Details

analyze110.0ms (1.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
0%	0%	50%	0.1%	0%	50%	0%	4
25%	12.5%	37.5%	0.1%	0%	50%	0%	5
26.7%	12.5%	34.3%	0.1%	0%	53.1%	0%	6
37%	15.6%	26.5%	0.1%	1.6%	54.6%	1.6%	7
40.8%	15.6%	22.6%	0.1%	2.3%	57%	2.3%	8
49.4%	17.2%	17.6%	0.1%	3.5%	58.1%	3.5%	9
53.3%	17.2%	15%	0.1%	4.1%	59.5%	4.1%	10
59.5%	18%	12.2%	0.1%	4.8%	60.2%	4.8%	11
62.5%	18%	10.8%	0.1%	5.1%	60.9%	5.1%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.1s (30.2%)

Results

1.4s	8256×	body	256	valid
823.0ms	1413×	body	1024	invalid
360.0ms	704×	body	512	invalid
291.0ms	1641×	body	256	invalid
110.0ms	499×	body	256	infinite
65.0ms	276×	body	256	unsamplable

Bogosity

preprocess53.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

454×	`neg-mul-1_binary64`
436×	`fma-def_binary64`
428×	`unswap-sqr_binary64`
424×	`div-sub_binary64`
419×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	119	44
3	257	44
4	670	44
5	1879	40
6	4230	40
7	7364	40
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 2 (*.f64 (PI.f64) k)) (-.f64 1/2 (/.f64 n 2))))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (+.f64 1/2 (/.f64 n -2))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (+.f64 1/2 (*.f64 -1/2 n))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 k 2)) (fma.f64 -1/2 n 1/2)) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (fma.f64 n -1/2 1/2)) (sqrt.f64 n))

Compiler

Compiled 20 to 17 computations (15% saved)

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l*_binary64`
561×	`associate-/r*_binary64`
453×	`div-sub_binary64`
450×	`distribute-frac-neg_binary64`
416×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	141	22
4	360	22
5	983	20
6	2213	20
7	5663	20

Stop Event

1×	node limit

Counts

1 → 7

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

eval2.0ms (0%)

Compiler: Compiled 102 to 64 computations (37.3% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	5	2	7
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	5	3	8

Error

0.4b

Counts

8 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) n)

Compiler

Compiled 56 to 38 computations (32.1% saved)

series64.0ms (0.6%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
25.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
17.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
8.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
3.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
2.0ms	k	@	-inf	(/.f64 1 (sqrt.f64 k))

rewrite104.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`log-prod_binary64`
382×	`pow2_binary64`
265×	`pow1/3_binary64`
260×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	307	51
2	3926	47

Stop Event

1×	node limit

Counts

4 → 105

Calls

Call 1

Inputs
(.f64 (.f64 2 (PI.f64)) n)
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (sqrt.f64 k))
(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 k) -1) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 k -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 k) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 k -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 k -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -1/2 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 k)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 -1/2 (log.f64 k)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 n (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1))))))

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
349×	`log-prod_binary64`
272×	`times-frac_binary64`
234×	`exp-prod_binary64`
224×	`exp-sum_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	306	3031
1	691	2796
2	2464	2468
3	6660	2462

Stop Event

1×	node limit

Counts

153 → 184

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 0 (.f64 2 (.f64 (PI.f64) n)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)
(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)
(pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)
(sqrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))
(log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))
(cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))
(exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 1))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 -1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1) (neg.f64 (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) -1)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))
(+.f64 0 (pow.f64 k -1/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)
(*.f64 1 (pow.f64 k -1/2))
(*.f64 (pow.f64 k -1/2) 1)
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))
(*.f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))
(*.f64 (sqrt.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 k -1/2)))
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k))))
(*.f64 (pow.f64 (cbrt.f64 k) -1) (cbrt.f64 (pow.f64 k -1/2)))
(pow.f64 k -1/2)
(pow.f64 (sqrt.f64 k) -1)
(pow.f64 (pow.f64 k -1/2) 1)
(pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)
(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)
(pow.f64 (sqrt.f64 (pow.f64 k -1/2)) 2)
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) -1)
(sqrt.f64 (/.f64 1 k))
(log.f64 (exp.f64 (pow.f64 k -1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
(log1p.f64 (expm1.f64 (pow.f64 k -1/2)))
(exp.f64 (*.f64 -1/2 (log.f64 k)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) -1))
(exp.f64 (.f64 (.f64 -1/2 (log.f64 k)) 1))
(+.f64 0 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 1)
(.f64 1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1)
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))
(.f64 (pow.f64 1 (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 k 1/2))))
(.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (*.f64 k 1/2))))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (*.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 k 1/2)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (sqrt.f64 2)) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2) (.f64 (sqrt.f64 2) (.f64 k k))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 3))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (sqrt.f64 2)) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 3))) (.f64 1/8 (.f64 k (.f64 k (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) 2))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(+.f64 0 (.f64 2 (.f64 (PI.f64) n)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (.f64 2 (PI.f64))))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(-.f64 (exp.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n)))) 1)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3) 1/3)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 3)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)) 1/3)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)) 1/3)
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(sqrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2)))
(sqrt.f64 (.f64 4 (pow.f64 (.f64 n (PI.f64)) 2)))
(fabs.f64 (.f64 (PI.f64) (.f64 2 n)))
(log.f64 (pow.f64 (exp.f64 n) (*.f64 2 (PI.f64))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(log.f64 (+.f64 1 (expm1.f64 (.f64 2 (.f64 (PI.f64) n)))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) 3) (pow.f64 n 3)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (.f64 2 (PI.f64)) 3)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 1))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (PI.f64) (.f64 2 n))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) 1)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (/.f64 (sqrt.f64 k) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 1) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k)))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (.f64 -1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1) (neg.f64 (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 1)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 3/2)))
(pow.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 3/2)))
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) -1)
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 3/2)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(+.f64 0 (pow.f64 k -1/2))
(pow.f64 k -1/2)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 k -1/2)))))
(pow.f64 k -1/2)
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k -1/2))) 1)
(pow.f64 k -1/2)
(*.f64 1 (pow.f64 k -1/2))
(pow.f64 k -1/2)
(*.f64 (pow.f64 k -1/2) 1)
(pow.f64 k -1/2)
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))
(*.f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 k -1/2)))
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 k -1/2)))
(pow.f64 k -1/2)
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k))))
(/.f64 -1 (neg.f64 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(*.f64 (pow.f64 (cbrt.f64 k) -1) (cbrt.f64 (pow.f64 k -1/2)))
(*.f64 (cbrt.f64 (pow.f64 k -1/2)) (/.f64 1 (cbrt.f64 k)))
(/.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 k))
(pow.f64 k -1/2)
(pow.f64 (sqrt.f64 k) -1)
(/.f64 -1 (neg.f64 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(pow.f64 (pow.f64 k -1/2) 1)
(pow.f64 k -1/2)
(pow.f64 (pow.f64 (pow.f64 k -1/2) 3) 1/3)
(pow.f64 k -1/2)
(pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3)
(pow.f64 k -1/2)
(pow.f64 (sqrt.f64 (pow.f64 k -1/2)) 2)
(pow.f64 k -1/2)
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 k))) -1)
(/.f64 -1 (neg.f64 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(sqrt.f64 (/.f64 1 k))
(log.f64 (exp.f64 (pow.f64 k -1/2)))
(pow.f64 k -1/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 k -1/2))))
(pow.f64 k -1/2)
(cbrt.f64 (pow.f64 (pow.f64 k -1/2) 3))
(pow.f64 k -1/2)
(expm1.f64 (log1p.f64 (pow.f64 k -1/2)))
(pow.f64 k -1/2)
(log1p.f64 (expm1.f64 (pow.f64 k -1/2)))
(pow.f64 k -1/2)
(exp.f64 (*.f64 -1/2 (log.f64 k)))
(pow.f64 k -1/2)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) -1))
(/.f64 -1 (neg.f64 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(exp.f64 (.f64 (.f64 -1/2 (log.f64 k)) 1))
(pow.f64 k -1/2)
(+.f64 0 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))) 1)
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(.f64 1 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 1)
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 n (-.f64 1/2 (.f64 k 1/2))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 1 (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 2 (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (.f64 (PI.f64) n) (-.f64 1/2 (.f64 k 1/2))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (*.f64 k 1/2))))
(.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 n (PI.f64)) 2))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1/2 (*.f64 k 1/2))))
(.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 n (PI.f64)) 2))) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 n))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (.f64 k 1/2))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1/2 (*.f64 k 1/2))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 2 (-.f64 1/2 (.f64 k 1/2))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (+.f64 1 (.f64 (.f64 k -1/2) 2)))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 2 (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 k 1/2)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 k 1/2)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 k 1/2)))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(cbrt.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) 3))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)))) 1))
(pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))
(pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k -1/2 1/2))

localize23.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))
✓	0.3b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.3b	(*.f64 (PI.f64) n)

Compiler

Compiled 50 to 30 computations (40% saved)

series11.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
1.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
1.0ms	n	@	0	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
1.0ms	n	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
1.0ms	k	@	inf	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

rewrite70.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

759×	`log-prod_binary64`
385×	`pow2_binary64`
262×	`pow1/3_binary64`
261×	`expm1-udef_binary64`
261×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	295	44
2	3931	40

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

Inputs
(*.f64 (PI.f64) n)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) n) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (PI.f64) n)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k)) (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 n 2)))) 1))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) n)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 1/2 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 1/2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1))))))

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-def_binary64`
505×	`associate-/l*_binary64`
505×	`unswap-sqr_binary64`
380×	`times-frac_binary64`
329×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	3082
1	669	2738
2	2325	2687

Stop Event

1×	node limit

Counts

140 → 164

Calls

Call 1

Inputs
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(+.f64 0 (*.f64 (PI.f64) n))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)
(pow.f64 (*.f64 (PI.f64) n) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))
(log.f64 (pow.f64 (exp.f64 n) (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) 1))
(+.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k) 1/2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))
(+.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)
(.f64 1 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k))))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 n 2)))))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 n 2)))) 1))

Outputs
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2))) (sqrt.f64 2))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 2)))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)) (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2) (.f64 (sqrt.f64 2) (.f64 k k))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 n 2))) 3))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 k (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 2)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))))) (.f64 (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 3)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 3))) (.f64 1/8 (.f64 k (.f64 k (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(+.f64 0 (*.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(*.f64 n (PI.f64))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)
(*.f64 n (PI.f64))
(pow.f64 (*.f64 (PI.f64) n) 1)
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 1/2)
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)
(*.f64 n (PI.f64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)
(*.f64 n (PI.f64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)
(*.f64 n (PI.f64))
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)
(*.f64 n (PI.f64))
(pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)
(*.f64 n (PI.f64))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))
(*.f64 n (PI.f64))
(log.f64 (pow.f64 (exp.f64 n) (PI.f64)))
(*.f64 n (PI.f64))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))
(*.f64 n (PI.f64))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) 1))
(*.f64 n (PI.f64))
(+.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))
(.f64 (pow.f64 k -1/2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))))
(.f64 (pow.f64 k -1/2) (.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2)) (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2) k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 k -1/2) (.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)))
(/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 k) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2)) (cbrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k) 1/2)
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(+.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 1 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2)) (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 2)) (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 k 1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) n) 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 n (PI.f64)) 2) 4)) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 n (PI.f64)) 2) 4)) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 2 (fma.f64 k -1/2 1/2)))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (*.f64 2 (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 k 1/2)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 k 1/2)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 k 1/2)))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 n 2)))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 n 2)))) 1))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))

eval144.0ms (1.4%)

Compiler: Compiled 7559 to 5137 computations (32% saved)

prune79.0ms (0.8%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	328	20	348
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	328	22	350

Error

0.0b

Counts

350 → 22

Alt Table

Click to see full alt table

Status	Error	Program
	11.3b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
	0.5b	(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	3.2b	(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.6b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
▶	0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2))) (sqrt.f64 k))
	20.3b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
	1.0b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
✓	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
▶	20.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	3.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.4b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.3b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	10.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
	12.9b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	20.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))

Compiler

Compiled 756 to 622 computations (17.7% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k)))
✓	0.1b	(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
✓	0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
✓	0.3b	(.f64 (PI.f64) (.f64 n 2))

Compiler

Compiled 70 to 46 computations (34.3% saved)

series22.0ms (0.2%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	k	@	0	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
2.0ms	n	@	-inf	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
2.0ms	n	@	0	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
2.0ms	n	@	inf	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
1.0ms	k	@	-inf	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))

rewrite73.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`log-prod_binary64`
387×	`pow2_binary64`
266×	`pow1/3_binary64`
261×	`log-pow_binary64`
261×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	73
1	302	55
2	4006	55

Stop Event

1×	node limit

Counts

4 → 148

Calls

Call 1

Inputs
(.f64 (PI.f64) (.f64 n 2))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2)) (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (sqrt.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 1/2) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) n) 1/2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 1 (neg.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) 1) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (/.f64 (sqrt.f64 (+.f64 n n)) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) 1))))))

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

366×	`associate-/r/_binary64`
325×	`log-prod_binary64`
296×	`associate-r_binary64`
253×	`associate-l_binary64`
231×	`sqr-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	3891
1	915	3636
2	4256	3548

Stop Event

1×	node limit

Counts

172 → 248

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1 (.f64 (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/48 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (.f64 -1/16 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4) 1/2)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)
(sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4))
(log.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))
(cbrt.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1))
(+.f64 0 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))) 1)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (pow.f64 k -1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 k -1/2)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 k -1/2)))
(.f64 (/.f64 -1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (pow.f64 k 1/4)))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 k 1/4)))
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 1)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) 2)
(pow.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2)) (sqrt.f64 k)) -1)
(pow.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) -1)
(pow.f64 (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2))) 1) -1)
(neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) 1))
(+.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1)
(.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) n) 1/2) (sqrt.f64 2))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 3)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2)
(fabs.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 1))
(+.f64 0 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 1)
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 1)
(.f64 1 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k))))
(.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k))))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 1 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) 1) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (/.f64 (sqrt.f64 (+.f64 n n)) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))))
(.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))))
(.f64 (/.f64 1 (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))
(pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 1)
(pow.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 3)
(pow.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2)) -1)
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) 3)) 1/3)
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2)) 1) -1)
(neg.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))))
(sqrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2))
(log.f64 (exp.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))
(cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) 3)))
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1))

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) k)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (+.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))) 1) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) -1/8) (*.f64 k k))))))
(-.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) k))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 k (.f64 k (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) -1/8))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (-.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) 1) (sqrt.f64 2)) (.f64 k (.f64 k (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) -1/8))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1 (.f64 (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/48 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (.f64 -1/16 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1 (.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (pow.f64 k 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 -1 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 k 3) (fma.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) -1/8)) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) -1/24)))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) -1/8) (*.f64 k k)))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (neg.f64 (.f64 k (.f64 k (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 (sqrt.f64 2) -1/8))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) k))) (neg.f64 (.f64 (pow.f64 k 3) (fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) -1/8) (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) -1/24))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (+.f64 (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) 1/8)) (.f64 k k))) (-.f64 (.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 2) k))) (.f64 (pow.f64 k 3) (fma.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) -1/8) (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3) -1/24)))))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 2) (exp.f64 (.f64 1/2 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 1/2) (.f64 k (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64))))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))))
(.f64 2 (.f64 n (PI.f64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)
(.f64 2 (.f64 n (PI.f64)))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(.f64 2 (.f64 n (PI.f64)))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)
(.f64 2 (.f64 n (PI.f64)))
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4) 1/2)
(sqrt.f64 (.f64 (pow.f64 (.f64 n (PI.f64)) 2) 4))
(fabs.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) 1/3)
(.f64 2 (.f64 n (PI.f64)))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)
(.f64 2 (.f64 n (PI.f64)))
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)
(.f64 2 (.f64 n (PI.f64)))
(pow.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)
(.f64 2 (.f64 n (PI.f64)))
(sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) n) 2) 4))
(sqrt.f64 (.f64 (pow.f64 (.f64 n (PI.f64)) 2) 4))
(fabs.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 n) 2) (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 2 (.f64 n (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3))
(.f64 2 (.f64 n (PI.f64)))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))
(.f64 2 (.f64 n (PI.f64)))
(cbrt.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))
(.f64 2 (.f64 n (PI.f64)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n))))
(.f64 2 (.f64 n (PI.f64)))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 0 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))) 1)
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (pow.f64 k -1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (+.f64 (neg.f64 k) 1)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (+.f64 (neg.f64 k) 1)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 2) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 2 (-.f64 1 k))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2) k)) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) 2) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 2 (-.f64 1 k))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))) k)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (+.f64 (neg.f64 k) 1)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (+.f64 (neg.f64 k) 1)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (/.f64 -1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(/.f64 (.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k)))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 1/2 k -1/2)))
(/.f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (+.f64 (neg.f64 k) 1)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 (/.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(/.f64 (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)) (sqrt.f64 k))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (neg.f64 k)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (neg.f64 k)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))) 2) (cbrt.f64 k)))
(/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) 2) (/.f64 (cbrt.f64 k) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k)))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (neg.f64 k)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (pow.f64 k 1/4)))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (neg.f64 k)) (pow.f64 k 1/4)))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 k 1/4)))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (neg.f64 k)) (pow.f64 k 1/4)))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 k 1/4)))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (neg.f64 k)) (pow.f64 k 1/4)))
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 3) 1/3)
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) 3)
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2))) -1)
(/.f64 (.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k)))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 1/2 k -1/2)))
(/.f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2)))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2)) (sqrt.f64 k)) -1)
(/.f64 (.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k)))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 1/2 k -1/2)))
(/.f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2)))
(pow.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) (sqrt.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) -1)
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(pow.f64 (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2))) 1) -1)
(/.f64 (.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 k)))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (fma.f64 1/2 k -1/2)))
(/.f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2)))
(neg.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2) k))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) 2) k))
(sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 2 (-.f64 1 k))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k)) 3))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(+.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (fabs.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1/2))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (fabs.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64))))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (pow.f64 (.f64 (PI.f64) n) 1/2) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 3)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(fabs.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3/2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1/2))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 1))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(+.f64 0 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))) 1)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 1)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(.f64 1 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k))))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (neg.f64 k)) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (neg.f64 k))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k))))
(.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (neg.f64 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (neg.f64 k)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))))
(.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 k))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (/.f64 1 (neg.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))))
(/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 1) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 1 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 k)) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(/.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k))
(/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) 1) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k)))
(/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 1) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 1 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k))))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))) (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (/.f64 (sqrt.f64 (+.f64 n n)) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))))
(/.f64 (.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (sqrt.f64 (+.f64 n n))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (/.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) (sqrt.f64 (+.f64 n n)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) k))))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k))))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))))
(.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4))) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 k 4))))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4)))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4))) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 k 4))))
(/.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4)) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4)) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 k 4))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 k 4))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (/.f64 k 4))) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (/.f64 k 4))))
(.f64 (/.f64 1 (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(.f64 (/.f64 1 (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) k)) (pow.f64 (sqrt.f64 (+.f64 n n)) k))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(/.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (pow.f64 (sqrt.f64 (+.f64 n n)) k) (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(.f64 (/.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) k)) (pow.f64 (sqrt.f64 (+.f64 n n)) k)) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (sqrt.f64 (+.f64 n n)) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)) (pow.f64 (sqrt.f64 (PI.f64)) k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(.f64 (/.f64 1 (pow.f64 (sqrt.f64 (PI.f64)) k)) (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (+.f64 n n)) k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (PI.f64)) k)) (pow.f64 (sqrt.f64 (+.f64 n n)) k))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 1)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 3)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))) 2)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2)) -1)
(/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 1/2 k -1/2)))
(/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2)))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) 3)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3)))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (fma.f64 1/2 k -1/2)) 1) -1)
(/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 1/2 k -1/2)))
(/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2)))
(neg.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k))))
(/.f64 (.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 1) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 1 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(sqrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 2))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(log.f64 (exp.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(cbrt.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 3))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) k) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3)))
(expm1.f64 (log1p.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(log1p.f64 (expm1.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k))

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k)
✓	0.2b	(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k))
✓	0.3b	(.f64 (PI.f64) (.f64 2 n))
✓	10.0b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))

Compiler

Compiled 50 to 33 computations (34% saved)

series14.0ms (0.1%)

Counts

4 → 72

Calls

21 calls:

Time	Variable		Point	Expression
3.0ms	k	@	-inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
2.0ms	k	@	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
1.0ms	k	@	inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
1.0ms	n	@	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
1.0ms	n	@	inf	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))

rewrite74.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`log-prod_binary64`
468×	`pow-unpow_binary64`
333×	`pow2_binary64`
226×	`pow1/3_binary64`
222×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	58
1	259	58
2	3391	58

Stop Event

1×	node limit

Counts

4 → 137

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(.f64 (PI.f64) (.f64 2 n))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (neg.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (-.f64 1 k)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) 2) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 n n) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (cbrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) (-.f64 1 k)) (.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) 3) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) 1) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (.f64 k k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (.f64 k k))) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (sqrt.f64 k)) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3) (pow.f64 k 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3) (pow.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1))))))

