backup-simplify]: Simplify n into n
7.747 * [backup-simplify]: Simplify (log n) into (log n)
7.747 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.747 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.747 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.748 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
7.749 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
7.749 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
7.750 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
7.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.751 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
7.752 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
7.753 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.753 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
7.753 * [backup-simplify]: Simplify (+ 0 0) into 0
7.754 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.755 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
7.756 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.756 * [taylor]: Taking taylor expansion of 0 in k
7.756 * [backup-simplify]: Simplify 0 into 0
7.756 * [backup-simplify]: Simplify 0 into 0
7.756 * [backup-simplify]: Simplify 0 into 0
7.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.757 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
7.759 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
7.760 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.760 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
7.760 * [backup-simplify]: Simplify (+ 0 0) into 0
7.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.762 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
7.764 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.764 * [taylor]: Taking taylor expansion of 0 in k
7.764 * [backup-simplify]: Simplify 0 into 0
7.764 * [backup-simplify]: Simplify 0 into 0
7.764 * [backup-simplify]: Simplify 0 into 0
7.764 * [backup-simplify]: Simplify 0 into 0
7.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.765 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.769 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
7.769 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.770 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
7.770 * [backup-simplify]: Simplify (+ 0 0) into 0
7.771 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.772 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
7.774 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
7.774 * [taylor]: Taking taylor expansion of 0 in k
7.774 * [backup-simplify]: Simplify 0 into 0
7.774 * [backup-simplify]: Simplify 0 into 0
7.775 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
7.775 * * * [progress]: simplifying candidates
7.775 * * * * [progress]: [ 1 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (pow PI 1/2))) (- 1/2 (/ k 2))) (sqrt k)))>
7.775 * * * * [progress]: [ 2 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (pow (sqrt PI) 1))) (- 1/2 (/ k 2))) (sqrt k)))>
7.775 * * * * [progress]: [ 3 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (exp (log (sqrt PI))))) (- 1/2 (/ k 2))) (sqrt k)))>
7.775 * * * * [progress]: [ 4 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (log (exp (sqrt PI))))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 5 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (* (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI))))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 6 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (cbrt (* (* (sqrt PI) (sqrt PI)) (sqrt PI))))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 7 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (* (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI))))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 8 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 9 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (* (sqrt 1) (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 10 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (pow PI (/ 1 2)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 11 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 12 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (fabs (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 13 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (* 1 (sqrt PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 14 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (posit16->real (real->posit16 (sqrt PI))))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 15 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (pow PI 1/2))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 16 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (pow (sqrt PI) 1))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 17 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (exp (log (sqrt PI))))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 18 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (log (exp (sqrt PI))))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 19 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (* (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI))))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 20 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (cbrt (* (* (sqrt PI) (sqrt PI)) (sqrt PI))))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 21 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (* (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI))))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 22 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 23 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (* (sqrt 1) (sqrt PI)))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 24 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (pow PI (/ 1 2)))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 25 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 26 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (fabs (sqrt PI)))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 27 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (* 1 (sqrt PI)))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 28 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (posit16->real (real->posit16 (sqrt PI))))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.776 * * * * [progress]: [ 29 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (pow