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

349×	`log-prod_binary64`
278×	`associate-r_binary64`
252×	`exp-prod_binary64`
237×	`associate-l_binary64`
221×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	378	4943
1	864	4115
2	3745	4070

Stop Event

1×	node limit

Counts

209 → 258

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 k -1)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/2)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) 2)
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) -1)
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) -1)
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))
(cbrt.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1))
(+.f64 0 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)
(.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))
(.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (neg.f64 k) 1)))
(.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k)))
(*.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))
(.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (-.f64 1 k)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))
(/.f64 (PI.f64) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (+.f64 n n)))
(/.f64 (+.f64 n n) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (PI.f64)))
(/.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(/.f64 (.f64 (PI.f64) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) n))
(/.f64 (neg.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k))))
(log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1))
(+.f64 0 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1)
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 k -1)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 k -1)))
(.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 k -1)))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k)))
(.f64 (pow.f64 k -1) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) 3) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k))
(*.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) 1) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) k))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (cbrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (.f64 k k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (.f64 k k))) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 k)))
(.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (cbrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (sqrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k)))
(*.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (sqrt.f64 k)) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3)
(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3) (pow.f64 k 3)) 1/3)
(pow.f64 (/.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1) -1)
(neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (neg.f64 k)))
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2))
(log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3) (pow.f64 k 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1))

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))
(pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 2 (*.f64 n (PI.f64))))
(fma.f64 2 (.f64 n (PI.f64)) (.f64 k (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(.f64 (PI.f64) (+.f64 (.f64 (.f64 k -2) (.f64 n (log.f64 (.f64 n (.f64 2 (PI.f64)))))) (+.f64 n n)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))
(fma.f64 (.f64 k -2) (.f64 n (.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (fma.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (*.f64 (PI.f64) (+.f64 n n))))
(+.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) -2) (.f64 (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2) k)))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(fma.f64 -2 (.f64 k (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (fma.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (fma.f64 2 (.f64 n (PI.f64)) (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2))))))
(fma.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (fma.f64 -1/3 (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 k 3))) (fma.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (*.f64 (PI.f64) (+.f64 n n)))))
(+.f64 (.f64 n (+.f64 (.f64 (.f64 -1/3 (pow.f64 k 3)) (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3))) (.f64 2 (PI.f64)))) (.f64 k (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) -2) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 2) k)))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(*.f64 2 (/.f64 n (/.f64 k (PI.f64))))
(.f64 2 (.f64 (/.f64 n k) (PI.f64)))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) (PI.f64)))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(fma.f64 2 (.f64 (/.f64 n k) (PI.f64)) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(fma.f64 2 (.f64 (/.f64 n k) (PI.f64)) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 n (.f64 2 (PI.f64))))))
(+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64))))))
(fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 2 (.f64 (/.f64 n k) (PI.f64)) (fma.f64 k (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (.f64 (PI.f64) (+.f64 n n))))))
(fma.f64 2 (.f64 (/.f64 n k) (PI.f64)) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) -2) (.f64 (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2) k))))
(+.f64 (.f64 -1/3 (.f64 (pow.f64 k 2) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) (+.f64 (.f64 k (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 -2 (.f64 n (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (PI.f64)))))))
(fma.f64 -1/3 (.f64 (.f64 k k) (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (fma.f64 2 (/.f64 n (/.f64 k (PI.f64))) (fma.f64 k (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 -2 (.f64 (.f64 n (PI.f64)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))))
(fma.f64 -1/3 (.f64 (.f64 n (PI.f64)) (.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (.f64 k k))) (fma.f64 2 (.f64 (/.f64 n k) (PI.f64)) (fma.f64 k (.f64 (.f64 n (PI.f64)) (pow.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (.f64 (.f64 -2 (.f64 n (PI.f64))) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))
(fma.f64 -1/3 (.f64 (.f64 (.f64 k k) (.f64 n (PI.f64))) (pow.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) 3)) (fma.f64 2 (.f64 (/.f64 n k) (PI.f64)) (.f64 (.f64 n (PI.f64)) (+.f64 (.f64 (log.f64 (.f64 n (.f64 2 (PI.f64)))) -2) (.f64 (pow.f64 (log.f64 (.f64 n (*.f64 2 (PI.f64)))) 2) k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))) k)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 k -1)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k))))
(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 2))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (neg.f64 (sqrt.f64 k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) 2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) -1)
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) -1)
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k) 3/2))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64))))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 2) 1/2)
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) 1/3)
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)) 1/3)
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(pow.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)) 1/3)
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 2))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 2) n) (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (+.f64 n n) 3)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(cbrt.f64 (*.f64 (pow.f64 (+.f64 n n) 3) (pow.f64 (PI.f64) 3)))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n))))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n))))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(exp.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1))
(.f64 2 (.f64 n (PI.f64)))
(*.f64 (PI.f64) (+.f64 n n))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 0 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(/.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) 1) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
(.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (neg.f64 k) 1)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) 2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 (-.f64 1 k) 2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) 2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 (-.f64 1 k) 2))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k)))
(*.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))
(*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k)))
(.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (-.f64 1 k)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (-.f64 1 k)) (pow.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) 2) (-.f64 1 k)) (pow.f64 (cbrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (-.f64 1 k) 2))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (-.f64 1 k) 2))
(pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 (-.f64 1 k) 2))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (-.f64 1 k)) (pow.f64 n (-.f64 1 k)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(/.f64 (PI.f64) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (+.f64 n n)))
(/.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) 1) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
(/.f64 (+.f64 n n) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (PI.f64)))
(/.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) 1) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
(/.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))
(/.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) 1) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) 1) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
(/.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (cbrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(/.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) 1) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(/.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) 1) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
(/.f64 (.f64 (PI.f64) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) n))
(/.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) 1) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
(/.f64 (neg.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)))
(/.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) 1) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 n (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1))
(pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
(+.f64 0 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k)))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 k -1))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k) 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 4))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) 4))
(.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)) k) 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k) 2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 k -1)))
(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) 2)))) (/.f64 1 k))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (.f64 (/.f64 1 k) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 (-.f64 1 k) 2))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) k))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 k -1)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 k -1)))
(.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (.f64 (/.f64 1 k) (pow.f64 (+.f64 n n) (-.f64 1 k))))
(.f64 (/.f64 1 k) (.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k))))
(*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) k))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 (neg.f64 k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (pow.f64 k -1) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) 3) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k))
(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) 2)))) (/.f64 1 k))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (.f64 (/.f64 1 k) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 (-.f64 1 k) 2))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) k))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(*.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) 1) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) k))
(.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (.f64 (/.f64 1 k) (pow.f64 (+.f64 n n) (-.f64 1 k))))
(.f64 (/.f64 1 k) (.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k))))
(*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) k))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (cbrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (cbrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (cbrt.f64 k)) (cbrt.f64 (.f64 k k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) (.f64 (cbrt.f64 (.f64 k k)) (cbrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (cbrt.f64 (.f64 k k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) 2))) (cbrt.f64 (*.f64 k k))))
(/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 2))) (/.f64 (cbrt.f64 (.f64 k k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 (-.f64 1 k) 2))) (cbrt.f64 (*.f64 k k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (.f64 k k))) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) (cbrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (cbrt.f64 k)) (cbrt.f64 (.f64 k k)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) (.f64 (cbrt.f64 (.f64 k k)) (cbrt.f64 k)))
(.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (cbrt.f64 (.f64 k k))) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (cbrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 2 (-.f64 1 k)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k)))
(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) 2)))) (/.f64 1 k))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (.f64 (/.f64 1 k) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 (-.f64 1 k) 2))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) k))
(*.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (sqrt.f64 k)) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (sqrt.f64 k)))
(.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (.f64 (/.f64 1 k) (pow.f64 (+.f64 n n) (-.f64 1 k))))
(.f64 (/.f64 1 k) (.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k))))
(*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) k))
(.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 4))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k))) 4))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2) 1/2)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3) 1/3)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) -1)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3) (pow.f64 k 3)) 1/3)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(pow.f64 (/.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1) -1)
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (neg.f64 k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 2))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3) (pow.f64 k 3)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1))
(/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k)
(/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(*.f64 n (PI.f64))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))

Compiler

Compiled 41 to 21 computations (48.8% saved)

series11.0ms (0.1%)

Counts

3 → 0

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
1.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
1.0ms	n	@	-inf	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
1.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
1.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))

rewrite59.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log-prod_binary64`
426×	`pow-prod-down_binary64`
296×	`pow2_binary64`
261×	`pow-unpow_binary64`
211×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	261	28
2	3012	28

Stop Event

1×	node limit

Counts

3 → 85

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 n (PI.f64))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 k)) (pow.f64 k 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) -1) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 n (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 n (PI.f64)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 n (PI.f64)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1) 2))))))

simplify54.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

466×	`log-prod_binary64`
386×	`fma-def_binary64`
368×	`unswap-sqr_binary64`
361×	`hypot-def_binary64`
337×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	207	4294968264
1	440	939
2	1449	939
3	6942	939

Stop Event

1×	node limit

Counts

85 → 104

Calls

Call 1

Inputs
(+.f64 0 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 1)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) 2)
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4)) 2))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 1) 1))
(+.f64 0 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 1)
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 k)) (pow.f64 k 1/6))
(/.f64 (.f64 -1 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) -1) (neg.f64 (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 1)
(pow.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 2)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) -1)
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k))) 1))
(exp.f64 (.f64 (.f64 3 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 1) 1))
(+.f64 0 (*.f64 n (PI.f64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)
(pow.f64 (*.f64 n (PI.f64)) 1)
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 2) 1/2)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) 2/3)
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) 6)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 4)
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64)))))
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3))
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))
(log1p.f64 (expm1.f64 (*.f64 n (PI.f64))))
(exp.f64 (log.f64 (*.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) 1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (PI.f64)))) 2))
(exp.f64 (.f64 (.f64 2 (log.f64 (*.f64 n (PI.f64)))) 1/2))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 n (PI.f64)))) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 n (PI.f64)))) 3))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (PI.f64))) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (PI.f64))) 1/2) 2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1) 2))

Outputs
(+.f64 0 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))) 1)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) 1/3)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) 3)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) 2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) 1))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 3/2)) 1/3))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6)) 3))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4)) 2))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 1/2))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) 1) 1))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(+.f64 0 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64))))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64)))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 2 k) (*.f64 n (PI.f64))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) (/.f64 2 k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64)))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 2 k) (*.f64 n (PI.f64))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) (/.f64 2 k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 1)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 k)) (pow.f64 k 1/6))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (pow.f64 k 1/6) (cbrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (cbrt.f64 k) (pow.f64 k 1/6)))
(/.f64 (.f64 -1 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) -1) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 1)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k) 1/2)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3) 1/3)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 3)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 2)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)))
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) -1)
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k))) 1))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (.f64 3 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 1/3))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 3))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 2))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 1) 1))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(+.f64 0 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) n))))
(*.f64 n (PI.f64))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) 1)
(*.f64 n (PI.f64))
(pow.f64 (*.f64 n (PI.f64)) 1)
(*.f64 n (PI.f64))
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 2)
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 2) 1/2)
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/3)
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) 2/3)
(.f64 (cbrt.f64 (pow.f64 (.f64 n (PI.f64)) 3/2)) (cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2)))
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3)
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) 6)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 4)
(*.f64 n (PI.f64))
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) 2))
(*.f64 n (PI.f64))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(*.f64 n (PI.f64))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 n (PI.f64)))))
(*.f64 n (PI.f64))
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3))
(*.f64 n (PI.f64))
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))
(*.f64 n (PI.f64))
(log1p.f64 (expm1.f64 (*.f64 n (PI.f64))))
(*.f64 n (PI.f64))
(exp.f64 (log.f64 (*.f64 n (PI.f64))))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) 1))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (PI.f64)))) 2))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (.f64 2 (log.f64 (*.f64 n (PI.f64)))) 1/2))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 n (PI.f64)))) 1/3))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 n (PI.f64)))) 3))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (PI.f64))) 1) 1))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (PI.f64))) 1/2) 2))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1) 2))
(*.f64 n (PI.f64))

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))
✓	0.3b	(/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2))))
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
✓	0.7b	(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))

Compiler

Compiled 66 to 46 computations (30.3% saved)

series76.0ms (0.7%)

Counts

4 → 60

Calls

21 calls:

Time	Variable		Point	Expression
34.0ms	n	@	0	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
12.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
7.0ms	n	@	inf	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
5.0ms	n	@	-inf	(/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2))))
4.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))

rewrite74.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`log-prod_binary64`
284×	`expm1-udef_binary64`
284×	`log1p-udef_binary64`
271×	`log-pow_binary64`
252×	`prod-diff_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	70
1	323	70
2	4527	60

Stop Event

1×	node limit

Counts

4 → 140

Calls

Call 1

Inputs
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2))))
(pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (PI.f64))) (/.f64 1 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k) (sqrt.f64 (.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (.f64 2 (PI.f64)))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (PI.f64)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2) (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (sqrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 1 (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))) (neg.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 k) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 k) (.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k 1/4) (.f64 (pow.f64 k 1/4) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 k) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 k 1/4) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (/.f64 (pow.f64 k 1/4) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 k) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 k) (sqrt.f64 n)) (pow.f64 (sqrt.f64 n) k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 n) (/.f64 1 (pow.f64 (sqrt.f64 n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 n) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 n) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (sqrt.f64 n) k) (sqrt.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 n) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (pow.f64 (sqrt.f64 n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 n)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 n)) 1))))))

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

413×	`associate-/l/_binary64`
304×	`log-prod_binary64`
292×	`associate-r_binary64`
237×	`associate-l_binary64`
206×	`sqr-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	415	4449
1	1005	4239
2	4243	4118

Stop Event

1×	node limit

Counts

200 → 249

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3))) (sqrt.f64 (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64)))))))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k)))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(sqrt.f64 n)
(+.f64 (.f64 -1/2 (.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (sqrt.f64 n))
(+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n)))
(+.f64 (.f64 -1/48 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3)) (sqrt.f64 n))) (+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (.f64 1/8 (.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n))))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(+.f64 0 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) 1)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 1)
(.f64 1 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (/.f64 1 (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k)))
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))
(*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k) (sqrt.f64 (.f64 2 (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (PI.f64)))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k)))
(sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2))))
(log.f64 (exp.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (PI.f64)))))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (PI.f64)))) 1))
(+.f64 0 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(+.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) 1)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1)
(.f64 1 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (pow.f64 (cbrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2) (cbrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (sqrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (neg.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 1 (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(.f64 (/.f64 1 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))) (neg.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1) (pow.f64 n (fma.f64 k -1/2 1/2)))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1)
(pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 3)
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)
(pow.f64 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))) -1)
(neg.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(sqrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 3)))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(exp.f64 (log.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1))
(+.f64 0 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) 1)
(*.f64 (sqrt.f64 k) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2))))
(*.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 1)
(*.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 k) (.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))))
(.f64 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (pow.f64 k 1/4) (.f64 (pow.f64 k 1/4) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(*.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(*.f64 (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
(*.f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2))))
(*.f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (/.f64 (pow.f64 k 1/4) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (/.f64 (pow.f64 k 1/4) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(*.f64 (/.f64 1 (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(*.f64 (/.f64 (cbrt.f64 k) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(*.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 n)) (pow.f64 (sqrt.f64 n) k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 1)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) 3)
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) 2)
(pow.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) -1)
(neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(sqrt.f64 (/.f64 k (pow.f64 n (*.f64 2 (fma.f64 k -1/2 1/2)))))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 3))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3)))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) 1))
(+.f64 0 (pow.f64 n (fma.f64 k -1/2 1/2)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) 1)
(*.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 1)
(*.f64 1 (pow.f64 n (fma.f64 k -1/2 1/2)))
(.f64 (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2)))
(*.f64 (sqrt.f64 n) (/.f64 1 (pow.f64 (sqrt.f64 n) k)))
(*.f64 (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(*.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 n) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 n) (fma.f64 k -1/2 1/2)))
(*.f64 (pow.f64 (sqrt.f64 n) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 n) (fma.f64 k -1/2 1/2)))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 n) k) (sqrt.f64 n)))
(/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 n) k))
(/.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (pow.f64 (sqrt.f64 n) k)))
(sqrt.f64 (pow.f64 n (*.f64 2 (fma.f64 k -1/2 1/2))))
(log.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 n)))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 n)) 1))

Outputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (*.f64 2 (PI.f64)))) (sqrt.f64 (PI.f64))))))
(.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (sqrt.f64 2)) (.f64 k (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (+.f64 (.f64 -1/2 (.f64 k (log.f64 (*.f64 2 (PI.f64))))) 1) (sqrt.f64 2)))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64))))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (PI.f64)))) (.f64 1/8 (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (sqrt.f64 2) (.f64 k k)) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2))))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 (.f64 -1/2 (sqrt.f64 2)) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2)))))))
(.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (PI.f64))))) (.f64 1/8 (.f64 k (.f64 k (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3))) (sqrt.f64 (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64)))))))
(fma.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)) (fma.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (PI.f64)))) (fma.f64 -1/48 (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (sqrt.f64 2) (pow.f64 k 3)) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3))) (.f64 1/8 (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (sqrt.f64 2) (.f64 k k)) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2)))))))
(+.f64 (.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (.f64 (.f64 -1/2 (sqrt.f64 2)) (.f64 k (log.f64 (.f64 2 (PI.f64))))))) (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2)))) (.f64 (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 k 3))) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 3)))))
(.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 k (log.f64 (.f64 2 (PI.f64))))) 1) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3))) (.f64 1/8 (.f64 k (.f64 k (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))))))))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (*.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k))))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 n (fma.f64 k -1/2 1/2))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (exp.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (-.f64 1/2 (.f64 1/2 k))))))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))) (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))) (log.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (*.f64 1/2 k))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k)))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k)))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k)))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (.f64 1/2 k)))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)) (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)) (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)) (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n)))))
(.f64 (sqrt.f64 k) (/.f64 1 (exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (sqrt.f64 k) (exp.f64 (neg.f64 (.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)) (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n)))))
(exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (log.f64 n) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 -1 (.f64 (log.f64 (/.f64 1 n)) (-.f64 1/2 (*.f64 1/2 k)))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))))
(exp.f64 (.f64 (-.f64 1/2 (.f64 1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))
(pow.f64 (exp.f64 (fma.f64 k -1/2 1/2)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 -1)))
(pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 n))))
(sqrt.f64 n)
(+.f64 (.f64 -1/2 (.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (sqrt.f64 n))
(fma.f64 -1/2 (.f64 k (.f64 (log.f64 n) (sqrt.f64 n))) (sqrt.f64 n))
(.f64 (+.f64 (.f64 -1/2 (*.f64 k (log.f64 n))) 1) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (+.f64 (.f64 -1/2 (*.f64 k (log.f64 n))) 1))
(+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n)))
(fma.f64 -1/2 (.f64 k (.f64 (log.f64 n) (sqrt.f64 n))) (fma.f64 1/8 (.f64 (.f64 k k) (*.f64 (pow.f64 (log.f64 n) 2) (sqrt.f64 n))) (sqrt.f64 n)))
(+.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (+.f64 (.f64 -1/2 (.f64 k (log.f64 n))) (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 n) 2))))))
(.f64 (sqrt.f64 n) (+.f64 (.f64 -1/2 (.f64 k (log.f64 n))) (+.f64 (.f64 (.f64 1/8 (.f64 k k)) (pow.f64 (log.f64 n) 2)) 1)))
(+.f64 (.f64 -1/48 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3)) (sqrt.f64 n))) (+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (.f64 1/8 (.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n))))
(fma.f64 -1/48 (.f64 (pow.f64 k 3) (.f64 (pow.f64 (log.f64 n) 3) (sqrt.f64 n))) (fma.f64 -1/2 (.f64 k (.f64 (log.f64 n) (sqrt.f64 n))) (fma.f64 1/8 (.f64 (.f64 k k) (*.f64 (pow.f64 (log.f64 n) 2) (sqrt.f64 n))) (sqrt.f64 n))))
(+.f64 (fma.f64 1/8 (.f64 (.f64 k k) (.f64 (sqrt.f64 n) (pow.f64 (log.f64 n) 2))) (sqrt.f64 n)) (.f64 (sqrt.f64 n) (+.f64 (.f64 (.f64 -1/48 (pow.f64 k 3)) (pow.f64 (log.f64 n) 3)) (.f64 -1/2 (.f64 k (log.f64 n))))))
(+.f64 (.f64 (sqrt.f64 n) (+.f64 (.f64 (.f64 -1/48 (pow.f64 k 3)) (pow.f64 (log.f64 n) 3)) (+.f64 (.f64 -1/2 (.f64 k (log.f64 n))) (.f64 (.f64 1/8 (.f64 k k)) (pow.f64 (log.f64 n) 2))))) (sqrt.f64 n))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(+.f64 0 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))) 1)
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 1)
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(.f64 1 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 -1/2 k 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 -1/2 k 1/2)))))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (.f64 2 (PI.f64)) (.f64 -1/2 k)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (/.f64 1 (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) k)))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k) (sqrt.f64 (.f64 2 (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k))
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))
(*.f64 (pow.f64 2 (fma.f64 -1/2 k 1/2)) (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)))
(*.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)))
(*.f64 (pow.f64 2 (fma.f64 -1/2 k 1/2)) (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) 2)) (fma.f64 -1/2 k 1/2)) (pow.f64 (cbrt.f64 (*.f64 2 (PI.f64))) (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))
(pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (fma.f64 k -1/2 1/2)))
(pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (fma.f64 -1/2 k 1/2)))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k) (sqrt.f64 (.f64 2 (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k))
(/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k) (sqrt.f64 (.f64 2 (PI.f64)))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (PI.f64)))) (neg.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k)))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k) (sqrt.f64 (.f64 2 (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (sqrt.f64 (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2))))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(log.f64 (exp.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 2 (PI.f64)))))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 2 (PI.f64)))) 1))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))
(+.f64 0 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(+.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))))
(.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) 1)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 1 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (pow.f64 (cbrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2) (cbrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (.f64 (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (*.f64 2 (fma.f64 -1/2 k 1/2))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 -1/2 k 1/2)))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))))
(.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (sqrt.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (.f64 (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) (pow.f64 2 (fma.f64 -1/2 k 1/2))))
(.f64 (pow.f64 2 (fma.f64 -1/2 k 1/2)) (.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (/.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))
(.f64 (neg.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 1 (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (.f64 (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (*.f64 2 (fma.f64 -1/2 k 1/2))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 -1/2 k 1/2)))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (.f64 (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) (pow.f64 2 (fma.f64 -1/2 k 1/2))))
(.f64 (pow.f64 2 (fma.f64 -1/2 k 1/2)) (.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (/.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (.f64 (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (*.f64 2 (fma.f64 -1/2 k 1/2))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 -1/2 k 1/2)))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))))
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(.f64 (.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (.f64 (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) (pow.f64 2 (fma.f64 -1/2 k 1/2))))
(.f64 (pow.f64 2 (fma.f64 -1/2 k 1/2)) (.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (/.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(/.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2))))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2))))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) (.f64 (cbrt.f64 (/.f64 k (pow.f64 n (*.f64 2 (fma.f64 -1/2 k 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2))))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))))
(.f64 (cbrt.f64 (/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 -1/2 k 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2)))))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 -1/2 k 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 n (*.f64 2 (fma.f64 -1/2 k 1/2)))))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (sqrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(/.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2))))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2))))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) (.f64 (cbrt.f64 (/.f64 k (pow.f64 n (*.f64 2 (fma.f64 -1/2 k 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2))))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(/.f64 (/.f64 (.f64 (pow.f64 2 (fma.f64 -1/2 k 1/2)) (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2))))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2))))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 -1/2 k 1/2)) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2)))))) (/.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2))))))
(.f64 (/.f64 1 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (.f64 (cbrt.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (.f64 (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (*.f64 2 (fma.f64 -1/2 k 1/2))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2))) (/.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 -1/2 k 1/2)))) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))))
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (/.f64 (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(.f64 (.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (.f64 (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) (pow.f64 2 (fma.f64 -1/2 k 1/2))))
(.f64 (pow.f64 2 (fma.f64 -1/2 k 1/2)) (.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (/.f64 (pow.f64 (PI.f64) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))) (neg.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1) (pow.f64 n (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (.f64 (cbrt.f64 (pow.f64 n (fma.f64 -1/2 k 1/2))) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k))) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2)))))
(.f64 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2)))) (.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 -1/2 k 1/2)) (sqrt.f64 k)) (cbrt.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)))))
(.f64 (.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3) 1/3)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 3)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(pow.f64 (/.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))) -1)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(sqrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 3)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(exp.f64 (log.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 -1/2 k 1/2) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) (sqrt.f64 k))
(/.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 k 1/2)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) (sqrt.f64 k))
(+.f64 0 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))) 1)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 1)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (cbrt.f64 k) (.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 k) (.f64 (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (.f64 (cbrt.f64 k) (pow.f64 n (+.f64 -1/2 (*.f64 k 1/2)))) (cbrt.f64 (sqrt.f64 k)))
(.f64 (pow.f64 n (+.f64 -1/2 (.f64 k 1/2))) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))))
(.f64 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))))
(.f64 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (/.f64 k (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (pow.f64 k 1/4) (.f64 (pow.f64 k 1/4) (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (pow.f64 n (neg.f64 (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2))))
(*.f64 (cbrt.f64 k) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2))))
(/.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(/.f64 (cbrt.f64 k) (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (pow.f64 n (fma.f64 k -1/2 1/2))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)))) (cbrt.f64 (pow.f64 n (*.f64 2 (fma.f64 -1/2 k 1/2)))))
(.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 k) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))))
(.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))) (/.f64 (cbrt.f64 k) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2))))))
(.f64 (/.f64 (pow.f64 k 1/4) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (/.f64 (pow.f64 k 1/4) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2))))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)))) (cbrt.f64 (pow.f64 n (*.f64 2 (fma.f64 -1/2 k 1/2)))))
(*.f64 (/.f64 1 (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(*.f64 (/.f64 (cbrt.f64 k) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(*.f64 (cbrt.f64 k) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k -1/2 1/2))))
(/.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(/.f64 (cbrt.f64 k) (/.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 n)) (pow.f64 (sqrt.f64 n) k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 1)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 3) 1/3)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) 3)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) 2)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(pow.f64 (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) -1)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(sqrt.f64 (/.f64 k (pow.f64 n (*.f64 2 (fma.f64 k -1/2 1/2)))))
(sqrt.f64 (/.f64 k (pow.f64 n (*.f64 2 (fma.f64 -1/2 k 1/2)))))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))) 3))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3)))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)) 3)))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))) 1))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 -1/2 k 1/2)))
(+.f64 0 (pow.f64 n (fma.f64 k -1/2 1/2)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 -1/2 k 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 -1/2 k 1/2))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 n (fma.f64 -1/2 k 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 n (fma.f64 -1/2 k 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))) 1)
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(*.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 1)
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(*.f64 1 (pow.f64 n (fma.f64 k -1/2 1/2)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(.f64 (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2)))) (cbrt.f64 (pow.f64 n (fma.f64 -1/2 k 1/2))))
(.f64 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 n (.f64 2 (fma.f64 -1/2 k 1/2)))) (cbrt.f64 (pow.f64 n (fma.f64 -1/2 k 1/2))))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2)))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 -1/2 k)))
(*.f64 (sqrt.f64 n) (/.f64 1 (pow.f64 (sqrt.f64 n) k)))
(/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 n) k))
(*.f64 (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(*.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 n) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 n) (fma.f64 k -1/2 1/2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 n) 2) (fma.f64 -1/2 k 1/2)) (pow.f64 (cbrt.f64 n) (fma.f64 -1/2 k 1/2)))
(*.f64 (pow.f64 (sqrt.f64 n) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 n) (fma.f64 k -1/2 1/2)))
(pow.f64 (sqrt.f64 n) (*.f64 2 (fma.f64 k -1/2 1/2)))
(pow.f64 (sqrt.f64 n) (*.f64 2 (fma.f64 -1/2 k 1/2)))
(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 n) k) (sqrt.f64 n)))
(*.f64 (sqrt.f64 n) (/.f64 1 (pow.f64 (sqrt.f64 n) k)))
(/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 n) k))
(/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 n) k))
(*.f64 (sqrt.f64 n) (/.f64 1 (pow.f64 (sqrt.f64 n) k)))
(/.f64 (neg.f64 (sqrt.f64 n)) (neg.f64 (pow.f64 (sqrt.f64 n) k)))
(*.f64 (sqrt.f64 n) (/.f64 1 (pow.f64 (sqrt.f64 n) k)))
(/.f64 (sqrt.f64 n) (pow.f64 (sqrt.f64 n) k))
(sqrt.f64 (pow.f64 n (*.f64 2 (fma.f64 k -1/2 1/2))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(log.f64 (exp.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 n (fma.f64 k -1/2 1/2)))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(cbrt.f64 (pow.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) 3))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(expm1.f64 (log1p.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(log1p.f64 (expm1.f64 (pow.f64 n (fma.f64 k -1/2 1/2))))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 n)))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 n)) 1))
(pow.f64 n (fma.f64 k -1/2 1/2))
(pow.f64 n (fma.f64 -1/2 k 1/2))

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2)))
✓	0.3b	(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.3b	(*.f64 (PI.f64) n)
✓	5.6b	(exp.f64 (log.f64 (*.f64 (PI.f64) n)))

Compiler

Compiled 65 to 32 computations (50.8% saved)

series6.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
1.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
0.0ms	k	@	inf	(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
0.0ms	k	@	0	(pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2)))
0.0ms	n	@	0	(exp.f64 (log.f64 (*.f64 (PI.f64) n)))

rewrite64.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

777×	`log-prod_binary64`
402×	`pow2_binary64`
274×	`pow1/3_binary64`
273×	`expm1-udef_binary64`
273×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	318	44
2	4091	40

Stop Event

1×	node limit

Counts

3 → 105

Calls

Call 1

Inputs

(exp.f64 (log.f64 (*.f64 (PI.f64) n)))

(/.f64 (pow.f64 (*.f64 2 (exp.f64 (log.f64 (*.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

(pow.f64 (*.f64 2 (exp.f64 (log.f64 (*.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 n (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2) (cbrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 n) 2) (*.f64 (cbrt.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (*.f64 (cbrt.f64 (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) n) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (PI.f64) n)))) (sqrt.f64 (log.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (PI.f64) n))) 2)) (cbrt.f64 (log.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 n) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 1/2 k)) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 1/2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))) (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 k -1/2 1/2) (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))) 1))))))

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

779×	`fma-def_binary64`
569×	`unswap-sqr_binary64`
513×	`associate-/l*_binary64`
380×	`times-frac_binary64`
329×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	319	3155
1	734	2811
2	2445	2760

Stop Event

1×	node limit

Counts

153 → 180

Calls

Call 1

Inputs
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(+.f64 0 (*.f64 (PI.f64) n))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(.f64 (.f64 (PI.f64) n) 1)
(.f64 1 (.f64 (PI.f64) n))
(.f64 (cbrt.f64 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 2) (cbrt.f64 (*.f64 (PI.f64) n)))
(.f64 (pow.f64 (cbrt.f64 n) 2) (.f64 (cbrt.f64 n) (PI.f64)))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) n))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
(.f64 (.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
(.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(pow.f64 (*.f64 (PI.f64) n) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) n)))) (sqrt.f64 (log.f64 (.f64 (PI.f64) n))))
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) n))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) n))))
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)
(pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))
(log.f64 (pow.f64 (exp.f64 n) (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(+.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) -1)
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))
(+.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)
(.f64 1 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k))))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 n 2)))))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 n 2)))) 1))

Outputs
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (+.f64 (log.f64 (.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (*.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (exp.f64 (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) (fma.f64 k -1/2 1/2))
(pow.f64 (exp.f64 (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (*.f64 (PI.f64) 2))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 (PI.f64) 2)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 (.f64 1/8 (sqrt.f64 2)) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)) (.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (.f64 k k))) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 (PI.f64) (.f64 n 2)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))) (fma.f64 1/8 (.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (PI.f64) (*.f64 n 2))) 3))))))))
(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 n (.f64 (PI.f64) 2)))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 (.f64 1/8 (sqrt.f64 2)) (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2))) (.f64 (.f64 -1/48 (sqrt.f64 2)) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 3))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (fma.f64 -1/2 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k (sqrt.f64 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 3))) (.f64 1/8 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 2)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(+.f64 0 (*.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 n) (PI.f64)))))
(*.f64 n (PI.f64))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) n))) 1)
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(.f64 (.f64 (PI.f64) n) 1)
(*.f64 n (PI.f64))
(.f64 1 (.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(.f64 (cbrt.f64 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 2))
(*.f64 n (PI.f64))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) n)) 2) (cbrt.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(.f64 (pow.f64 (cbrt.f64 n) 2) (.f64 (cbrt.f64 n) (PI.f64)))
(*.f64 n (PI.f64))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) n))
(*.f64 n (PI.f64))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (PI.f64)))
(*.f64 n (PI.f64))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n))
(*.f64 n (PI.f64))
(.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
(*.f64 n (PI.f64))
(.f64 (.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
(*.f64 n (PI.f64))
(.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))
(*.f64 n (PI.f64))
(.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 n (PI.f64))
(pow.f64 (*.f64 (PI.f64) n) 1)
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) 3) 1/3)
(*.f64 n (PI.f64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) 3)
(*.f64 n (PI.f64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)
(*.f64 n (PI.f64))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) n)))) (sqrt.f64 (log.f64 (.f64 (PI.f64) n))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 n (PI.f64))))) (sqrt.f64 (log.f64 (.f64 n (PI.f64)))))
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) n)))
(pow.f64 (E.f64) (log.f64 (*.f64 n (PI.f64))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) n))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) n))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (PI.f64)))) 2)) (cbrt.f64 (log.f64 (.f64 n (PI.f64)))))
(pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)) 1/3)
(*.f64 n (PI.f64))
(pow.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)) 1/3)
(*.f64 n (PI.f64))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) 2))
(*.f64 n (PI.f64))
(log.f64 (pow.f64 (exp.f64 n) (PI.f64)))
(*.f64 n (PI.f64))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) n))))
(*.f64 n (PI.f64))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) 3))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 n 3)))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 n 3) (pow.f64 (PI.f64) 3)))
(*.f64 n (PI.f64))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(+.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 2 (.f64 k -1/2) 1)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2))) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 2 (.f64 k -1/2) 1)) k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))))
(.f64 (pow.f64 k -1/2) (.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 2 (.f64 k -1/2) 1))) (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)))))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (pow.f64 k -1/2) (.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 2 (.f64 k -1/2) 1))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 2 (.f64 k -1/2) 1))) (cbrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (pow.f64 k 1/4)) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (pow.f64 k 1/4)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 2 (.f64 k -1/2) 1))) (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (PI.f64)) (fma.f64 k -1/2 1/2))))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3) 1/3)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) 1) -1)
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (neg.f64 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 2 (*.f64 k -1/2) 1)) k))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
(+.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 1 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 2 (.f64 k -1/2) 1))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 2 (.f64 k -1/2) 1))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k -1/2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 k 1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) 2) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (fma.f64 k -1/2 1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 2 (fma.f64 k -1/2 1/2)))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (*.f64 2 (fma.f64 k -1/2 1/2)))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (fma.f64 2 (*.f64 k -1/2) 1))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 1/2 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 k 1/2)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 k 1/2)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k 1/2))))
(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 k 1/2)))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) 3))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (*.f64 n 2)))))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))
(exp.f64 (.f64 (.f64 (fma.f64 k -1/2 1/2) (log.f64 (.f64 (PI.f64) (.f64 n 2)))) 1))
(pow.f64 (exp.f64 (+.f64 (log.f64 (*.f64 (PI.f64) 2)) (log.f64 n))) (fma.f64 k -1/2 1/2))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) (fma.f64 k -1/2 1/2))

eval579.0ms (5.6%)

Compiler: Compiled 25050 to 15071 computations (39.8% saved)

prune380.0ms (3.7%)

Pruning

26 alts after pruning (23 fresh and 3 done)

	Pruned	Kept	Total
New	1101	20	1121
Fresh	12	3	15
Picked	1	0	1
Done	3	3	6
Total	1117	26	1143

Error

Counts

1143 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	21.6b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
	20.4b	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.4b	(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (sqrt.f64 k))
	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2))) (sqrt.f64 k))
▶	20.3b	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
▶	0.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
	20.2b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
	20.3b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
	10.3b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	20.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	10.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
	10.9b	(sqrt.f64 (/.f64 (/.f64 (+.f64 n n) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (PI.f64))) k))
	10.9b	(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)) k))
	10.9b	(sqrt.f64 (/.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n)))) k))
	12.9b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) k))
	30.5b	(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
	30.5b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
	30.5b	(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
▶	30.5b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
▶	12.9b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
	20.1b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
	39.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))

Compiler

Compiled 749 to 564 computations (24.7% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
✓	0.1b	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
✓	0.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
	0.3b	(*.f64 n (PI.f64))

Compiler

Compiled 59 to 29 computations (50.8% saved)

series34.0ms (0.3%)

Counts

3 → 12

Calls

15 calls:

Time	Variable		Point	Expression
8.0ms	n	@	0	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
7.0ms	n	@	inf	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
6.0ms	n	@	-inf	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
5.0ms	k	@	0	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
1.0ms	k	@	-inf	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))

rewrite65.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`log-prod_binary64`
413×	`pow-unpow_binary64`
325×	`pow-pow_binary64`
317×	`pow2_binary64`
222×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	53
1	253	49
2	3281	44

Stop Event

1×	node limit

Counts

3 → 111

Calls

Call 1

Inputs

(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) k)))

(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))

(pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) k)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/6) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) (*.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))) (/.f64 1 (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) 1) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/6) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) 1) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1/2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1/3 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1/2 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k)) (sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (-.f64 1/3 (*.f64 k 1/2))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/6) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (cbrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) (cbrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) (cbrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))) -1/2) (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (sqrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (sqrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))) (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/6) (sqrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 3/2) (pow.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (neg.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 n (*.f64 (PI.f64) 2)) (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 3/2) (pow.f64 (sqrt.f64 (*.f64 k (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/6) (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 n)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))) (sqrt.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (*.f64 k 1/2)) (pow.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)) (pow.f64 2 (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (*.f64 k 1/2)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (*.f64 2 (*.f64 k 1/2))) (pow.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 n) (*.f64 k 1/2)) (pow.f64 (PI.f64) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) k) (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) 1/6) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 2) k) (pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (*.f64 1/4 k)) (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) (*.f64 1/4 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (exp.f64 (log1p.f64 k))) (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (sqrt.f64 k)) (exp.f64 (log1p.f64 (sqrt.f64 k)))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))) (*.f64 k 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 k (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (*.f64 (PI.f64) 2))) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 k (log.f64 (sqrt.f64 (*.f64 n (*.f64 (PI.f64) 2))))) 1))))))

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l*_binary64`
545×	`times-frac_binary64`
395×	`fma-def_binary64`
329×	`unswap-sqr_binary64`
268×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	2906
1	671	2815
2	2237	2747

Stop Event

1×	node limit

Counts

123 → 220

Calls

Call 1

Inputs
1
(+.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) 1)
(+.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) 2))) 1))
(+.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (+.f64 1 (.f64 1/6 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) 3))))))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(+.f64 0 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))) 1)
(.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (cbrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))) (/.f64 1 (neg.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(.f64 (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) 1) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) 1) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1/2 k)))
(.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1/3 k)))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1/2 k)) (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/4) (sqrt.f64 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (neg.f64 k)) (sqrt.f64 (/.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1/3 (.f64 k 1/2))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(.f64 (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) -1/2) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 1)
(pow.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))) 1/2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 3) 1/3)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) 3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) 2)
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k))) -1)
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2) (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k))) 1) -1)
(neg.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (neg.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(log.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2) (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))) 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) 1))
(+.f64 0 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) 1)
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) 1)
(.f64 1 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))
(.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/6))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (cbrt.f64 (.f64 n (*.f64 (PI.f64) 2))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/4))
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (PI.f64)))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/2)
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) 1)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 2) 1/4)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) 3/2)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) 2)
(fabs.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))) 1))
(+.f64 0 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) 1)
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)) 1)
(.f64 1 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) (sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(.f64 (pow.f64 2 (.f64 k 1/2)) (pow.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))
(.f64 (pow.f64 (.f64 n (PI.f64)) (.f64 k 1/2)) (pow.f64 2 (.f64 k 1/2)))
(.f64 (pow.f64 1 (.f64 k 1/2)) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))
(.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k 1/2)))
(.f64 (pow.f64 (.f64 2 n) (.f64 k 1/2)) (pow.f64 (PI.f64) (.f64 k 1/2)))
(.f64 (pow.f64 1 k) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))
(.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/6) k))
(.f64 (pow.f64 (sqrt.f64 2) k) (pow.f64 (sqrt.f64 (.f64 n (PI.f64))) k))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 1/4 k)) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 1/4 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (exp.f64 (log1p.f64 k))) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))
(/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (exp.f64 (log1p.f64 (sqrt.f64 k)))) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (*.f64 k 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))
(exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))))
(exp.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k 1/2)))
(exp.f64 (.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) 1))