PI 1/2)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 30 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (pow (sqrt PI) 1)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 31 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (exp (log (sqrt PI)))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 32 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (log (exp (sqrt PI)))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 33 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (* (* (cbrt (sqrt PI)) (cbrt (sqrt PI))) (cbrt (sqrt PI)))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 34 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (cbrt (* (* (sqrt PI) (sqrt PI)) (sqrt PI)))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 35 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (* (sqrt (* (cbrt PI) (cbrt PI))) (sqrt (cbrt PI)))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 36 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 37 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (* (sqrt 1) (sqrt PI))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 38 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (pow PI (/ 1 2))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 39 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 40 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (fabs (sqrt PI))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 41 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (* 1 (sqrt PI))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 42 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (posit16->real (real->posit16 (sqrt PI)))) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.777 * * * * [progress]: [ 43 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (+ (+ (log n) (log 2)) (log (sqrt PI))) (log (sqrt (sqrt PI)))) (log (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 44 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (+ (log (* n 2)) (log (sqrt PI))) (log (sqrt (sqrt PI)))) (log (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 45 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (log (* (* n 2) (sqrt PI))) (log (sqrt (sqrt PI)))) (log (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 46 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI)))) (log (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 47 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 48 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 49 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 50 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 51 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 52 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
7.777 * * * * [progress]: [ 53 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
7.778 * * * * [progress]: [ 54 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1/2) (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (/ k 2))) (sqrt k)))>
7.778 * * * * [progress]: [ 55 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
7.778 * * * * [progress]: [ 56 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
7.778 * * * * [progress]: [ 57 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1) (- 1/2 (/ k 2))) (sqrt k)))>
7.778 * * * * [progress]: [ 58 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
7.778 * * * * [progress]: [ 59 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
7.778 * * * * [progress]: [ 60 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1) (- 1/2 (/ k 2))) (sqrt k)))>
7.778 * * * * [progress]: [ 61 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1/2) (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- (/ k 2)))) (sqrt k)))>
7.778 * * * * [progress]: [ 62 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1/2) (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- (/ k 2)))) (sqrt k)))>
7.778 * * * * [progress]: [ 63 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (pow (sqrt (sqrt PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
7.778 * * * * [progress]: [ 64 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) 1) (sqrt k)))>
7.778 * * * * [progress]: [ 65 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))) (sqrt k)))>
7.778 * * * * [progress]: [ 66 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))) (sqrt k)))>
7.778 * * * * [progress]: [ 67 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))) (cbrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))) (cbrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))) (sqrt k)))>
7.778 * * * * [progress]: [ 68 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))) (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))) (sqrt k)))>
7.778 * * * * [progress]: [ 69 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))) (sqrt k)))>
7.778 * * * * [progress]: [ 70 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
7.778 * * * * [progress]: [ 71 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
7.778 * * * * [progress]: [ 72 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))) (sqrt k)))>
7.778 * * * * [progress]: [ 73 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.778 * * * * [progress]: [ 74 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.778 * * * * [progress]: [ 75 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))>
7.778 * * * * [progress]: [ 76 / 78 ] 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)))>
7.778 * * * * [progress]: [ 77 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
7.778 * * * * [progress]: [ 78 / 78 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
7.779 * [simplify]: Simplifying:
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* (* (sqrt PI) (sqrt PI)) (sqrt PI))
  (sqrt (* (cbrt PI) (cbrt PI)))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (sqrt 1)
  (sqrt PI)
  (/ 1 2)
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* (* (sqrt PI) (sqrt PI)) (sqrt PI))
  (sqrt (* (cbrt PI) (cbrt PI)))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (sqrt 1)
  (sqrt PI)
  (/ 1 2)
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* (* (sqrt PI) (sqrt PI)) (sqrt PI))
  (sqrt (* (cbrt PI) (cbrt PI)))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (sqrt 1)
  (sqrt PI)
  (/ 1 2)