Outputs
1
(+.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) 1)
(fma.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 1)
(+.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) 2))) 1))
(fma.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 1/2 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)) 1))
(fma.f64 (.f64 k k) (.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2) 1/2) (fma.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 1))
(+.f64 (.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2))) (+.f64 1 (.f64 1/6 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) 3))))))
(fma.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (fma.f64 1/2 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)) 1) (.f64 1/6 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 3)))))
(fma.f64 k (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) (fma.f64 1/2 (.f64 (.f64 k k) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))) 2)) (fma.f64 1/6 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) 3)) 1)))
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(pow.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) k)
(+.f64 0 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))) 1)
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (pow.f64 k -1/2)))
(.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 1 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))))
(.f64 (cbrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (cbrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))))
(.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/6)))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6)) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) 3) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (pow.f64 k -1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k)))))
(/.f64 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 k -1/2)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (pow.f64 k -1/2)))
(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))) (/.f64 1 (neg.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (/.f64 1 (neg.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))))
(.f64 1 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(.f64 (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))
(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (pow.f64 k -1/2)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (neg.f64 k)))
(.f64 (sqrt.f64 (/.f64 n (/.f64 k (.f64 2 (PI.f64))))) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (neg.f64 k)))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (neg.f64 k)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) 1) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/6) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) 3) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k)))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) 1) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (/.f64 1 (neg.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))))
(.f64 1 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1/2 k)))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/4) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (-.f64 1/2 k)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 k)))
(.f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k)) (pow.f64 k -1/2))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1/3 k)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (-.f64 1/3 k)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/3 k)))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))
(.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k) (sqrt.f64 k))))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1/2 k)) (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/4) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/4) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (-.f64 1/2 k)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 k)))
(.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (neg.f64 k)) (sqrt.f64 (/.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))
(.f64 (sqrt.f64 (/.f64 n (/.f64 k (.f64 2 (PI.f64))))) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (neg.f64 k)))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64)))) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (neg.f64 k)))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (-.f64 1/3 (.f64 k 1/2))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1/3 (.f64 k 1/2))) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/6) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/3 (.f64 k 1/2))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k -1/2 1/3)) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))
(.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k) (sqrt.f64 k))))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (cbrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))) (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(/.f64 (.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))) (sqrt.f64 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))))
(/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (cbrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(.f64 (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (cbrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))) (cbrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(.f64 (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) -1/2) (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(.f64 (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))) -1/2) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))))
(.f64 (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) -1/2) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))) (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(.f64 (/.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))) (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/6) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))))
(/.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))))
(/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) 3) (.f64 (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))) (sqrt.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))))
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))) 1/2)
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
(sqrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 3) 1/3)
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) 3)
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) 2)
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k))) -1)
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2) (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))) 3)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))) 3)))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k))) 1) -1)
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(neg.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (neg.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))))
(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))) (/.f64 1 (neg.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))))
(.f64 1 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))
(sqrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(log.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k)) 3))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2) (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))) 3)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))) 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(exp.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) (-.f64 1 k)) (sqrt.f64 k))) 1))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (-.f64 1 k)) (sqrt.f64 k))
(+.f64 0 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) 1)
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))) 1)
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(.f64 1 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/6))
(.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) 1/6))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) 3)
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) (cbrt.f64 (.f64 n (*.f64 (PI.f64) 2))))
(.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) 1/6))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) 3)
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/4))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (PI.f64)))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/2)
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) 1)
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 2) 1/4)
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 2) 1/4)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2) 1/4)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3) 1/6)
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3) 1/6)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 3/2)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/6) 3)
(.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) 1/6))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6))
(pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) 3)
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) 2)
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(fabs.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 3/2))
(cbrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (PI.f64) 2))) 1/2))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2)))) 1))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(+.f64 0 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))) 1)
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)) 1)
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(.f64 1 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) (cbrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))) (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k)))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)) (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))) (cbrt.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) k)))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))
(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)) (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k)))
(.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))) (sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(.f64 (pow.f64 2 (.f64 k 1/2)) (pow.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))
(.f64 (pow.f64 (.f64 n (PI.f64)) (.f64 k 1/2)) (pow.f64 2 (.f64 k 1/2)))
(.f64 (pow.f64 2 (.f64 k 1/2)) (pow.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))
(.f64 (pow.f64 1 (.f64 k 1/2)) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 2 (.f64 k 1/2))) (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 (.f64 2 k) 1/2)) (pow.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 k 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 1 k)) (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 k 1/2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 k 1/2)))
(.f64 (pow.f64 (.f64 2 n) (.f64 k 1/2)) (pow.f64 (PI.f64) (.f64 k 1/2)))
(.f64 (pow.f64 1 k) (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) 2))) k) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/6) k))
(.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) k) (pow.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) 1/6) k))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) k) (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6) k))
(.f64 (pow.f64 (sqrt.f64 2) k) (pow.f64 (sqrt.f64 (.f64 n (PI.f64))) k))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 1/4 k)) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (*.f64 1/4 k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (exp.f64 (log1p.f64 k))) (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (exp.f64 (log1p.f64 k))) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
(/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (log1p.f64 k))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)) (exp.f64 (log1p.f64 (sqrt.f64 k)))) (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (exp.f64 (log1p.f64 (sqrt.f64 k)))) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)))
(/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (exp.f64 (log1p.f64 (sqrt.f64 k)))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(log.f64 (exp.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k)))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (*.f64 k 3)))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (*.f64 k 3)))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 k 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(log1p.f64 (expm1.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) k))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) 2))))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(exp.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) (.f64 k 1/2)))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)
(exp.f64 (.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))))) 1))
(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) k)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 n k) (PI.f64))
✓	10.0b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series8.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	k	@	-inf	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
1.0ms	n	@	-inf	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
1.0ms	n	@	0	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
1.0ms	n	@	inf	(*.f64 (/.f64 n k) (PI.f64))
1.0ms	n	@	inf	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))

rewrite52.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

953×	`pow1_binary64`
882×	`add-log-exp_binary64`
882×	`log1p-expm1-u_binary64`
882×	`expm1-log1p-u_binary64`
862×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	189	21
2	2390	21

Stop Event

1×	node limit

Counts

2 → 47

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(*.f64 (/.f64 n k) (PI.f64))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))) (cbrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4) (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2)))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2))) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (/.f64 n k)) 1/2) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (/.f64 n k) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 n (/.f64 k (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 k n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 k (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (PI.f64)) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 n (PI.f64))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 n (PI.f64)) 1) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 n (PI.f64)) (cbrt.f64 (*.f64 k k))) (cbrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 n) (PI.f64)) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (neg.f64 n)) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 n k) 3) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 n k) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))))))))

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

775×	`log-prod_binary64`
493×	`associate-l_binary64`
492×	`fma-def_binary64`
451×	`associate-r_binary64`
283×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	874
1	242	832
2	823	790
3	4728	790

Stop Event

1×	node limit

Counts

71 → 71

Calls

Call 1

Inputs
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1)
(.f64 1 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(.f64 (cbrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/4) (pow.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2))) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1/2))
(.f64 (pow.f64 (.f64 2 (/.f64 n k)) 1/2) (sqrt.f64 (PI.f64)))
(pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/2)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))) 1)
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 3)
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/4) 2)
(fabs.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(-.f64 (+.f64 1 (*.f64 (/.f64 n k) (PI.f64))) 1)
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 1 (/.f64 k (*.f64 n (PI.f64))))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (neg.f64 (*.f64 n (PI.f64))) (neg.f64 k))
(/.f64 (/.f64 (*.f64 n (PI.f64)) 1) k)
(/.f64 (/.f64 (.f64 n (PI.f64)) (cbrt.f64 (.f64 k k))) (cbrt.f64 k))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))
(/.f64 (*.f64 (neg.f64 n) (PI.f64)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) (neg.f64 n)) (neg.f64 k))
(pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 1)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 3)
(pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2)
(sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2))
(log.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 n k) 3) (pow.f64 (PI.f64) 3)))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 n k) 3)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (PI.f64))))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64))))
(exp.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))))

Outputs
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 1 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 (cbrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))
(.f64 (cbrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 (/.f64 n k)) (PI.f64)))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k)))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 2 k))))))
(.f64 (cbrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2))) (cbrt.f64 (sqrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(.f64 (cbrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 (/.f64 n k)) (PI.f64)))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k)))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 2 k))))))
(.f64 (cbrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2))) (cbrt.f64 (sqrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/4) (pow.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 (*.f64 2 (/.f64 n k)) (PI.f64)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 2 k))))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 2 (/.f64 n k))))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2))) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 (*.f64 2 (/.f64 n k)) (PI.f64)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n (/.f64 2 k))))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 2)))) (sqrt.f64 (cbrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))
(.f64 (pow.f64 (.f64 2 (/.f64 n k)) 1/2) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 2 (/.f64 n k))))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)) 3/2))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(fabs.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(+.f64 1 (-.f64 (sqrt.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64))) 1))
(+.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 0)
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(-.f64 (+.f64 1 (*.f64 (/.f64 n k) (PI.f64))) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 1 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (neg.f64 (*.f64 n (PI.f64))) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (/.f64 (*.f64 n (PI.f64)) 1) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (/.f64 (.f64 n (PI.f64)) (cbrt.f64 (.f64 k k))) (cbrt.f64 k))
(/.f64 (.f64 n (PI.f64)) (.f64 (cbrt.f64 k) (cbrt.f64 (*.f64 k k))))
(.f64 (/.f64 n (cbrt.f64 k)) (/.f64 (PI.f64) (cbrt.f64 (.f64 k k))))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 (neg.f64 n) (PI.f64)) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 (PI.f64) (neg.f64 n)) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3) 1/3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 n k) 3) (pow.f64 (PI.f64) 3)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 n k) 3)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
	0.2b	(/.f64 1 (sqrt.f64 k))
	0.3b	(*.f64 n (PI.f64))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))

Compiler

Compiled 38 to 20 computations (47.4% saved)

series3.0ms (0%)

Counts

1 → 0

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
0.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
0.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
0.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
0.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))

rewrite49.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`log-prod_binary64`
417×	`exp-prod_binary64`
355×	`pow-prod-down_binary64`
276×	`pow2_binary64`
237×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	15
1	240	13
2	2776	13

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 1) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 k)) (pow.f64 k 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) -1) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 n (PI.f64))) k))) 1) 1))))))

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

956×	`fma-def_binary64`
578×	`distribute-rgt-in_binary64`
528×	`times-frac_binary64`
322×	`associate-l_binary64`
310×	`log-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	670
1	225	649
2	629	622
3	3638	622

Stop Event

1×	node limit

Counts

38 → 66

Calls

Call 1

Inputs
(+.f64 0 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 1)
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 k)) (pow.f64 k 1/6))
(/.f64 (.f64 -1 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) -1) (neg.f64 (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 1)
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(pow.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 2)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k))) 1))
(exp.f64 (.f64 (.f64 3 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 1) 1))

Outputs
(+.f64 0 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64))))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))))) 3)
(.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) (/.f64 2 k)))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64)))))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) (/.f64 2 k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 1)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (/.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 k)) (pow.f64 k 1/6))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (pow.f64 k 1/6) (cbrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (cbrt.f64 k) (pow.f64 k 1/6)))
(/.f64 (.f64 -1 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) -1) (neg.f64 (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 1)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k) 1/2)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3) 1/3)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 3)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 2)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)))
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) -1)
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64))))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64))))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64)))))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64))))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k))))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k))) 1))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (.f64 3 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 1/3))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 3))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 2))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 1) 1))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (/.f64 n (/.f64 (/.f64 k (PI.f64)) 2)))
(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)))

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 n (PI.f64)))
	0.3b	(*.f64 n (PI.f64))
✓	0.3b	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
✓	0.4b	(/.f64 (sqrt.f64 k) (sqrt.f64 2))

Compiler

Compiled 32 to 16 computations (50% saved)

series6.0ms (0.1%)

Counts

3 → 0

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	k	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 2))
1.0ms	n	@	-inf	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
1.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 2))
1.0ms	k	@	-inf	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
1.0ms	n	@	-inf	(sqrt.f64 (*.f64 n (PI.f64)))

rewrite67.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log-prod_binary64`
349×	`pow-prod-down_binary64`
284×	`pow2_binary64`
232×	`pow-unpow_binary64`
200×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	233	26
2	3028	26

Stop Event

1×	node limit

Counts

3 → 138

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 k) (sqrt.f64 2))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(sqrt.f64 (*.f64 n (PI.f64)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 k 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 k 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 k 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 k 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 k 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 k 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 k) (*.f64 (pow.f64 k 1/6) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 k 1/2) 1/6) (cbrt.f64 (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 k 1/2)) (pow.f64 (*.f64 k 1/2) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 k 1/2) 1/4) (pow.f64 (*.f64 k 1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k 1/4) (*.f64 (pow.f64 k 1/4) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (pow.f64 k 1/6) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (sqrt.f64 k) (pow.f64 2 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 2)) (pow.f64 (*.f64 k 1/2) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k 1/4) (cbrt.f64 2)) (/.f64 (pow.f64 k 1/4) (pow.f64 2 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/4) (/.f64 (sqrt.f64 k) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) (pow.f64 2 1/4)) (/.f64 (pow.f64 k 1/6) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 k 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 k 1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 k 1/2) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 k 1/2) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 k 1/2) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 2 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 2 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (/.f64 2 k)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 k 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 k 1/2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 2 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 k 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 k 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 k 1/2) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 k 1/2) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 k 1/2) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 k))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 k 1/2))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))) (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) (sqrt.f64 (/.f64 2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (*.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (sqrt.f64 (/.f64 2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 1 (neg.f64 (sqrt.f64 (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) 1) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) (sqrt.f64 (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 1) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (sqrt.f64 (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (*.f64 k 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 k 1/2))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 k 1/2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 (*.f64 k 1/2))) (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (cbrt.f64 (*.f64 k 1/2))) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 k 1/2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 (*.f64 k 1/2))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 k 1/2) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 k 1/2)) -1/2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 k 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 k 1/2) 1/4)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) (pow.f64 (*.f64 k 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 k 1/2) 1/4)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 k 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1) (sqrt.f64 (/.f64 2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 2)) (pow.f64 2 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 n (PI.f64)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) (pow.f64 (*.f64 k 1/2) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 n (PI.f64)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) (pow.f64 (*.f64 k 1/2) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 k 1/2) (*.f64 n (PI.f64))))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 k 1/2)))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 n (PI.f64))) (pow.f64 (*.f64 n (PI.f64)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) (cbrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 n (PI.f64)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (*.f64 n (PI.f64)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 n (PI.f64)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 n (PI.f64))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1) 1))))))

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-/r*_binary64`
418×	`associate-*l/_binary64`
386×	`unswap-sqr_binary64`
375×	`fma-def_binary64`
299×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	1699
1	706	1630
2	2442	1598

Stop Event

1×	node limit

Counts

138 → 184

Calls

Call 1

Inputs
(+.f64 0 (sqrt.f64 (*.f64 k 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 k 1/2)))) 1)
(*.f64 (sqrt.f64 k) (pow.f64 2 -1/2))
(.f64 (sqrt.f64 (.f64 k 1/2)) 1)
(.f64 1 (sqrt.f64 (.f64 k 1/2)))
(.f64 (cbrt.f64 k) (.f64 (pow.f64 k 1/6) (pow.f64 2 -1/2)))
(.f64 (pow.f64 (.f64 k 1/2) 1/6) (cbrt.f64 (*.f64 k 1/2)))
(.f64 (cbrt.f64 (.f64 k 1/2)) (pow.f64 (*.f64 k 1/2) 1/6))
(.f64 (pow.f64 (.f64 k 1/2) 1/4) (pow.f64 (*.f64 k 1/2) 1/4))
(.f64 (pow.f64 k 1/4) (.f64 (pow.f64 k 1/4) (pow.f64 2 -1/2)))
(*.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 2 -1/2) (sqrt.f64 k))
(*.f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (pow.f64 k 1/6) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (sqrt.f64 2)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (sqrt.f64 k) (pow.f64 2 1/6)))
(.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 2)) (pow.f64 (.f64 k 1/2) 1/6))
(*.f64 (/.f64 (pow.f64 k 1/4) (cbrt.f64 2)) (/.f64 (pow.f64 k 1/4) (pow.f64 2 1/6)))
(*.f64 (pow.f64 2 -1/4) (/.f64 (sqrt.f64 k) (pow.f64 2 1/4)))
(*.f64 (/.f64 (cbrt.f64 k) (pow.f64 2 1/4)) (/.f64 (pow.f64 k 1/6) (pow.f64 2 1/4)))
(pow.f64 (sqrt.f64 (*.f64 k 1/2)) 1)
(pow.f64 (*.f64 k 1/2) 1/2)
(pow.f64 (pow.f64 (*.f64 k 1/2) 3/2) 1/3)
(pow.f64 (pow.f64 (*.f64 k 1/2) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 k 1/2) 1/4) 2)
(pow.f64 (sqrt.f64 (/.f64 2 k)) -1)
(pow.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 2 3/2)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 (/.f64 2 k)) 1) -1)
(neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (*.f64 k 1/2))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 k 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 k 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 k 1/2) 3/2))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 2 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 k 1/2))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 k 1/2))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 k 1/2))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 k 1/2))) 1))
(exp.f64 (.f64 (log.f64 (.f64 k 1/2)) 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 k 1/2) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 k 1/2) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 k 1/2) 1/4)) 2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 k))) -1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 k 1/2))) 1) 1))
(+.f64 0 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))) 1)
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 2 k)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))) 1)
(.f64 1 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) (cbrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))))
(.f64 (cbrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))))
(.f64 (cbrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (.f64 n (PI.f64)) 1/6) (sqrt.f64 (/.f64 2 k))))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))))
(.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (sqrt.f64 (/.f64 2 k))))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 2 k))))
(.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (/.f64 1 (neg.f64 (sqrt.f64 (*.f64 k 1/2)))))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 2))
(.f64 (pow.f64 k -1/2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 2 -1/2)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) (pow.f64 2 -1/2)))
(.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 2 -1/2)))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 2 -1/2)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (PI.f64))) 1) (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/6) (sqrt.f64 (.f64 k 1/2))))
(.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) 1) (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (sqrt.f64 (.f64 k 1/2))))
(.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 k 1/2))))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k 1/2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 k 1/2) 1/6)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (PI.f64))) (cbrt.f64 (.f64 k 1/2))) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))))
(.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (cbrt.f64 (.f64 k 1/2))) (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 k 1/2) 1/6)))
(.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 (.f64 k 1/2))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 k 1/2) 1/6)))
(.f64 (pow.f64 (sqrt.f64 (.f64 k 1/2)) -1/2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 k 1/2) 1/4)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 k 1/2) 1/4)) (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/6) (pow.f64 (*.f64 k 1/2) 1/4)))
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 k 1/2) 1/4)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 k 1/2) 1/4)))
(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) 1) (sqrt.f64 (/.f64 2 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 2)))
(.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) 1) (sqrt.f64 2))
(.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 2)) (pow.f64 2 1/6))
(.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(pow.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))) 1)
(pow.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) 2)
(pow.f64 (sqrt.f64 (/.f64 (.f64 k 1/2) (.f64 n (PI.f64)))) -1)
(pow.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 3/2) (pow.f64 (.f64 k 1/2) 3/2)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 k 1/2) (.f64 n (PI.f64)))) 1) -1)
(neg.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 (.f64 k 1/2)))))
(sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 3/2) (pow.f64 (.f64 k 1/2) 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))) 1))
(exp.f64 (.f64 (.f64 3 (log.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))))) 2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 k 1/2) (*.f64 n (PI.f64))))) -1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) 1) 1))
(+.f64 0 (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64))))) 1)
(.f64 (sqrt.f64 (.f64 n (PI.f64))) 1)
(.f64 1 (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (cbrt.f64 (.f64 n (PI.f64))) (pow.f64 (*.f64 n (PI.f64)) 1/6))
(.f64 (pow.f64 (.f64 n (PI.f64)) 1/6) (cbrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))
(.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4))
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))
(pow.f64 (*.f64 n (PI.f64)) 1/2)
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 2) 1/4)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) 3)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 2)
(fabs.f64 (sqrt.f64 (*.f64 n (PI.f64))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64))))))
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (PI.f64)))) 1))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (*.f64 n (PI.f64)))) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 n (PI.f64)) 1/6)) 3))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (*.f64 n (PI.f64)))) 2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (PI.f64))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (PI.f64))) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1) 1))

Outputs
(+.f64 0 (sqrt.f64 (*.f64 k 1/2)))
(sqrt.f64 (*.f64 k 1/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 k 1/2))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 k 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 k 1/2)))) 1)
(sqrt.f64 (*.f64 k 1/2))
(*.f64 (sqrt.f64 k) (pow.f64 2 -1/2))
(.f64 (sqrt.f64 (.f64 k 1/2)) 1)
(sqrt.f64 (*.f64 k 1/2))
(.f64 1 (sqrt.f64 (.f64 k 1/2)))
(sqrt.f64 (*.f64 k 1/2))
(.f64 (cbrt.f64 k) (.f64 (pow.f64 k 1/6) (pow.f64 2 -1/2)))
(.f64 (cbrt.f64 k) (.f64 (pow.f64 2 -1/2) (pow.f64 k 1/6)))
(.f64 (pow.f64 2 -1/2) (.f64 (cbrt.f64 k) (pow.f64 k 1/6)))
(.f64 (.f64 (cbrt.f64 k) (pow.f64 2 -1/2)) (pow.f64 k 1/6))
(.f64 (pow.f64 (.f64 k 1/2) 1/6) (cbrt.f64 (*.f64 k 1/2)))
(sqrt.f64 (*.f64 k 1/2))
(.f64 (cbrt.f64 (.f64 k 1/2)) (pow.f64 (*.f64 k 1/2) 1/6))
(sqrt.f64 (*.f64 k 1/2))
(.f64 (pow.f64 (.f64 k 1/2) 1/4) (pow.f64 (*.f64 k 1/2) 1/4))
(sqrt.f64 (*.f64 k 1/2))
(.f64 (pow.f64 k 1/4) (.f64 (pow.f64 k 1/4) (pow.f64 2 -1/2)))
(*.f64 (sqrt.f64 k) (pow.f64 2 -1/2))
(*.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (sqrt.f64 k) (sqrt.f64 2))
(*.f64 (pow.f64 2 -1/2) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) (pow.f64 2 -1/2))
(*.f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (pow.f64 k 1/6) (sqrt.f64 2)))
(/.f64 (*.f64 (cbrt.f64 k) (pow.f64 k 1/6)) (sqrt.f64 2))
(*.f64 (/.f64 (cbrt.f64 k) (sqrt.f64 2)) (pow.f64 k 1/6))
(*.f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (sqrt.f64 2)))
(*.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (sqrt.f64 k) (sqrt.f64 2))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (sqrt.f64 k) (pow.f64 2 1/6)))
(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 2 1/6)) (cbrt.f64 2))
(.f64 (/.f64 (cbrt.f64 k) (cbrt.f64 2)) (pow.f64 (.f64 k 1/2) 1/6))
(.f64 (pow.f64 (.f64 k 1/2) 1/6) (/.f64 (cbrt.f64 k) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 k 1/4) (cbrt.f64 2)) (/.f64 (pow.f64 k 1/4) (pow.f64 2 1/6)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (sqrt.f64 k) (pow.f64 2 1/6)))
(/.f64 (/.f64 (sqrt.f64 k) (pow.f64 2 1/6)) (cbrt.f64 2))
(*.f64 (pow.f64 2 -1/4) (/.f64 (sqrt.f64 k) (pow.f64 2 1/4)))
(/.f64 (pow.f64 2 -1/4) (/.f64 (pow.f64 2 1/4) (sqrt.f64 k)))
(*.f64 (/.f64 (cbrt.f64 k) (pow.f64 2 1/4)) (/.f64 (pow.f64 k 1/6) (pow.f64 2 1/4)))
(/.f64 (*.f64 (cbrt.f64 k) (pow.f64 k 1/6)) (sqrt.f64 2))
(*.f64 (/.f64 (cbrt.f64 k) (sqrt.f64 2)) (pow.f64 k 1/6))
(pow.f64 (sqrt.f64 (*.f64 k 1/2)) 1)
(sqrt.f64 (*.f64 k 1/2))
(pow.f64 (*.f64 k 1/2) 1/2)
(sqrt.f64 (*.f64 k 1/2))
(pow.f64 (pow.f64 (*.f64 k 1/2) 3/2) 1/3)
(sqrt.f64 (*.f64 k 1/2))
(pow.f64 (pow.f64 (*.f64 k 1/2) 1/6) 3)
(sqrt.f64 (*.f64 k 1/2))
(pow.f64 (pow.f64 (*.f64 k 1/2) 1/4) 2)
(sqrt.f64 (*.f64 k 1/2))
(pow.f64 (sqrt.f64 (/.f64 2 k)) -1)
(/.f64 1 (sqrt.f64 (/.f64 2 k)))
(pow.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 2 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 2 3/2)))
(pow.f64 (/.f64 (sqrt.f64 (/.f64 2 k)) 1) -1)
(/.f64 1 (sqrt.f64 (/.f64 2 k)))
(neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (sqrt.f64 2))))
(*.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (sqrt.f64 k) (sqrt.f64 2))
(sqrt.f64 (*.f64 k 1/2))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 k 1/2))))
(sqrt.f64 (*.f64 k 1/2))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 k 1/2)))))
(sqrt.f64 (*.f64 k 1/2))
(cbrt.f64 (pow.f64 (*.f64 k 1/2) 3/2))
(sqrt.f64 (*.f64 k 1/2))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 2 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 k 1/2))))
(sqrt.f64 (*.f64 k 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 k 1/2))))
(sqrt.f64 (*.f64 k 1/2))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 k 1/2))))
(sqrt.f64 (*.f64 k 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 k 1/2))) 1))
(sqrt.f64 (*.f64 k 1/2))
(exp.f64 (.f64 (log.f64 (.f64 k 1/2)) 1/2))
(sqrt.f64 (*.f64 k 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 k 1/2) 3/2)) 1/3))
(sqrt.f64 (*.f64 k 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 k 1/2) 1/6)) 3))
(sqrt.f64 (*.f64 k 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 k 1/2) 1/4)) 2))
(sqrt.f64 (*.f64 k 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 2 k))) -1))
(/.f64 1 (sqrt.f64 (/.f64 2 k)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 k 1/2))) 1) 1))
(sqrt.f64 (*.f64 k 1/2))
(+.f64 0 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))) 1)
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 2 k)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))) 1)
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 1 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) (cbrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))) (cbrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))) (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2))))
(.f64 (cbrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))) (cbrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))) (cbrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2))))
(.f64 (cbrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (.f64 n (PI.f64)) 1/6) (sqrt.f64 (/.f64 2 k))))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (sqrt.f64 (/.f64 2 k))))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 2 k))))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (PI.f64))))
(.f64 (sqrt.f64 (/.f64 2 k)) (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))))
(.f64 (neg.f64 (sqrt.f64 (.f64 n (PI.f64)))) (/.f64 1 (neg.f64 (sqrt.f64 (*.f64 k 1/2)))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (pow.f64 k -1/2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 2 -1/2)))
(.f64 (/.f64 (pow.f64 k -1/2) (pow.f64 2 -1/2)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (cbrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) (pow.f64 2 -1/2)))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 2 -1/2)))
(.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) (pow.f64 2 -1/2)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) (pow.f64 2 -1/2)))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 2 -1/2)))
(*.f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 2 -1/2)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (pow.f64 2 -1/2)) (sqrt.f64 k))
(.f64 (/.f64 (cbrt.f64 (.f64 n (PI.f64))) 1) (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/6) (sqrt.f64 (.f64 k 1/2))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) 1) (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (sqrt.f64 (.f64 k 1/2))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 k 1/2))))
(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 k 1/2))))
(/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 k 1/2)) (sqrt.f64 (PI.f64))))
(.f64 (/.f64 1 (cbrt.f64 (.f64 k 1/2))) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 k 1/2) 1/6)))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 (/.f64 (cbrt.f64 (.f64 n (PI.f64))) (cbrt.f64 (.f64 k 1/2))) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))) (/.f64 (cbrt.f64 (.f64 n (PI.f64))) (cbrt.f64 (.f64 k 1/2))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))) (/.f64 (cbrt.f64 (.f64 n (PI.f64))) (cbrt.f64 (.f64 k 1/2))))
(.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (cbrt.f64 (.f64 k 1/2))) (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 k 1/2) 1/6)))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 (.f64 k 1/2))) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 k 1/2) 1/6)))
(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 k 1/2))))
(/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 k 1/2)) (sqrt.f64 (PI.f64))))
(.f64 (pow.f64 (sqrt.f64 (.f64 k 1/2)) -1/2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 k 1/2) 1/4)))
(/.f64 (pow.f64 (sqrt.f64 (.f64 k 1/2)) -1/2) (/.f64 (pow.f64 (.f64 k 1/2) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (/.f64 (cbrt.f64 (.f64 n (PI.f64))) (pow.f64 (.f64 k 1/2) 1/4)) (/.f64 (pow.f64 (.f64 n (PI.f64)) 1/6) (pow.f64 (*.f64 k 1/2) 1/4)))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 (.f64 k 1/2) 1/4)) (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (*.f64 k 1/2) 1/4)))
(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 k 1/2))))
(/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 k 1/2)) (sqrt.f64 (PI.f64))))
(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) 1) (sqrt.f64 (/.f64 2 k)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 2)))
(.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 2))))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) 1) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (cbrt.f64 2)) (pow.f64 2 1/6))
(.f64 (pow.f64 2 1/6) (.f64 (cbrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64))))))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 2 1/6)))
(.f64 (cbrt.f64 2) (.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (pow.f64 2 1/6)))
(.f64 (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(pow.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))) 1)
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(pow.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)) 1/2)
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))) 3) 1/3)
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) 3)
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) 2)
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(pow.f64 (sqrt.f64 (/.f64 (.f64 k 1/2) (.f64 n (PI.f64)))) -1)
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(pow.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 3/2) (pow.f64 (.f64 k 1/2) 3/2)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 3/2) (pow.f64 (.f64 k 1/2) 3/2)))
(pow.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 k 1/2) (.f64 n (PI.f64)))) 1) -1)
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(neg.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (neg.f64 (sqrt.f64 (.f64 k 1/2)))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))) 3))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 n (PI.f64)) 3/2) (pow.f64 (.f64 k 1/2) 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2)))) 1))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(exp.f64 (.f64 (.f64 3 (log.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2))))) 1/3))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))))) 3))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (*.f64 k 1/2))))) 2))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 k 1/2) (*.f64 n (PI.f64))))) -1))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k 1/2)))) 1) 1))
(sqrt.f64 (*.f64 (/.f64 n k) (/.f64 (PI.f64) 1/2)))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) (/.f64 n 1/2)))
(+.f64 0 (sqrt.f64 (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 n (PI.f64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64)))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (PI.f64)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64))))) 1)
(sqrt.f64 (*.f64 n (PI.f64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) 1)
(sqrt.f64 (*.f64 n (PI.f64)))
(.f64 1 (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.f64 (*.f64 n (PI.f64)))
(.f64 (cbrt.f64 (.f64 n (PI.f64))) (pow.f64 (*.f64 n (PI.f64)) 1/6))
(sqrt.f64 (*.f64 n (PI.f64)))
(.f64 (pow.f64 (.f64 n (PI.f64)) 1/6) (cbrt.f64 (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n))
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))
(.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (pow.f64 (*.f64 n (PI.f64)) 1/4))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64)))
(pow.f64 (*.f64 n (PI.f64)) 1/2)
(sqrt.f64 (*.f64 n (PI.f64)))
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1)
(sqrt.f64 (*.f64 n (PI.f64)))
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 2) 1/4)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3) 1/6)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2) 1/3)
(sqrt.f64 (*.f64 n (PI.f64)))
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) 3/2)
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/6) 3)
(sqrt.f64 (*.f64 n (PI.f64)))
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) 1/4) 2)
(sqrt.f64 (*.f64 n (PI.f64)))
(fabs.f64 (sqrt.f64 (*.f64 n (PI.f64))))
(sqrt.f64 (*.f64 n (PI.f64)))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(sqrt.f64 (*.f64 n (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64))))))
(sqrt.f64 (*.f64 n (PI.f64)))
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) 3/2))
(sqrt.f64 (*.f64 n (PI.f64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(sqrt.f64 (*.f64 n (PI.f64)))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(sqrt.f64 (*.f64 n (PI.f64)))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))))
(sqrt.f64 (*.f64 n (PI.f64)))
(exp.f64 (.f64 (log.f64 (.f64 n (PI.f64))) 1/2))
(sqrt.f64 (*.f64 n (PI.f64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 n (PI.f64)))) 1))
(sqrt.f64 (*.f64 n (PI.f64)))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (*.f64 n (PI.f64)))) 1/3))
(sqrt.f64 (*.f64 n (PI.f64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 n (PI.f64)) 1/6)) 3))
(sqrt.f64 (*.f64 n (PI.f64)))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (*.f64 n (PI.f64)))) 2))
(sqrt.f64 (*.f64 n (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (PI.f64))) 1) 1/2))
(sqrt.f64 (*.f64 n (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 n (PI.f64))) 1/2) 1))
(sqrt.f64 (*.f64 n (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (*.f64 n (PI.f64)))) 1) 1))
(sqrt.f64 (*.f64 n (PI.f64)))

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
✓	0.3b	(*.f64 (PI.f64) (+.f64 n n))
✓	3.5b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
✓	10.4b	(log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))

Compiler

Compiled 79 to 36 computations (54.4% saved)

series138.0ms (1.3%)

Counts

4 → 72

Calls

21 calls:

Time	Variable		Point	Expression
58.0ms	k	@	inf	(log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
21.0ms	n	@	0	(log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
17.0ms	n	@	-inf	(log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
16.0ms	k	@	-inf	(log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
16.0ms	n	@	inf	(log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))

rewrite86.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

719×	`log-prod_binary64`
597×	`prod-diff_binary64`
246×	`expm1-udef_binary64`
245×	`log1p-udef_binary64`
236×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	61
1	303	60
2	4166	60

Stop Event

1×	node limit

Counts

4 → 207

Calls

Call 1

Inputs
(log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
(*.f64 (PI.f64) (+.f64 n n))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (fma.f64 (neg.f64 (sqrt.f64 (log.f64 k))) (sqrt.f64 (log.f64 k)) (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (.f64 2 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2))) (log.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/4 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (/.f64 1 (neg.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 1 k) (log.f64 (PI.f64))) (log.f64 (.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (/.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (log.f64 k)) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (-.f64 1 k) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (-.f64 1 k) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 1 (pow.f64 (cbrt.f64 k) 2))) (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (cbrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 1 (sqrt.f64 k))) (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))) (.f64 1/4 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) 1)) (log.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1)) (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) 1)) (log.f64 (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (cbrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) (sqrt.f64 k))) (log.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (sqrt.f64 k))) (log.f64 (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (log.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (log.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (log.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (log.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (log.f64 (/.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2))) (log.f64 (/.f64 k (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (/.f64 k (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (-.f64 1 k) (log.f64 (PI.f64))) (log.f64 (/.f64 k (pow.f64 (+.f64 n n) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 -1) (log.f64 (neg.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (sqrt.f64 k))) (log.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (neg.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (neg.f64 (neg.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)) (log.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 k))) (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2) (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 3 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (log.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/3 (.f64 3 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 3) (pow.f64 (log.f64 k) 3)) (fma.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (fma.f64 (log.f64 k) (log.f64 k) (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (log.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (log.f64 k) (log.f64 k))) (fma.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))) (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (log.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (log.f64 (/.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k) (neg.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2) (.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1/2) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1/2) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (-.f64 1 k) (neg.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)) (neg.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)) (neg.f64 (log.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)) (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/2 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (/.f64 1 k) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (PI.f64) n) 1) (.f64 (.f64 (PI.f64) n) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))) (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (+.f64 n n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 (PI.f64) n) 3) (pow.f64 (.f64 (PI.f64) n) 3)) (fma.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n) (-.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 2 (pow.f64 n 3)) (PI.f64)) (fma.f64 n n 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 0 (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (.f64 2 (pow.f64 n 3))) (fma.f64 n n 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) 0) 0)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (+.f64 n n) (cbrt.f64 (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (PI.f64) n (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 n (PI.f64) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (PI.f64) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 n) 2) (.f64 (cbrt.f64 n) (PI.f64)) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (PI.f64)) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (PI.f64) n) 1 (.f64 (.f64 (PI.f64) n) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) n)) (cbrt.f64 (.f64 (PI.f64) n))) (cbrt.f64 (.f64 (PI.f64) n)) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n) (.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n) (.f64 (PI.f64) n))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2))) (-.f64 1 k)) (pow.f64 (.f64 (+.f64 n n) (cbrt.f64 (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (-.f64 1 k)) (pow.f64 (.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 n n) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (+.f64 n n) (cbrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (+.f64 n n) (sqrt.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 1))))))

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

380×	`associate-r_binary64`
370×	`associate-l_binary64`
219×	`fma-def_binary64`
166×	`distribute-rgt-in_binary64`
150×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	602	6972
1	1447	6972

Stop Event

1×	node limit

Counts

279 → 230

Calls

Call 1

Inputs
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/6 (.f64 (pow.f64 k 3) (+.f64 (.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(+.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 0)
(+.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (fma.f64 (neg.f64 (sqrt.f64 (log.f64 k))) (sqrt.f64 (log.f64 k)) (log.f64 k)))
(+.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(+.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (log.f64 k)))
(+.f64 0 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(+.f64 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (.f64 2 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(+.f64 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2))) (log.f64 (.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 k))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 k))))
(+.f64 (.f64 1/4 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(+.f64 (log.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (/.f64 1 (neg.f64 k))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(+.f64 (.f64 (-.f64 1 k) (log.f64 (PI.f64))) (log.f64 (.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (/.f64 1 k))))
(+.f64 (neg.f64 (log.f64 k)) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(+.f64 (fma.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(+.f64 (fma.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (*.f64 (log.f64 k) 1)))
(+.f64 (fma.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (*.f64 (log.f64 k) 1)))
(+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (*.f64 (log.f64 k) 1)))
(+.f64 (fma.f64 (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (-.f64 1 k) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(+.f64 (fma.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(+.f64 (fma.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(+.f64 (fma.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(+.f64 (fma.f64 (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (-.f64 1 k) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(+.f64 (log.f64 (/.f64 1 (pow.f64 (cbrt.f64 k) 2))) (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (cbrt.f64 k))))
(+.f64 (log.f64 (/.f64 1 (sqrt.f64 k))) (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (sqrt.f64 k))))
(+.f64 (log.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))) (.f64 1/4 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(+.f64 (log.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) 1)) (log.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k)))
(+.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1)) (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k)))
(+.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) 1)) (log.f64 (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) k)))
(+.f64 (log.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(+.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 k))))
(+.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (cbrt.f64 k))))
(+.f64 (log.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) (sqrt.f64 k))) (log.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))))
(+.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (sqrt.f64 k))) (log.f64 (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (sqrt.f64 k))))
(+.f64 (log.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(-.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (log.f64 (.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) k)))
(-.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (log.f64 (.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k))))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (log.f64 k))
(-.f64 0 (log.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(-.f64 0 (log.f64 (/.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1)))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)
(-.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2))) (log.f64 (/.f64 k (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(-.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (/.f64 k (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(-.f64 (log.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (neg.f64 k)))
(-.f64 (*.f64 (-.f64 1 k) (log.f64 (PI.f64))) (log.f64 (/.f64 k (pow.f64 (+.f64 n n) (-.f64 1 k)))))
(-.f64 (log.f64 -1) (log.f64 (neg.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(-.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (sqrt.f64 k))) (log.f64 (sqrt.f64 k)))
(-.f64 (log.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (neg.f64 (neg.f64 k))))
(-.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)) (log.f64 k))
(-.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (cbrt.f64 k)))
(-.f64 (log.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 k))) (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(.f64 1 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(.f64 1/2 (.f64 2 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2))
(.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2) (cbrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 3 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 2 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 -1 (log.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(.f64 1/3 (.f64 3 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 3) (pow.f64 (log.f64 k) 3)) (fma.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (fma.f64 (log.f64 k) (log.f64 k) (.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) (log.f64 k)))))
(/.f64 (-.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (log.f64 k) (log.f64 k))) (fma.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (log.f64 k)))
(pow.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(pow.f64 (pow.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)
(neg.f64 (log.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(neg.f64 (log.f64 (/.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1)))
(sqrt.f64 (pow.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2))
(cbrt.f64 (pow.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3))
(expm1.f64 (log1p.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log1p.f64 (-.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1))
(exp.f64 (log.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1))
(fma.f64 1 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (log.f64 k)))
(fma.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 (log.f64 k)))
(fma.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 1/2 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k) (neg.f64 (log.f64 k)))
(fma.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2) (.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1/2) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1/2) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (log.f64 k)))
(fma.f64 (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (log.f64 k)))
(fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (-.f64 1 k) (neg.f64 (log.f64 k)))
(fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)) (neg.f64 (log.f64 k)))
(fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)) (neg.f64 (log.f64 k)))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)) (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(fma.f64 (.f64 1/2 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (/.f64 1 k) 1/2))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/2)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(pow.f64 (exp.f64 1/2) (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) 2)
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(+.f64 (.f64 (.f64 (PI.f64) n) 1) (.f64 (.f64 (PI.f64) n) 1))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))) (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)
(/.f64 (+.f64 (pow.f64 (.f64 (PI.f64) n) 3) (pow.f64 (.f64 (PI.f64) n) 3)) (fma.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n) (-.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))
(/.f64 (.f64 (.f64 2 (pow.f64 n 3)) (PI.f64)) (fma.f64 n n 0))
(/.f64 (*.f64 0 (PI.f64)) 0)
(/.f64 (.f64 (PI.f64) (.f64 2 (pow.f64 n 3))) (fma.f64 n n 0))
(/.f64 (*.f64 (PI.f64) 0) 0)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) 1/3)
(pow.f64 (*.f64 (+.f64 n n) (cbrt.f64 (PI.f64))) 3)
(pow.f64 (*.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) 2)
(sqrt.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (+.f64 n n)))
(cbrt.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(fma.f64 1 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))
(fma.f64 (pow.f64 (cbrt.f64 n) 2) (.f64 (cbrt.f64 n) (PI.f64)) (.f64 (PI.f64) n))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))
(fma.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (PI.f64)) (.f64 (PI.f64) n))
(fma.f64 (.f64 (PI.f64) n) 1 (.f64 (*.f64 (PI.f64) n) 1))
(fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) n)) (cbrt.f64 (.f64 (PI.f64) n))) (cbrt.f64 (.f64 (PI.f64) n)) (*.f64 (PI.f64) n))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (PI.f64) n))
(fma.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n))
(fma.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (*.f64 (PI.f64) n))
(fma.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) (.f64 (PI.f64) n))
(fma.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 (PI.f64) n))
(fma.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n) (.f64 (PI.f64) n))
(fma.f64 (.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n) (.f64 (PI.f64) n))
(+.f64 0 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)
(.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))
(.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k)))
(*.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))
(.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2))) (-.f64 1 k)) (pow.f64 (*.f64 (+.f64 n n) (cbrt.f64 (PI.f64))) (-.f64 1 k)))
(.f64 (pow.f64 (.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (-.f64 1 k)) (pow.f64 (*.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (-.f64 1 k)))
(/.f64 (PI.f64) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (+.f64 n n)))
(/.f64 (+.f64 n n) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (PI.f64)))
(/.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n))))
(/.f64 (cbrt.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (*.f64 (+.f64 n n) (cbrt.f64 (PI.f64)))))
(/.f64 (.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (*.f64 (+.f64 n n) (sqrt.f64 (PI.f64)))))
(/.f64 (neg.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)))
(sqrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2))
(log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1))