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (* (+ (+ (+ (+ (log n) (log 2)) (log (sqrt PI))) (log (sqrt (sqrt PI)))) (log (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))
  (* (+ (+ (+ (log (* n 2)) (log (sqrt PI))) (log (sqrt (sqrt PI)))) (log (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))
  (* (+ (+ (log (* (* n 2) (sqrt PI))) (log (sqrt (sqrt PI)))) (log (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))
  (* (+ (log (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI)))) (log (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))
  (* (log (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))
  (* (log (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI)))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1/2)
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (/ k 2))
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1)
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1)
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1/2)
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- (/ k 2)))
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) 1/2)
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- (/ k 2)))
  (pow (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))
  (pow (sqrt (sqrt PI)) (- 1/2 (/ k 2)))
  (log (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))
  (exp (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))) (cbrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))
  (* (* (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2)))) (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))))
  (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI)))
  (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI)))
  (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
7.780 * * [simplify]: iteration 0: 129 enodes
7.836 * * [simplify]: iteration 1: 319 enodes
8.017 * * [simplify]: iteration 2: 996 enodes
8.255 * * [simplify]: iteration complete: 2002 enodes
8.255 * * [simplify]: Extracting #0: cost 35 inf + 0
8.256 * * [simplify]: Extracting #1: cost 200 inf + 2
8.258 * * [simplify]: Extracting #2: cost 485 inf + 492
8.263 * * [simplify]: Extracting #3: cost 731 inf + 4302
8.276 * * [simplify]: Extracting #4: cost 583 inf + 49572
8.324 * * [simplify]: Extracting #5: cost 231 inf + 171328
8.359 * * [simplify]: Extracting #6: cost 71 inf + 234919
8.434 * * [simplify]: Extracting #7: cost 7 inf + 265575
8.508 * * [simplify]: Extracting #8: cost 1 inf + 265402
8.556 * * [simplify]: Extracting #9: cost 0 inf + 265599
8.600 * * [simplify]: Extracting #10: cost 0 inf + 265559
8.674 * [simplify]: Simplified to:
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* PI (sqrt PI))
  (fabs (cbrt PI))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  1
  (sqrt PI)
  1/2
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* PI (sqrt PI))
  (fabs (cbrt PI))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  1
  (sqrt PI)
  1/2
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (log (sqrt PI))
  (exp (sqrt PI))
  (* (cbrt (sqrt PI)) (cbrt (sqrt PI)))
  (cbrt (sqrt PI))
  (* PI (sqrt PI))
  (fabs (cbrt PI))
  (sqrt (cbrt PI))
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  1
  (sqrt PI)
  1/2
  (sqrt (sqrt PI))
  (sqrt (sqrt PI))
  (real->posit16 (sqrt PI))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (* (* n 2) PI)
  (pow (* (* n 2) PI) (+ (sqrt (/ k 2)) (sqrt 1/2)))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (* (* n 2) PI)
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* (sqrt (sqrt PI)) (* n 2)) (sqrt PI)) (- 1/2 (/ k 2)))
  (pow (sqrt (sqrt PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (sqrt (sqrt PI)) (* n 2)) (sqrt PI))
  (* (* (sqrt (sqrt PI)) (* n 2)) (sqrt PI))
  (* (* (sqrt (sqrt PI)) (* n 2)) (sqrt PI))
  (- (+ (+ (* (exp (/ (+ (log (* 2 PI)) (log n)) 2)) (* (* (* k (log n)) (* k (log n))) 1/8)) (* (* 1/4 (* (exp (/ (+ (log (* 2 PI)) (log n)) 2)) (log (* 2 PI)))) (* (log n) (* k k)))) (+ (* (* (exp (/ (+ (log (* 2 PI)) (log n)) 2)) (* k k)) (* (* (log (* 2 PI)) (log (* 2 PI))) 1/8)) (exp (/ (+ (log (* 2 PI)) (log n)) 2)))) (/ (* k (+ (* (exp (/ (+ (log (* 2 PI)) (log n)) 2)) (log n)) (* (exp (/ (+ (log (* 2 PI)) (log n)) 2)) (log (* 2 PI))))) 2))
  (exp (* (- 1/2 (/ k 2)) (+ (log (* 2 PI)) (log n))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2))))
8.685 * * * [progress]: adding candidates to table
9.122 * [progress]: [Phase 3 of 3] Extracting.
9.122 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (/ (* (pow (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>)
9.125 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2 PI) n) n k)
9.125 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (/ (* (pow (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>)
9.184 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))>)
9.220 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (/ (* (pow (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>)
9.278 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (/ (* (pow (* (* n 2) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k)))> #<alt (λ (k n) (/ (pow (* (* (* (* n 2) (sqrt PI)) (sqrt (sqrt PI))) (sqrt (sqrt PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (fabs (cbrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>)
9.349 * * * [regime]: Found split indices: #<option (#s(si 0 255))>
9.349 * [simplify]: Simplifying:
  (/ (* (pow (* (* n 2) (sqrt PI)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k))
9.349 * * [simplify]: iteration 0: 15 enodes
9.351 * * [simplify]: iteration 1: 18 enodes
9.351 * * [simplify]: iteration complete: 18 enodes
9.352 * * [simplify]: Extracting #0: cost 1 inf + 0
9.352 * * [simplify]: Extracting #1: cost 3 inf + 0
9.352 * * [simplify]: Extracting #2: cost 6 inf + 0
9.352 * * [simplify]: Extracting #3: cost 8 inf + 1
9.352 * * [simplify]: Extracting #4: cost 11 inf + 42
9.352 * * [simplify]: Extracting #5: cost 11 inf + 44
9.352 * * [simplify]: Extracting #6: cost 8 inf + 87
9.352 * * [simplify]: Extracting #7: cost 3 inf + 711
9.352 * * [simplify]: Extracting #8: cost 0 inf + 2536
9.352 * [simplify]: Simplified to:
  (/ (* (pow (* (sqrt PI) (* n 2)) (- 1/2 (/ k 2))) (pow (sqrt PI) (- 1/2 (/ k 2)))) (sqrt k))
18.574 * [regime-testing]: Baseline error score: 0.37378201708110764
18.577 * [regime-testing]: Oracle error score: 0.03781773515128407
18.581 * [regime-testing]: End program error score: 0.37378201708110764