Outputs
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 -1 (log.f64 k)) (+.f64 (.f64 1/6 (.f64 (pow.f64 k 3) (+.f64 (.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 k 2) (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (+.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (.f64 -1 k))))) (log.f64 (/.f64 -1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (.f64 n (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (.f64 2 (.f64 n (PI.f64))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 -2 (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (+.f64 (.f64 -1/3 (.f64 (pow.f64 k 3) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))) (+.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (pow.f64 k 2) (.f64 n (.f64 (pow.f64 (log.f64 (.f64 2 (*.f64 n (PI.f64)))) 2) (PI.f64)))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 0)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (fma.f64 (neg.f64 (sqrt.f64 (log.f64 k))) (sqrt.f64 (log.f64 k)) (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 0 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (.f64 2 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2))) (log.f64 (.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (/.f64 1 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 1/4 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (/.f64 1 (neg.f64 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 (-.f64 1 k) (log.f64 (PI.f64))) (log.f64 (.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (/.f64 1 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (neg.f64 (log.f64 k)) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (*.f64 (log.f64 k) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (*.f64 (log.f64 k) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (*.f64 (log.f64 k) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (-.f64 1 k) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (log.f64 k) 1))) (fma.f64 (neg.f64 (log.f64 k)) 1 (.f64 (log.f64 k) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (-.f64 1 k) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)) (neg.f64 (.f64 (cbrt.f64 (log.f64 k)) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))) (.f64 (cbrt.f64 (log.f64 k)) (*.f64 (cbrt.f64 (log.f64 k)) (cbrt.f64 (log.f64 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 1 (pow.f64 (cbrt.f64 k) 2))) (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (cbrt.f64 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 1 (sqrt.f64 k))) (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (sqrt.f64 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))) (.f64 1/4 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) 1)) (log.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1)) (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) 1)) (log.f64 (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (cbrt.f64 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) (sqrt.f64 k))) (log.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (/.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (sqrt.f64 k))) (log.f64 (/.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (sqrt.f64 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (log.f64 (.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (log.f64 (.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 0 (log.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 0 (log.f64 (/.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2))) (log.f64 (/.f64 k (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (/.f64 k (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (log.f64 (neg.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (*.f64 (-.f64 1 k) (log.f64 (PI.f64))) (log.f64 (/.f64 k (pow.f64 (+.f64 n n) (-.f64 1 k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 -1) (log.f64 (neg.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (sqrt.f64 k))) (log.f64 (sqrt.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (neg.f64 (neg.f64 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)) (log.f64 k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) (pow.f64 (cbrt.f64 k) 2))) (log.f64 (cbrt.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (log.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 k))) (.f64 k (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 1 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 1/2 (.f64 2 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2) (cbrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 3 (log.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 2 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 -1 (log.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 1/3 (.f64 3 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) 3) (pow.f64 (log.f64 k) 3)) (fma.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (fma.f64 (log.f64 k) (log.f64 k) (.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) (log.f64 k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (-.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (.f64 (log.f64 k) (log.f64 k))) (fma.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (pow.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3) 1/3)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(neg.f64 (log.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(neg.f64 (log.f64 (/.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) 1)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (pow.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(cbrt.f64 (pow.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(expm1.f64 (log1p.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log1p.f64 (-.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1))
(log1p.f64 (+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k)) k) -1))
(exp.f64 (log.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (log.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 1 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 1 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))) (neg.f64 (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (neg.f64 (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 1/2 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k) (neg.f64 (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2) (.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1/2) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (.f64 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1/2) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))) (cbrt.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (sqrt.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) (neg.f64 (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1) (-.f64 1 k) (neg.f64 (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (pow.f64 (cbrt.f64 (-.f64 1 k)) 2)) (cbrt.f64 (-.f64 1 k)) (neg.f64 (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (-.f64 1 k))) (sqrt.f64 (-.f64 1 k)) (neg.f64 (log.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 1/2 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)) (cbrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 1/2 (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (sqrt.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (pow.f64 (/.f64 1 k) 1/2))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/2)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (exp.f64 1/2) (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (E.f64) (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3) 1/3)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/4) 2)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (sqrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (.f64 (.f64 (PI.f64) n) 1) (.f64 (.f64 (PI.f64) n) 1))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))) (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (+.f64 (pow.f64 (.f64 (PI.f64) n) 3) (pow.f64 (.f64 (PI.f64) n) 3)) (fma.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n) (-.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (-.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)) (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))) (-.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (.f64 (.f64 2 (pow.f64 n 3)) (PI.f64)) (fma.f64 n n 0))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (*.f64 0 (PI.f64)) 0)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (.f64 (PI.f64) (.f64 2 (pow.f64 n 3))) (fma.f64 n n 0))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (*.f64 (PI.f64) 0) 0)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3) 1/3)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (*.f64 (+.f64 n n) (cbrt.f64 (PI.f64))) 3)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(pow.f64 (*.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) 2)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) 2)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (+.f64 n n)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 3))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (+.f64 n n)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(cbrt.f64 (*.f64 (+.f64 n n) (pow.f64 (PI.f64) 3)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (+.f64 n n))) 1))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (PI.f64) n (*.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 n (PI.f64) (*.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 1 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (pow.f64 (cbrt.f64 n) 2) (.f64 (cbrt.f64 n) (PI.f64)) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) n) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (PI.f64)) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (PI.f64) n) 1 (.f64 (*.f64 (PI.f64) n) 1))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) n)) (cbrt.f64 (.f64 (PI.f64) n))) (cbrt.f64 (.f64 (PI.f64) n)) (*.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 (PI.f64) n)) (*.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (.f64 (sqrt.f64 n) (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (*.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 n (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(fma.f64 (.f64 (PI.f64) (sqrt.f64 n)) (sqrt.f64 n) (.f64 (PI.f64) n))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 0 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1)
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2)) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(*.f64 (pow.f64 (PI.f64) (-.f64 1 k)) (pow.f64 (+.f64 n n) (-.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(*.f64 (pow.f64 (+.f64 n n) (-.f64 1 k)) (pow.f64 (PI.f64) (-.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (pow.f64 1 (-.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2))) (-.f64 1 k)) (pow.f64 (*.f64 (+.f64 n n) (cbrt.f64 (PI.f64))) (-.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(.f64 (pow.f64 (.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (-.f64 1 k)) (pow.f64 (*.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (-.f64 1 k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (PI.f64) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (+.f64 n n)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (+.f64 n n) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (PI.f64)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (cbrt.f64 (.f64 (+.f64 n n) (pow.f64 (PI.f64) 2))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (*.f64 (+.f64 n n) (cbrt.f64 (PI.f64)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (.f64 (+.f64 n n) (sqrt.f64 (PI.f64))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (*.f64 (+.f64 n n) (sqrt.f64 (PI.f64)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(/.f64 (neg.f64 (.f64 (PI.f64) (+.f64 n n))) (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(sqrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 2))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n)))))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))
(exp.f64 (.f64 (.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1))
(log.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))) k))

eval604.0ms (5.9%)

Compiler: Compiled 19624 to 11257 computations (42.6% saved)

prune251.0ms (2.4%)

Pruning

33 alts after pruning (29 fresh and 4 done)

	Pruned	Kept	Total
New	996	21	1017
Fresh	10	8	18
Picked	0	1	1
Done	4	3	7
Total	1010	33	1043

Error

Counts

1043 → 33

Alt Table

Click to see full alt table

Status	Error	Program
	21.6b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
	40.4b	(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.4b	(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (sqrt.f64 k))
	23.7b	(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (pow.f64 (.f64 k 1/2) 1/6) 3))
	20.1b	(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
	0.5b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
	20.2b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
	20.3b	(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 k 1/2)) (sqrt.f64 (PI.f64))))
	30.1b	(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
	30.1b	(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
	33.0b	(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
▶	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	20.2b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	20.2b	(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
	20.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	30.7b	(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
	30.7b	(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
✓	10.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
	10.9b	(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
	12.9b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) k))
	30.5b	(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
	30.5b	(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
	10.8b	(sqrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
	30.5b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
	30.5b	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
	30.8b	(sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 3)))
▶	30.5b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
▶	32.2b	(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
✓	30.5b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
✓	12.9b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
▶	20.1b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
▶	39.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))

Compiler

Compiled 825 to 661 computations (19.9% saved)

localize28.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.2b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.3b	(.f64 (.f64 2 (PI.f64)) n)

Compiler

Compiled 53 to 38 computations (28.3% saved)

series4.0ms (0%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	k	@	0	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	k	@	-inf	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	n	@	0	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	k	@	inf	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.0ms	n	@	inf	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite52.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`log-prod_binary64`
505×	`pow-unpow_binary64`
387×	`pow2_binary64`
265×	`pow1/3_binary64`
261×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	307	23
2	3794	22

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 1))))))

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

833×	`log-prod_binary64`
692×	`associate-l_binary64`
636×	`associate-r_binary64`
415×	`unswap-sqr_binary64`
241×	`exp-sum_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	96	934
1	232	900
2	812	813
3	5741	813

Stop Event

1×	node limit

Counts

33 → 41

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 0 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 1)
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 1)
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 3)
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)) 1/3)
(pow.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 1))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))))
(.f64 (sqrt.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n))))) (pow.f64 k -1/2))
(.f64 (pow.f64 (sqrt.f64 (exp.f64 (-.f64 1 k))) (-.f64 (log.f64 (.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) (pow.f64 k -1/2))
(+.f64 0 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))))))
(.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))) 1)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 1)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)) 1/2)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3) 1/3)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 3)
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (pow.f64 k -1/4)) 2)
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 k -1/4)) 2)
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(pow.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(pow.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)) 1/3)
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1))) 3))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 (pow.f64 k -1/2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(cbrt.f64 (.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (-.f64 1 k)) 3)))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) (pow.f64 k -1)))) 1))
(sqrt.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) (/.f64 1 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (PI.f64) (/.f64 k n))
✓	10.0b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	k	@	0	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
0.0ms	k	@	-inf	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
0.0ms	k	@	inf	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
0.0ms	n	@	inf	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
0.0ms	n	@	-inf	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

rewrite52.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`log-prod_binary64`
411×	`exp-prod_binary64`
284×	`pow-prod-down_binary64`
250×	`pow2_binary64`
223×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	195	21
2	2641	21

Stop Event

1×	node limit

Counts

2 → 99

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(/.f64 (PI.f64) (/.f64 k n))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) (/.f64 n k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 n (/.f64 (PI.f64) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (PI.f64) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n k) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) k) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 k n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) k) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 (/.f64 k n))) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) 1) (/.f64 n k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (PI.f64) (neg.f64 k)) (neg.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (PI.f64) k) 1) n)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (PI.f64) k) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (PI.f64) k) (sqrt.f64 n)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k)))) 2)) (cbrt.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))) (sqrt.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (PI.f64) (/.f64 (neg.f64 k) n)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 k (*.f64 (PI.f64) n))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (PI.f64)) 1) (log.f64 (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (PI.f64)) (*.f64 (log.f64 (/.f64 k n)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (PI.f64)) 1) (*.f64 (log.f64 (/.f64 k n)) 1)))))))

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

677×	`associate-*l/_binary64`
574×	`associate-*r/_binary64`
425×	`associate-/l*_binary64`
252×	`times-frac_binary64`
231×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	253	1470
1	588	1422
2	1621	1422
3	7836	1422

Stop Event

1×	node limit

Counts

123 → 134

Calls

Call 1

Inputs
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(+.f64 0 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) 1)
(.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1)
(.f64 1 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))
(.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) (cbrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/2)
(pow.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1)
(pow.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) 1/4)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))))
(fabs.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))) 1) 1))
(+.f64 0 (*.f64 (PI.f64) (/.f64 n k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (PI.f64) (/.f64 n k)) 1)
(.f64 1 (.f64 (PI.f64) (/.f64 n k)))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) k) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (/.f64 k n))))
(*.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 (/.f64 k n))) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (PI.f64) 1) (/.f64 n k))
(*.f64 (/.f64 (PI.f64) (neg.f64 k)) (neg.f64 n))
(.f64 (.f64 (/.f64 (PI.f64) k) 1) n)
(.f64 (.f64 (/.f64 (PI.f64) k) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
(.f64 (.f64 (/.f64 (PI.f64) k) (sqrt.f64 n)) (sqrt.f64 n))
(pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)
(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 3)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -1)
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))))
(neg.f64 (/.f64 (PI.f64) (/.f64 (neg.f64 k) n)))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(cbrt.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3))
(cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) -3)) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 2))
(exp.f64 (.f64 (log.f64 (/.f64 k (.f64 (PI.f64) n))) -1))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1) 1))
(exp.f64 (-.f64 (*.f64 (log.f64 (PI.f64)) 1) (log.f64 (/.f64 k n))))
(exp.f64 (-.f64 (log.f64 (PI.f64)) (*.f64 (log.f64 (/.f64 k n)) 1)))
(exp.f64 (-.f64 (.f64 (log.f64 (PI.f64)) 1) (.f64 (log.f64 (/.f64 k n)) 1)))

Outputs
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(+.f64 0 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))
(.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 2 (/.f64 (PI.f64) k))))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 2 (/.f64 n k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 2 (/.f64 (PI.f64) k))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(.f64 1 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) (cbrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/2)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) 1/4)
(pow.f64 (*.f64 4 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) -2)) 1/4)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3) 1/6)
(pow.f64 (.f64 8 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 3)) 1/6)
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))))))
(fabs.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2)) 1/3))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6)) 3))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1) 1/2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1/2) 1))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))) 1) 1))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
(+.f64 0 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(.f64 (.f64 (PI.f64) (/.f64 n k)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 1 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) -2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) -2)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) k) n)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) 1) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) 1) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 k n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) k) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) k) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 1 n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (/.f64 k n)) 2)) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (/.f64 k n))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 k n)) -2) (/.f64 (PI.f64) (cbrt.f64 (/.f64 k n))))
(*.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))))
(/.f64 (pow.f64 (/.f64 k n) -1/2) (/.f64 (sqrt.f64 (/.f64 k n)) (PI.f64)))
(*.f64 (/.f64 (pow.f64 (/.f64 k n) -1/2) (sqrt.f64 (/.f64 k n))) (PI.f64))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (sqrt.f64 (/.f64 k n))) (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (/.f64 k n))))
(/.f64 (/.f64 (PI.f64) (sqrt.f64 (/.f64 k n))) (sqrt.f64 (/.f64 k n)))
(/.f64 (PI.f64) (*.f64 (sqrt.f64 (/.f64 k n)) (sqrt.f64 (/.f64 k n))))
(*.f64 (/.f64 (PI.f64) 1) (/.f64 n k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (/.f64 (PI.f64) (neg.f64 k)) (neg.f64 n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 (PI.f64) k) 1) n)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 (PI.f64) k) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(.f64 (.f64 (/.f64 (PI.f64) k) (sqrt.f64 n)) (sqrt.f64 n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2) 1/2)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3) 1/3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (exp.f64 1) (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)) 1/3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (/.f64 (/.f64 k (*.f64 (PI.f64) n)) 1) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))) 2)) (cbrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k))))) (sqrt.f64 (log.f64 (.f64 n (/.f64 (PI.f64) k)))))
(neg.f64 (/.f64 (PI.f64) (/.f64 (neg.f64 k) n)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(cbrt.f64 (/.f64 (pow.f64 (PI.f64) 3) (pow.f64 (/.f64 k n) 3)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 k (.f64 (PI.f64) n)) -3)) 1/3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k)))) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (log.f64 (/.f64 k (.f64 (PI.f64) n))) -1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) 1) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (-.f64 (*.f64 (log.f64 (PI.f64)) 1) (log.f64 (/.f64 k n))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (-.f64 (log.f64 (PI.f64)) (*.f64 (log.f64 (/.f64 k n)) 1)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (-.f64 (.f64 (log.f64 (PI.f64)) 1) (.f64 (log.f64 (/.f64 k n)) 1)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (/.f64 n k) (PI.f64))
✓	4.0b	(-.f64 (+.f64 1 (*.f64 (/.f64 n k) (PI.f64))) 1)
✓	10.0b	(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))

Compiler

Compiled 54 to 26 computations (51.9% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	n	@	-inf	(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
0.0ms	n	@	0	(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
0.0ms	k	@	-inf	(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
0.0ms	k	@	inf	(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
0.0ms	n	@	inf	(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))

rewrite59.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

585×	`prod-diff_binary64`
572×	`log-prod_binary64`
464×	`fma-def_binary64`
302×	`pow2_binary64`
209×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	263	21
2	3606	21

Stop Event

1×	node limit

Counts

2 → 132

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (*.f64 (/.f64 n k) (PI.f64))) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))) (cbrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4) (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2) 4))) (sqrt.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2) 4)) 1/2) (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 (/.f64 n k) (PI.f64))))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 n k) (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 n k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 (/.f64 n k) (PI.f64) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 n k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n k) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (PI.f64) (/.f64 n k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 n k) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2) (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 n k)) 2) (*.f64 (cbrt.f64 (/.f64 n k)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 n k)) (*.f64 (sqrt.f64 (/.f64 n k)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 n (PI.f64)) (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n 1) (/.f64 (PI.f64) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 n (cbrt.f64 (*.f64 k k))) (/.f64 (PI.f64) (cbrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) (-.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 n k)) 2)) (cbrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (PI.f64) (sqrt.f64 (/.f64 n k))) (sqrt.f64 (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 k (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2)) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (/.f64 n k) (PI.f64) 2) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 n (/.f64 k (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (PI.f64) (/.f64 k n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (-.f64 1 (*.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1) (fma.f64 (/.f64 n k) (PI.f64) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (PI.f64)) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 n (PI.f64))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1)) (neg.f64 (fma.f64 (/.f64 n k) (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 3)) (+.f64 1 (-.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 2) (fma.f64 (/.f64 n k) (PI.f64) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 2)) (-.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 n (PI.f64)) 1) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 n (PI.f64)) (cbrt.f64 (*.f64 k k))) (cbrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 n) (PI.f64)) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (neg.f64 n)) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (*.f64 n (PI.f64))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2)) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 n k) (PI.f64) 2) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (*.f64 (*.f64 (/.f64 n k) (PI.f64)) (fma.f64 (/.f64 n k) (PI.f64) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (*.f64 (/.f64 n k) (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (/.f64 n k) (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 n (*.f64 (/.f64 1 k) (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 n k) (PI.f64) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (PI.f64) (/.f64 n k) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 n k) (PI.f64)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2) (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 2) (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 2) (*.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 n k)) 2) (*.f64 (cbrt.f64 (/.f64 n k)) (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) (*.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 n k)) (*.f64 (sqrt.f64 (/.f64 n k)) (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3)) (/.f64 1 (fma.f64 (*.f64 (/.f64 n k) (PI.f64)) (fma.f64 (/.f64 n k) (PI.f64) -1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2)) (/.f64 1 (-.f64 1 (*.f64 (/.f64 n k) (PI.f64)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 n (PI.f64)) (/.f64 1 k) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) 2) (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 n 1) (/.f64 (PI.f64) k) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 n (cbrt.f64 (*.f64 k k))) (/.f64 (PI.f64) (cbrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) (-.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 1) (fma.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 n k)) 2)) (cbrt.f64 (/.f64 n k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (PI.f64) (sqrt.f64 (/.f64 n k))) (sqrt.f64 (/.f64 n k)) 0)))))

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
439×	`distribute-rgt-in_binary64`
412×	`associate-/l*_binary64`
399×	`distribute-lft-in_binary64`
297×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	280	2101
1	623	2025
2	1854	2021

Stop Event

1×	node limit

Counts

156 → 173

Calls

Call 1

Inputs
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (*.f64 n (PI.f64)) k)
(+.f64 0 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))) 1)
(.f64 1 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1)
(.f64 (cbrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/4) (pow.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1/2))
(pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/2)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))) 1)
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 3)
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/4) 2)
(fabs.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))) 1))
(+.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1))
(+.f64 1 (*.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1))
(+.f64 (*.f64 (/.f64 n k) (PI.f64)) 0)
(+.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) -1)
(+.f64 0 (*.f64 (/.f64 n k) (PI.f64)))
(+.f64 -1 (fma.f64 (/.f64 n k) (PI.f64) 1))
(+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))))
(.f64 1 (.f64 (/.f64 n k) (PI.f64)))
(.f64 n (.f64 (/.f64 1 k) (PI.f64)))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(.f64 (.f64 (/.f64 n k) (PI.f64)) 1)
(.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 2) (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(.f64 (pow.f64 (cbrt.f64 (/.f64 n k)) 2) (.f64 (cbrt.f64 (/.f64 n k)) (PI.f64)))
(.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(.f64 (sqrt.f64 (/.f64 n k)) (.f64 (sqrt.f64 (/.f64 n k)) (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(*.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(.f64 (.f64 n (PI.f64)) (/.f64 1 k))
(*.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))
(*.f64 (/.f64 n 1) (/.f64 (PI.f64) k))
(.f64 (/.f64 n (cbrt.f64 (.f64 k k))) (/.f64 (PI.f64) (cbrt.f64 k)))
(*.f64 (+.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) (-.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1))
(.f64 (.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))
(.f64 (.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 n k)) 2)) (cbrt.f64 (/.f64 n k)))
(.f64 (.f64 (PI.f64) (sqrt.f64 (/.f64 n k))) (sqrt.f64 (/.f64 n k)))
(/.f64 1 (/.f64 k (*.f64 n (PI.f64))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2)) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1)))
(/.f64 1 (/.f64 (fma.f64 (/.f64 n k) (PI.f64) 2) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1)))
(/.f64 n (/.f64 k (PI.f64)))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2)))
(/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (-.f64 1 (*.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) -1))))
(/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1) (fma.f64 (/.f64 n k) (PI.f64) 2))
(/.f64 (*.f64 n (PI.f64)) k)
(/.f64 (neg.f64 (*.f64 n (PI.f64))) (neg.f64 k))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1)) (neg.f64 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 3)) (+.f64 1 (-.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 2) (fma.f64 (/.f64 n k) (PI.f64) -1))))
(/.f64 (-.f64 1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 2)) (-.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1)))
(/.f64 (/.f64 (*.f64 n (PI.f64)) 1) k)
(/.f64 (/.f64 (.f64 n (PI.f64)) (cbrt.f64 (.f64 k k))) (cbrt.f64 k))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))
(/.f64 (*.f64 (neg.f64 n) (PI.f64)) (neg.f64 k))
(/.f64 (*.f64 (PI.f64) (neg.f64 n)) (neg.f64 k))
(pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 1)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 3)
(pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2)
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3) 1/3)
(pow.f64 (/.f64 k (*.f64 n (PI.f64))) -1)
(pow.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2)) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1)) -1)
(pow.f64 (/.f64 (fma.f64 (/.f64 n k) (PI.f64) 2) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1)) -1)
(sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2))
(log.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64)))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3))
(hypot.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (.f64 (*.f64 (/.f64 n k) (PI.f64)) (fma.f64 (/.f64 n k) (PI.f64) -1))))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (PI.f64))))
(expm1.f64 (.f64 (log1p.f64 (.f64 (/.f64 n k) (PI.f64))) 1))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64))))
(exp.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 n k) (PI.f64))) 1))
(fma.f64 1 (*.f64 (/.f64 n k) (PI.f64)) 0)
(fma.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 1) -1)
(fma.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)
(fma.f64 n (*.f64 (/.f64 1 k) (PI.f64)) 0)
(fma.f64 (/.f64 n k) (PI.f64) 0)
(fma.f64 (PI.f64) (/.f64 n k) 0)
(fma.f64 (*.f64 (/.f64 n k) (PI.f64)) 1 0)
(fma.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 1 -1)
(fma.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 2) (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 0)
(fma.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 2) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 2) (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 2) (*.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) -1)
(fma.f64 (pow.f64 (cbrt.f64 (/.f64 n k)) 2) (*.f64 (cbrt.f64 (/.f64 n k)) (PI.f64)) 0)
(fma.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 2) 0)
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)) 0)
(fma.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) 0)
(fma.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) -1)
(fma.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) (*.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) -1)
(fma.f64 (sqrt.f64 (/.f64 n k)) (*.f64 (sqrt.f64 (/.f64 n k)) (PI.f64)) 0)
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)) 0)
(fma.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))) 0)
(fma.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 3)) (/.f64 1 (fma.f64 (.f64 (/.f64 n k) (PI.f64)) (fma.f64 (/.f64 n k) (PI.f64) -1) 1)) -1)
(fma.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)) 0)
(fma.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2)) (/.f64 1 (-.f64 1 (.f64 (/.f64 n k) (PI.f64)))) -1)
(fma.f64 (*.f64 n (PI.f64)) (/.f64 1 k) 0)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) 2) (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) 1)
(fma.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) 1)
(fma.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)) 0)
(fma.f64 (/.f64 n 1) (/.f64 (PI.f64) k) 0)
(fma.f64 (/.f64 n (cbrt.f64 (*.f64 k k))) (/.f64 (PI.f64) (cbrt.f64 k)) 0)
(fma.f64 (+.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) (-.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) 0)
(fma.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 1) (fma.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)) -1) 1)
(fma.f64 (*.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) 0)
(fma.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) 0)
(fma.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 n k)) 2)) (cbrt.f64 (/.f64 n k)) 0)
(fma.f64 (*.f64 (PI.f64) (sqrt.f64 (/.f64 n k))) (sqrt.f64 (/.f64 n k)) 0)

Outputs
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(+.f64 0 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 1 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 (cbrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))
(.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))
(.f64 (cbrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2))) (cbrt.f64 (sqrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) (cbrt.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))
(.f64 (cbrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2))) (cbrt.f64 (sqrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 2))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 2))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 2))
(.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/4) (pow.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))) 1/4))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 2) 4))) (sqrt.f64 (cbrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 2) 4))) (sqrt.f64 (cbrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 2) 4))) (sqrt.f64 (cbrt.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) 2)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 2) 4))) (sqrt.f64 (cbrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))))
(pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/2)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)) 3/2))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 3)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 1/4) 2)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(fabs.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(log.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64)))))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64)))) 1/2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 (/.f64 n k) (PI.f64))))) 1))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) 2)))
(+.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(+.f64 1 (*.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(+.f64 (*.f64 (/.f64 n k) (PI.f64)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(+.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(+.f64 0 (*.f64 (/.f64 n k) (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(+.f64 -1 (fma.f64 (/.f64 n k) (PI.f64) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 1 (.f64 (/.f64 n k) (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 n (.f64 (/.f64 1 k) (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 (/.f64 n k) (PI.f64))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (.f64 (/.f64 n k) (PI.f64)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 2) (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (pow.f64 (cbrt.f64 (/.f64 n k)) 2) (.f64 (cbrt.f64 (/.f64 n k)) (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (sqrt.f64 (/.f64 n k)) (.f64 (sqrt.f64 (/.f64 n k)) (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 3)) (+.f64 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2) (fma.f64 n (/.f64 (PI.f64) k) 2)))
(*.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2)) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2)) (fma.f64 n (/.f64 (PI.f64) k) 2))
(.f64 (.f64 n (PI.f64)) (/.f64 1 k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 (/.f64 n 1) (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (/.f64 n (cbrt.f64 (.f64 k k))) (/.f64 (PI.f64) (cbrt.f64 k)))
(/.f64 n (/.f64 (cbrt.f64 (*.f64 k k)) (/.f64 (PI.f64) (cbrt.f64 k))))
(*.f64 (+.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) (-.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 n k)) 2)) (cbrt.f64 (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(.f64 (.f64 (PI.f64) (sqrt.f64 (/.f64 n k))) (sqrt.f64 (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 1 (/.f64 k (*.f64 n (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2)) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1)))
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 3)) (+.f64 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2) (fma.f64 n (/.f64 (PI.f64) k) 2)))
(/.f64 1 (/.f64 (fma.f64 (/.f64 n k) (PI.f64) 2) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1)))
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2)) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2)) (fma.f64 n (/.f64 (PI.f64) k) 2))
(/.f64 n (/.f64 k (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (PI.f64) (/.f64 k n))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2)))
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 3)) (+.f64 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2) (fma.f64 n (/.f64 (PI.f64) k) 2)))
(/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (-.f64 1 (*.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) -1))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3)) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (-.f64 1 (*.f64 -1 (fma.f64 (/.f64 n k) (PI.f64) 1)))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 3)) (+.f64 1 (+.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 3)) (+.f64 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2) (+.f64 1 (fma.f64 n (/.f64 (PI.f64) k) 1))))
(/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1) (fma.f64 (/.f64 n k) (PI.f64) 2))
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2)) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2)) (fma.f64 n (/.f64 (PI.f64) k) 2))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (neg.f64 (*.f64 n (PI.f64))) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 3)) (+.f64 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2) (fma.f64 n (/.f64 (PI.f64) k) 2)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1)) (neg.f64 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2)) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2)) (fma.f64 n (/.f64 (PI.f64) k) 2))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 3)) (+.f64 1 (-.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 2) (fma.f64 (/.f64 n k) (PI.f64) -1))))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) -1) 3)) (+.f64 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) -1) 2) (-.f64 1 (fma.f64 n (/.f64 (PI.f64) k) -1))))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) -1) 3)) (fma.f64 (fma.f64 n (/.f64 (PI.f64) k) -1) (+.f64 (fma.f64 n (/.f64 (PI.f64) k) -1) -1) 1))
(/.f64 (-.f64 1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 2)) (-.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1)))
(/.f64 (-.f64 1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) -1) 2)) (-.f64 1 (fma.f64 n (/.f64 (PI.f64) k) -1)))
(/.f64 (/.f64 (*.f64 n (PI.f64)) 1) k)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (/.f64 (.f64 n (PI.f64)) (cbrt.f64 (.f64 k k))) (cbrt.f64 k))
(.f64 (/.f64 n (cbrt.f64 (.f64 k k))) (/.f64 (PI.f64) (cbrt.f64 k)))
(/.f64 n (/.f64 (cbrt.f64 (*.f64 k k)) (/.f64 (PI.f64) (cbrt.f64 k))))
(/.f64 (/.f64 (*.f64 n (PI.f64)) (sqrt.f64 k)) (sqrt.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 (neg.f64 n) (PI.f64)) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(/.f64 (*.f64 (PI.f64) (neg.f64 n)) (neg.f64 k))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 2)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(pow.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3) 1/3)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(pow.f64 (/.f64 k (*.f64 n (PI.f64))) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(pow.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2)) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1)) -1)
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 3)) (+.f64 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2) (fma.f64 n (/.f64 (PI.f64) k) 2)))
(pow.f64 (/.f64 (fma.f64 (/.f64 n k) (PI.f64) 2) (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1)) -1)
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2)) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2)) (fma.f64 n (/.f64 (PI.f64) k) 2))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 2))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(log.f64 (pow.f64 (exp.f64 (/.f64 n k)) (PI.f64)))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64)))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(hypot.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (.f64 (*.f64 (/.f64 n k) (PI.f64)) (fma.f64 (/.f64 n k) (PI.f64) -1))))
(hypot.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (.f64 (*.f64 (PI.f64) (/.f64 n k)) (fma.f64 (/.f64 n k) (PI.f64) -1))))
(hypot.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 (.f64 (*.f64 n (/.f64 (PI.f64) k)) (fma.f64 n (/.f64 (PI.f64) k) -1))))
(hypot.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) (fma.f64 n (/.f64 (PI.f64) k) -1)))))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(expm1.f64 (.f64 (log1p.f64 (.f64 (/.f64 n k) (PI.f64))) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(exp.f64 (log.f64 (*.f64 (/.f64 n k) (PI.f64))))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 n k) (PI.f64))) 1))
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 1 (*.f64 (/.f64 n k) (PI.f64)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 1) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 n (*.f64 (/.f64 1 k) (PI.f64)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (/.f64 n k) (PI.f64) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (PI.f64) (/.f64 n k) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (*.f64 (/.f64 n k) (PI.f64)) 1 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 1 -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 2) (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 2) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 2) (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 2) (*.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (pow.f64 (cbrt.f64 (/.f64 n k)) 2) (*.f64 (cbrt.f64 (/.f64 n k)) (PI.f64)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 2) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 n k)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) (*.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) -1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (sqrt.f64 (/.f64 n k)) (*.f64 (sqrt.f64 (/.f64 n k)) (PI.f64)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (/.f64 n k)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))) 0)
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) (fma.f64 (/.f64 n k) (PI.f64) 2))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 3)) (+.f64 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2) (fma.f64 n (/.f64 (PI.f64) k) 2)))
(fma.f64 (+.f64 1 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 3)) (/.f64 1 (fma.f64 (.f64 (/.f64 n k) (PI.f64)) (fma.f64 (/.f64 n k) (PI.f64) -1) 1)) -1)
(fma.f64 (+.f64 1 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 3)) (/.f64 1 (fma.f64 (.f64 (PI.f64) (/.f64 n k)) (fma.f64 (/.f64 n k) (PI.f64) -1) 1)) -1)
(fma.f64 (+.f64 1 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3)) (/.f64 1 (fma.f64 (/.f64 n k) (.f64 (PI.f64) (fma.f64 n (/.f64 (PI.f64) k) -1)) 1)) -1)
(+.f64 -1 (/.f64 (+.f64 1 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 3)) (fma.f64 n (*.f64 (/.f64 (PI.f64) k) (fma.f64 n (/.f64 (PI.f64) k) -1)) 1)))
(fma.f64 (+.f64 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2) -1) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)) 0)
(*.f64 (+.f64 -1 (pow.f64 (fma.f64 (/.f64 n k) (PI.f64) 1) 2)) (/.f64 1 (fma.f64 (/.f64 n k) (PI.f64) 2)))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 n (/.f64 (PI.f64) k) 1) 2)) (fma.f64 n (/.f64 (PI.f64) k) 2))
(fma.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 2)) (/.f64 1 (-.f64 1 (.f64 (/.f64 n k) (PI.f64)))) -1)
(fma.f64 (-.f64 1 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) (/.f64 1 (-.f64 1 (.f64 (PI.f64) (/.f64 n k)))) -1)
(fma.f64 (-.f64 1 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 2)) (/.f64 1 (-.f64 1 (.f64 n (/.f64 (PI.f64) k)))) -1)
(+.f64 -1 (/.f64 (-.f64 1 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 2)) (-.f64 1 (/.f64 (PI.f64) (/.f64 k n)))))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 1 k) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) 2) (cbrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) -1)) 1)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (/.f64 n 1) (/.f64 (PI.f64) k) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (/.f64 n (cbrt.f64 (*.f64 k k))) (/.f64 (PI.f64) (cbrt.f64 k)) 0)
(.f64 (/.f64 n (cbrt.f64 (.f64 k k))) (/.f64 (PI.f64) (cbrt.f64 k)))
(/.f64 n (/.f64 (cbrt.f64 (*.f64 k k)) (/.f64 (PI.f64) (cbrt.f64 k))))
(fma.f64 (+.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) (-.f64 (sqrt.f64 (fma.f64 (/.f64 n k) (PI.f64) 1)) 1) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))) 1) (fma.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)) -1) 1)
(fma.f64 (+.f64 1 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))) (fma.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)) -1) 1)
(fma.f64 (+.f64 1 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))) (fma.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)) -1) 1)
(fma.f64 (+.f64 1 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))) (fma.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (PI.f64)) -1) 1)
(fma.f64 (*.f64 (/.f64 n k) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (*.f64 (/.f64 n k) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (*.f64 (PI.f64) (pow.f64 (cbrt.f64 (/.f64 n k)) 2)) (cbrt.f64 (/.f64 n k)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))
(fma.f64 (*.f64 (PI.f64) (sqrt.f64 (/.f64 n k))) (sqrt.f64 (/.f64 n k)) 0)
(*.f64 (PI.f64) (/.f64 n k))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) (/.f64 k n))

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2)
✓	0.3b	(.f64 (.f64 2 (/.f64 n k)) (PI.f64))
✓	21.9b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))

Compiler

Compiled 41 to 22 computations (46.3% saved)

series84.0ms (0.8%)

Counts

3 → 48

Calls

18 calls:

Time	Variable		Point	Expression
17.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2)
16.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2)
14.0ms	k	@	-inf	(pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2)
14.0ms	k	@	0	(pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2)
11.0ms	k	@	inf	(pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2)

rewrite65.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

567×	`log-prod_binary64`
423×	`exp-prod_binary64`
327×	`pow-prod-down_binary64`
290×	`pow2_binary64`
239×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	235	38
2	2913	38

Stop Event

1×	node limit

Counts

3 → 114

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (.f64 2 (/.f64 n k)) (PI.f64))
(pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6) (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4) (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (/.f64 n k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 2 n) k)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (*.f64 2 n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 9/2) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 2) 3/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/4) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/3) (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (*.f64 2 n) k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (*.f64 2 n) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (*.f64 2 n) k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (*.f64 2 n) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 n) (PI.f64)) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 2 n)) k)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 9/2) 2/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 2) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/4) 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 2)) (cbrt.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))) (sqrt.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (*.f64 2 n) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1) 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 1) 2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (*.f64 2 n) k) 3/2) (pow.f64 (PI.f64) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) 3/2) (pow.f64 (/.f64 (*.f64 2 n) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/4) (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 3/2) (pow.f64 (*.f64 (/.f64 n k) (PI.f64)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 4) (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 5/2) (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 9/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 9/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/4 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 3/4) 2))))))

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

927×	`fma-def_binary64`
467×	`log-div_binary64`
319×	`associate-*r/_binary64`
307×	`associate-*l/_binary64`
275×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	2723
1	644	2654
2	1911	2353
3	7581	2353

Stop Event

1×	node limit

Counts

162 → 174

Calls

Call 1

Inputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(+.f64 0 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1)
(.f64 1 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))
(.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) (cbrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))
(.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6))
(.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/4) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (sqrt.f64 (/.f64 (.f64 2 n) k)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (.f64 2 n) k)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 2)) (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))
(pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/2)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2) 1/3)
(pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 1)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 2) 1/4)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 9/2) 1/9)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 3/2)
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 2) 3/4)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/4) 2)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(pow.f64 (exp.f64 1/3) (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))
(fabs.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 1))
(exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 3/4))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3/2))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6)) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4)) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1) 1/3))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1/3) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 1) 1))
(+.f64 0 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (.f64 2 n) k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (.f64 2 n) k)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (.f64 2 n) k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (.f64 2 n) k)))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 1)
(/.f64 (.f64 (.f64 2 n) (PI.f64)) k)
(/.f64 (.f64 (PI.f64) (.f64 2 n)) k)
(pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2) 2/3)
(pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 2)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 2) 1/2)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 9/2) 2/9)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 6)
(pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 3)
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 2) 3/2)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/4) 4)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 4/3)
(pow.f64 (exp.f64 1) (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 2)) (cbrt.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) (sqrt.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(sqrt.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 2))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (*.f64 2 n) k)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3))
(expm1.f64 (log1p.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(log1p.f64 (expm1.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(exp.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 2/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3))
(exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 3/2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1) 2/3))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1/3) 2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 1) 2))
(+.f64 0 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2))) 1)
(.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))
(.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2) 1)
(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))
(.f64 1 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2))
(.f64 (pow.f64 (/.f64 (.f64 2 n) k) 3/2) (pow.f64 (PI.f64) 3/2))
(.f64 (pow.f64 (PI.f64) 3/2) (pow.f64 (/.f64 (.f64 2 n) k) 3/2))
(.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/4))
(.f64 (pow.f64 2 3/2) (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 3/2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 4) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6))
(.f64 (pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 5/2) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4))
(sqrt.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3))
(log.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2))))
(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 9/2))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(exp.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3))
(exp.f64 (.f64 (.f64 2 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 3/4))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 9/2)) 1/3))
(exp.f64 (.f64 (.f64 3/4 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 1) 3/2))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1/3) 3))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 1) 3))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 3/4) 2))

Outputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (/.f64 (PI.f64) k) -2))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (pow.f64 (/.f64 -1 n) -3/2) (pow.f64 (.f64 (/.f64 -2 k) (PI.f64)) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (/.f64 (PI.f64) k) -2))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (pow.f64 (/.f64 -1 n) -3/2) (pow.f64 (.f64 (/.f64 -2 k) (PI.f64)) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (/.f64 (PI.f64) k) -2))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (pow.f64 (/.f64 -1 n) -3/2) (pow.f64 (.f64 (/.f64 -2 k) (PI.f64)) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (/.f64 (PI.f64) k) -2))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (*.f64 (/.f64 (PI.f64) k) -2)) (log.f64 (/.f64 -1 n))))
(.f64 (pow.f64 (/.f64 -1 n) -3/2) (pow.f64 (.f64 (/.f64 -2 k) (PI.f64)) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 (.f64 n (PI.f64)) -2))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 n (.f64 (PI.f64) -2)))))
(.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (.f64 n (*.f64 (PI.f64) -2)) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 (.f64 n (PI.f64)) -2))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 n (.f64 (PI.f64) -2)))))
(.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (.f64 n (*.f64 (PI.f64) -2)) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 (.f64 n (PI.f64)) -2))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 n (.f64 (PI.f64) -2)))))
(.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (.f64 n (*.f64 (PI.f64) -2)) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 (.f64 n (PI.f64)) -2))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 n (.f64 (PI.f64) -2)))))
(.f64 (pow.f64 (/.f64 -1 k) 3/2) (pow.f64 (.f64 n (*.f64 (PI.f64) -2)) 3/2))
(+.f64 0 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))))))))
(.f64 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(.f64 1 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) (cbrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/4) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (sqrt.f64 (/.f64 (.f64 2 n) k)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 2 (/.f64 k n))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k 2))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 (.f64 2 n) k)))
(*.f64 (sqrt.f64 (/.f64 2 (/.f64 k n))) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k 2))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 2)) (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))
(.f64 (fabs.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))))) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))))
(.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))
(pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/2)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2) 1/3)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 2) 1/4)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 9/2) 1/9)
(.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 9/2) 1/18) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 9/2) 1/18))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 9/2) 1/18) (pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 9/2) 1/18))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 3/2)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 2) 3/4)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/4) 2)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (exp.f64 1/3) (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2)))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2)))))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(fabs.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1/3))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 1))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 3/4))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3/2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6)) 3))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4)) 2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 1) 1/2))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1) 1/3))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1/3) 1))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 1) 1))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))))
(+.f64 0 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (.f64 2 n) k))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (.f64 2 n) k)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 2 (/.f64 k n)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 2 (/.f64 k n))))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 n (/.f64 k 2))))))
(.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (.f64 2 (/.f64 n k))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (.f64 2 n) k)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (.f64 2 n) k)))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 1)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(/.f64 (.f64 (.f64 2 n) (PI.f64)) k)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(/.f64 (.f64 (PI.f64) (.f64 2 n)) k)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2) 2/3)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 2)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 2) 1/2)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/3)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 9/2) 2/9)
(.f64 (.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 9/2) 1/18) (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 9/2) 1/18)) (.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 9/2) 1/18) (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 9/2) 1/18)))
(.f64 (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 9/2) 1/18) (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 9/2) 1/18)) (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 9/2) 1/18) (pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 9/2) 1/18)))
(.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 9/2) 1/18) (pow.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 9/2) 1/18) 3))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 6)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 3)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 2) 3/2)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/4) 4)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 4/3)
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (exp.f64 1) (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 2)) (cbrt.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 2)) (cbrt.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))))) 2)) (cbrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) (sqrt.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))) (sqrt.f64 (log.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2)))))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))))))
(sqrt.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) (/.f64 (*.f64 2 n) k)))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(expm1.f64 (log1p.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(log1p.f64 (expm1.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 2/3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3)) 1/3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))))) 3/2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 1) 1))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1) 2/3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1/3) 2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 1) 2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))
(+.f64 0 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 3/2)))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))) 3/2)))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 3/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2))) 1)
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2) 1)
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(.f64 1 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(.f64 (pow.f64 (/.f64 (.f64 2 n) k) 3/2) (pow.f64 (PI.f64) 3/2))
(*.f64 (pow.f64 (/.f64 2 (/.f64 k n)) 3/2) (pow.f64 (PI.f64) 3/2))
(*.f64 (pow.f64 (/.f64 n (/.f64 k 2)) 3/2) (pow.f64 (PI.f64) 3/2))
(.f64 (pow.f64 (.f64 2 (/.f64 n k)) 3/2) (pow.f64 (PI.f64) 3/2))
(.f64 (pow.f64 (PI.f64) 3/2) (pow.f64 (/.f64 (.f64 2 n) k) 3/2))
(*.f64 (pow.f64 (/.f64 2 (/.f64 k n)) 3/2) (pow.f64 (PI.f64) 3/2))
(*.f64 (pow.f64 (/.f64 n (/.f64 k 2)) 3/2) (pow.f64 (PI.f64) 3/2))
(.f64 (pow.f64 (.f64 2 (/.f64 n k)) 3/2) (pow.f64 (PI.f64) 3/2))
(.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/4))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(.f64 (pow.f64 2 3/2) (pow.f64 (.f64 (/.f64 n k) (PI.f64)) 3/2))
(.f64 (pow.f64 2 3/2) (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 3/2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 4) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/6))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 1/6) (pow.f64 (cbrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 4))
(.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 1/6) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))) 4))
(.f64 (pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 5/2) (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 1/4))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 1/4) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 5/2))
(.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (/.f64 k 2))) 1/4) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n (/.f64 k 2)))) 5/2))
(sqrt.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(log.f64 (exp.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 9/2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 3/2)) 1))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)))) 3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (.f64 2 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 3/4))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64)) 9/2)) 1/3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (.f64 3/4 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 1) 3/2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1) 1))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/2)) 1/3) 3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)))) 1) 3))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64))) 3/4) 2))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))) 3/2)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))
✓	0.2b	(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)
	0.3b	(*.f64 (PI.f64) (+.f64 n n))
✓	19.1b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))

Compiler

Compiled 65 to 29 computations (55.4% saved)

series11.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	k	@	0	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
2.0ms	k	@	0	(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)
1.0ms	n	@	0	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
1.0ms	n	@	inf	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
1.0ms	n	@	-inf	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))

rewrite58.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

661×	`log-prod_binary64`
596×	`prod-diff_binary64`
230×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
213×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	291	39
2	4037	39

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4) 1/3) (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))) (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 3/2) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3/2) (pow.f64 (/.f64 1 k) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2) 3/2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3/2) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)) 1))))))

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
594×	`distribute-rgt-in_binary64`
589×	`distribute-lft-in_binary64`
215×	`associate-+l+_binary64`
203×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	3100
1	560	2844
2	1924	2258

Stop Event

1×	node limit

Counts

90 → 110

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -3/2 (.f64 k (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 -3/2 (.f64 k (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (pow.f64 k 2) (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 3/4 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))))))
(+.f64 (.f64 -3/2 (.f64 k (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 (pow.f64 k 2) (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 3/4 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))) (.f64 (pow.f64 k 3) (.f64 (+.f64 (.f64 -9/16 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 -9/8 (.f64 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/4 (+.f64 (.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))))) (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (pow.f64 1 1/3) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4) 1/3) (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4) 1/3))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/2)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) -1)
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1))
(+.f64 0 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))) (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))) 1)
(.f64 1 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1)
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4))
(.f64 (pow.f64 1 3/2) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3/2) (pow.f64 (/.f64 1 k) 3/2))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2) 3/2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3/2))
(.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3/2) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3/2))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3))
(log.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))
(cbrt.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))
(log1p.f64 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))
(exp.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)) 1))

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) 3) (pow.f64 k 3)))
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))
(pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k)))
(.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 3/2))
(+.f64 (.f64 -3/2 (.f64 k (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(fma.f64 -3/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(fma.f64 -3/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))))) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))))
(.f64 (+.f64 (.f64 (.f64 k -3/2) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 1) (.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2)))
(+.f64 (.f64 -3/2 (.f64 k (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (.f64 (pow.f64 k 2) (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 3/4 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))))))
(fma.f64 -3/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 (.f64 k k) (.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (fma.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 3/4 (.f64 0 (pow.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 2))))))))
(fma.f64 -3/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))))) (fma.f64 (.f64 k k) (.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (fma.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 0)) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k)))))
(fma.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (.f64 (.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2)) (+.f64 (.f64 (.f64 k k) (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2))) (.f64 (.f64 k -3/2) (log.f64 (.f64 2 (*.f64 (PI.f64) n)))))))
(+.f64 (.f64 -3/2 (.f64 k (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 (pow.f64 k 2) (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 3/4 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))))) (.f64 (pow.f64 k 3) (.f64 (+.f64 (.f64 -9/16 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 -9/8 (.f64 (+.f64 (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 1/4 (+.f64 (.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))))))) (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))))))
(+.f64 (fma.f64 -3/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (fma.f64 (.f64 k k) (.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (fma.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 3/4 (.f64 0 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2))))) (.f64 (pow.f64 k 3) (.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (fma.f64 -9/16 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (fma.f64 -9/8 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 0 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2))) (.f64 1/4 (fma.f64 -2 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) 2)))))))))
(+.f64 (fma.f64 -3/2 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))))) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k)))) (fma.f64 (pow.f64 k 3) (.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (fma.f64 -9/16 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) (fma.f64 1/4 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 3) 0) (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 0)))) (.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (.f64 (fma.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 0) (.f64 k k)))))
(+.f64 (.f64 (+.f64 (.f64 (.f64 k -3/2) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 1) (.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2))) (.f64 (.f64 (pow.f64 k -3/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2)) (+.f64 (.f64 (.f64 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (.f64 k k)) (.f64 (pow.f64 k 3) (.f64 -9/16 (pow.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 3))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (log.f64 (/.f64 -1 k))))
(.f64 (pow.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3/2) (pow.f64 (/.f64 -1 k) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (log.f64 (/.f64 -1 k))))
(.f64 (pow.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3/2) (pow.f64 (/.f64 -1 k) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (log.f64 (/.f64 -1 k))))
(.f64 (pow.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3/2) (pow.f64 (/.f64 -1 k) 3/2))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (log.f64 (/.f64 -1 k))))
(.f64 (pow.f64 (neg.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) 3/2) (pow.f64 (/.f64 -1 k) 3/2))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) 1)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(.f64 (fabs.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(.f64 (pow.f64 1 1/3) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4) 1/3) (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4) 1/3))
(.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/4)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/4)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 1/2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 3)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 2)
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(pow.f64 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))) -1)
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)) 1/3))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) 1))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(+.f64 0 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))) (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))
(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2))) (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))) 1)
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 1 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1)
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/4))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (pow.f64 1 3/2) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 3/2) (pow.f64 (/.f64 1 k) 3/2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 2) 3/2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3/2))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 2) 3/2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3/2))
(.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3/2) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 3/2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)))) (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(log.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(cbrt.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 3))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(expm1.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(log1p.f64 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(exp.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2)) 1))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)

eval271.0ms (2.6%)

Compiler: Compiled 15258 to 9410 computations (38.3% saved)

prune183.0ms (1.8%)

Pruning

38 alts after pruning (29 fresh and 9 done)

	Pruned	Kept	Total
New	818	9	827
Fresh	4	20	24
Picked	0	1	1
Done	0	8	8
Total	822	38	860

Error

Counts

860 → 38

Alt Table

Click to see full alt table

Status	Error	Program
	21.6b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
	46.7b	(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
	33.1b	(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
	33.1b	(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
	32.8b	(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
	30.8b	(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.4b	(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (sqrt.f64 k))
	30.2b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
	20.1b	(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
	0.5b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
	20.2b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
	20.3b	(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 k 1/2)) (sqrt.f64 (PI.f64))))
	30.1b	(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
	30.1b	(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
	33.0b	(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
✓	0.4b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	20.2b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	20.2b	(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
	20.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	30.7b	(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
✓	10.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
	10.9b	(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
	12.9b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) k))
	30.5b	(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
	30.5b	(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
	10.8b	(sqrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
	30.5b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
	30.5b	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
✓	30.5b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
✓	32.2b	(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
	32.1b	(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))
✓	30.5b	(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
	30.5b	(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
✓	12.9b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
	32.7b	(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
✓	20.1b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
✓	39.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))

Compiler

Compiled 503 to 405 computations (19.5% saved)

regimes148.0ms (1.4%)

Counts

72 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 k 1/2)) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))
(sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 3)))
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (pow.f64 (.f64 k 1/2) 1/6) 3))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
(sqrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)) k))
(sqrt.f64 (/.f64 (/.f64 (+.f64 n n) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (PI.f64))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (/.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n)))) k))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))

Outputs
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))

Calls

4 calls:

35.0ms	(.f64 (.f64 2 (PI.f64)) n)
33.0ms	n
32.0ms	k
18.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.3b	1	`k`
0.3b	1	`n`
0.3b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 960 to 581 computations (39.5% saved)

regimes140.0ms (1.4%)

Counts

71 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 k 1/2)) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))
(sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 3)))
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (pow.f64 (.f64 k 1/2) 1/6) 3))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
(sqrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)) k))
(sqrt.f64 (/.f64 (/.f64 (+.f64 n n) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (PI.f64))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (/.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n)))) k))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
(.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))

Outputs
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))

Calls

4 calls:

34.0ms	n
33.0ms	(.f64 (.f64 2 (PI.f64)) n)
32.0ms	k
18.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.3b	1	`k`
0.3b	1	`n`
0.3b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 942 to 572 computations (39.3% saved)

regimes132.0ms (1.3%)

Counts

69 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 k 1/2)) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))
(sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 3)))
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (pow.f64 (.f64 k 1/2) 1/6) 3))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
(sqrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)) k))
(sqrt.f64 (/.f64 (/.f64 (+.f64 n n) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (PI.f64))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (/.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n)))) k))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2))) (sqrt.f64 k))

Outputs
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2))) (sqrt.f64 k))

Calls

4 calls:

32.0ms	(.f64 (.f64 2 (PI.f64)) n)
31.0ms	n
30.0ms	k
17.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.3b	1	`k`
0.3b	1	`n`
0.3b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 905 to 549 computations (39.3% saved)

regimes133.0ms (1.3%)

Counts

68 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (*.f64 k 1/2)) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))
(sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (/.f64 n k) (PI.f64))) 3)))
(pow.f64 (exp.f64 1/2) (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (pow.f64 (.f64 k 1/2) 1/6) 3))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (+.f64 n n))))) k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k)) 1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
(/.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (fma.f64 k 1/2 -1/2))) (sqrt.f64 k))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) k) 3/2) 1/3)
(sqrt.f64 (.f64 (/.f64 n k) (/.f64 (.f64 2 (PI.f64)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(sqrt.f64 (/.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 k (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) k))))
(sqrt.f64 (/.f64 (/.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k)) k))
(sqrt.f64 (/.f64 (/.f64 (+.f64 n n) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) k) (PI.f64))) k))
(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(sqrt.f64 (/.f64 (/.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) k) (.f64 (PI.f64) (+.f64 n n)))) k))
(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 2 (*.f64 n (PI.f64))) k))))
(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (+.f64 1/2 (.f64 k -1/2))) (log.f64 (.f64 2 (.f64 n (PI.f64))))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Calls

4 calls:

32.0ms	n
31.0ms	k
31.0ms	(.f64 (.f64 2 (PI.f64)) n)
17.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`
0.4b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 886 to 537 computations (39.4% saved)

regimes58.0ms (0.6%)

Counts

34 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Calls

3 calls:

17.0ms	(.f64 (.f64 2 (PI.f64)) n)
16.0ms	n
16.0ms	k

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 363 to 227 computations (37.5% saved)

regimes42.0ms (0.4%)

Counts

33 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

Outputs
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

Calls

2 calls:

16.0ms	n
16.0ms	k

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`

Compiler

Compiled 341 to 210 computations (38.4% saved)

regimes104.0ms (1%)

Counts

32 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)))))

Outputs
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k))

Calls

2 calls:

68.0ms	n
27.0ms	k

Results

Error	Segments	Branch
0.4b	2	`k`
7.3b	5	`n`

Compiler

Compiled 327 to 201 computations (38.5% saved)

bsearch16.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	1.0040140462930126e-15	4.718235442039631e-15

Results

14.0ms

96×

body

256

valid

Compiler

Compiled 185 to 151 computations (18.4% saved)

regimes74.0ms (0.7%)

Counts

30 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))
(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(pow.f64 (pow.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 1/6) 3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3/4) 2/3)
(pow.f64 (pow.f64 (.f64 (/.f64 (.f64 2 n) k) (PI.f64)) 3) 1/6)

Outputs
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1)))

Calls

2 calls:

40.0ms	n
27.0ms	k

Results

Error	Segments	Branch
12.7b	2	`k`
15.8b	3	`n`

Compiler

Compiled 301 to 184 computations (38.9% saved)

bsearch4.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
3.0ms	1.6428479655408899	200104.13736841845

Results

3.0ms	16×	body	256	valid
0.0ms	3×	body	256	infinite

Compiler

Compiled 49 to 41 computations (16.3% saved)

regimes56.0ms (0.5%)

Counts

22 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (/.f64 n k)) (PI.f64)) 3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (*.f64 2 n) k) (PI.f64))) 1/2))

Outputs
(/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))

Calls

2 calls:

30.0ms	n
20.0ms	k

Results

Error	Segments	Branch
12.7b	2	`k`
15.8b	3	`n`

Compiler

Compiled 213 to 128 computations (39.9% saved)

bsearch4.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
4.0ms	1.6428479655408899	200104.13736841845

Results

3.0ms	16×	body	256	valid
0.0ms	1×	body	256	infinite

Compiler

Compiled 50 to 42 computations (16% saved)

regimes43.0ms (0.4%)

Counts

16 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))

Outputs
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))

Calls

2 calls:

24.0ms	n
15.0ms	k

Results

Error	Segments	Branch
12.7b	2	`k`
15.8b	3	`n`

Compiler

Compiled 154 to 92 computations (40.3% saved)

bsearch4.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
4.0ms	1.6428479655408899	200104.13736841845

Results

2.0ms	16×	body	256	valid
1.0ms	6×	body	256	infinite

Compiler

Compiled 50 to 42 computations (16% saved)

regimes34.0ms (0.3%)

Counts

14 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))
(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))) 1)
(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))

Outputs
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1)))

Calls

2 calls:

15.0ms	k
15.0ms	n

Results

Error	Segments	Branch
22.6b	2	`k`
23.0b	2	`n`

Compiler

Compiled 136 to 82 computations (39.7% saved)

bsearch4.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
3.0ms	1.6428479655408899	200104.13736841845

Results

3.0ms	16×	body	256	valid
0.0ms	3×	body	256	infinite

Compiler

Compiled 51 to 43 computations (15.7% saved)

regimes15.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(/.f64 1 (sqrt.f64 (.f64 (/.f64 k (.f64 n (PI.f64))) 1/2)))

Outputs
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))

Calls

2 calls:

6.0ms	n
6.0ms	k

Results

Error	Segments	Branch
30.1b	1	`k`
30.1b	1	`n`

Compiler

Compiled 94 to 58 computations (38.3% saved)

regimes15.0ms (0.1%)

Accuracy

Total -0.2b remaining (-0.7%)

Threshold costs -0.2b (-0.7%)

Counts

8 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 n (/.f64 k (PI.f64)))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k (PI.f64)) n)))
(sqrt.f64 (.f64 2 (.f64 n (*.f64 (/.f64 1 k) (PI.f64)))))

Outputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))

Calls

2 calls:

6.0ms	n
5.0ms	k

Results

Error	Segments	Branch
30.5b	1	`k`
30.5b	1	`n`

Compiler

Compiled 74 to 47 computations (36.5% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
7×	`+-commutative_binary64`
5×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	390
1	110	390
2	118	390
3	122	390
4	124	390

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 646501806116397/633825300114114700748351602688) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k)))
(if (<=.f64 k 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2))) (sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1))))
(if (<=.f64 k 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2))) (sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1))))
(if (<=.f64 k 2) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1))))
(if (<=.f64 k 2) (/.f64 1 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) (sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (*.f64 (/.f64 n k) (PI.f64))) 1))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))

Outputs
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 1/2 k))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 k 1/2))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 n))) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 k -1/2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 k) 2)) (pow.f64 k -1/2))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 646501806116397/633825300114114700748351602688) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (-.f64 1 k)) k)))
(if (<=.f64 k 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2))) (sqrt.f64 (*.f64 2 (+.f64 (fma.f64 (/.f64 n k) (PI.f64) -1) 1))))
(if (<=.f64 k 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2))) (sqrt.f64 (*.f64 2 (+.f64 1 (fma.f64 (/.f64 n k) (PI.f64) -1)))))
(if (<=.f64 k 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2))) (sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1))))
(if (<=.f64 k 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2))) (sqrt.f64 (.f64 2 (+.f64 (+.f64 1 (.f64 (PI.f64) (/.f64 n k))) -1))))
(if (<=.f64 k 2) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (.f64 k 1/2))) (sqrt.f64 (.f64 2 (+.f64 -1 (+.f64 1 (.f64 (PI.f64) (/.f64 n k)))))))
(if (<=.f64 k 2) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (.f64 (/.f64 n k) (PI.f64))) 1))))
(if (<=.f64 k 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 2 k))) (sqrt.f64 (.f64 2 (+.f64 (+.f64 1 (.f64 (PI.f64) (/.f64 n k))) -1))))
(if (<=.f64 k 2) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 2 k))) (sqrt.f64 (.f64 2 (+.f64 -1 (+.f64 1 (.f64 (PI.f64) (/.f64 n k)))))))
(if (<=.f64 k 2) (/.f64 1 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) (sqrt.f64 (.f64 2 (-.f64 (+.f64 1 (*.f64 (/.f64 n k) (PI.f64))) 1))))
(if (<=.f64 k 2) (/.f64 1 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) (sqrt.f64 (.f64 2 (+.f64 (+.f64 1 (*.f64 (PI.f64) (/.f64 n k))) -1))))
(if (<=.f64 k 2) (/.f64 1 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) (sqrt.f64 (.f64 2 (+.f64 -1 (+.f64 1 (*.f64 (PI.f64) (/.f64 n k)))))))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (.f64 2 (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))

Compiler

Compiled 270 to 210 computations (22.2% saved)

soundness153.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

667×	`associate-/l*_binary64`
561×	`associate-/r*_binary64`
453×	`div-sub_binary64`
450×	`distribute-frac-neg_binary64`
416×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	141	22
4	360	22
5	983	20
6	2213	20
7	5663	20
0	392	3891
1	915	3636
2	4256	3548

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 454 to 335 computations (26.2% saved)

end118.0ms (1.1%)

Compiler: Compiled 246 to 155 computations (37% saved)