Details

analyze108.0ms (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)

sample2.6s (22.9%)

Results

1.3s	8256×	body	256	valid
724.0ms	1343×	body	1024	invalid
232.0ms	724×	body	512	invalid
190.0ms	1611×	body	256	invalid
82.0ms	462×	body	256	infinite
64.0ms	259×	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)

simplify38.0ms (0.3%)

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)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 38 computations (32.1% saved)

series65.0ms (0.6%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
24.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
20.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
8.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
2.0ms	k	@	-inf	(/.f64 1 (sqrt.f64 k))
2.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite67.0ms (0.6%)

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

Outputs
((#(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 (pow.f64 (cbrt.f64 (.f64 2 (.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))))))
((#(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 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.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 (pow.f64 (sqrt.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 (/.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)))) 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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 (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 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 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 (.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))))))

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
354×	`log-prod_binary64`
272×	`times-frac_binary64`
238×	`exp-prod_binary64`
225×	`exp-sum_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	306	3027
1	696	2800
2	2465	2472
3	6614	2466

Stop Event

1×	node limit

Counts

153 → 185

Calls

Call 1

Inputs
(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 (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 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 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 (pow.f64 (cbrt.f64 (.f64 2 (.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))
(+.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 (pow.f64 (sqrt.f64 k) -1/2) (pow.f64 (sqrt.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 (pow.f64 (sqrt.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 (/.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 (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 (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 (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 (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 (pow.f64 k -1/2) 3) (pow.f64 (sqrt.f64 (pow.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)) 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 (.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))

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

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 50 to 30 computations (40% saved)

series9.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

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

rewrite62.0ms (0.5%)

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

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

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simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
539×	`distribute-rgt-in_binary64`
524×	`distribute-lft-in_binary64`
467×	`unswap-sqr_binary64`
367×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	3006
1	668	2738
2	2308	2687

Stop Event

1×	node limit

Counts

140 → 162

Calls

Call 1

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

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

eval140.0ms (1.2%)

Compiler: Compiled 7490 to 5061 computations (32.4% saved)

prune83.0ms (0.7%)

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	323	24	347
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	323	26	349

Error

0.0b

Counts

349 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	10.7b	(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 2)
	11.1b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	1.8b	(/.f64 (pow.f64 (.f64 2 (expm1.f64 (log1p.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 1 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
▶	0.3b	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
	22.7b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	0.4b	(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))) (sqrt.f64 k))
▶	3.4b	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
▶	0.4b	(/.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)))
	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (.f64 2 (+.f64 1/2 (*.f64 k -1/2)))))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 (-.f64 1 k) 2)))
	3.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 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)))))
	22.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	3.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k -1/2))) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.2b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
▶	12.5b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	26.4b	(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 3/2) (pow.f64 k 3/2)))

Compiler

Compiled 916 to 758 computations (17.2% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)))
✓	0.2b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
✓	0.2b	(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))

Compiler

Compiled 70 to 46 computations (34.3% saved)

series23.0ms (0.2%)

Counts

4 → 24

Calls

18 calls:

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

rewrite70.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`log-prod_binary64`
698×	`pow-unpow_binary64`
378×	`pow2_binary64`
260×	`pow1/3_binary64`
256×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	298	57
2	3808	53

Stop Event

1×	node limit

Counts

4 → 121

Calls

Call 1

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

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

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

422×	`associate-/r*_binary64`
279×	`associate-/l/_binary64`
277×	`log-prod_binary64`
244×	`associate-r_binary64`
219×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	306	2891
1	697	2777
2	3107	2606

Stop Event

1×	node limit

Counts

145 → 193

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

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.2b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
✓	9.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 50 to 33 computations (34% saved)

series14.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

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

rewrite66.0ms (0.6%)

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	50
1	259	50
2	3391	50

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

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

Outputs

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

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

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-*l/_binary64`
607×	`associate-/r*_binary64`
266×	`log-prod_binary64`
242×	`associate-r_binary64`
225×	`exp-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	337	4442
1	787	3848
2	3186	3803

Stop Event

1×	node limit

Counts

176 → 209

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

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 67 to 38 computations (43.3% saved)

series15.0ms (0.1%)

Counts

3 → 48

Calls

18 calls:

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

rewrite68.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`log-prod_binary64`
379×	`pow2_binary64`
261×	`pow1/3_binary64`
257×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	307	52
2	4016	52

Stop Event

1×	node limit

Counts

3 → 122

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

803×	`fma-def_binary64`
573×	`distribute-rgt-in_binary64`
524×	`unswap-sqr_binary64`
506×	`times-frac_binary64`
196×	`log-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	344	4645
1	807	3911
2	2868	3891

Stop Event

1×	node limit

Counts

170 → 253

Calls

Call 1

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

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

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))
✓	0.2b	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
✓	3.3b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
✓	9.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))

Compiler

Compiled 77 to 45 computations (41.6% saved)

series81.0ms (0.7%)

Counts

3 → 36

Calls

18 calls:

Time	Variable		Point	Expression
32.0ms	n	@	0	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
17.0ms	n	@	inf	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
16.0ms	n	@	-inf	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
6.0ms	k	@	-inf	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))
3.0ms	k	@	0	(log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)))

rewrite71.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

694×	`log-prod_binary64`
467×	`pow-unpow_binary64`
352×	`pow2_binary64`
240×	`pow1/3_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
1	283	59
2	3571	59

Stop Event

1×	node limit

Counts

3 → 138

Calls

Call 1

Inputs

(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))))

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

Outputs

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simplify110.0ms (1%)

Algorithm

1×	egg-herbie

Rules

564×	`log-prod_binary64`
505×	`associate-l_binary64`
462×	`associate-r_binary64`
389×	`exp-prod_binary64`
272×	`exp-sum_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	5827
1	483	5722
2	1266	5140
3	6090	5096

Stop Event

1×	node limit

Counts

174 → 137

Calls

Call 1

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

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
✓	0.3b	(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
✓	1.0b	(log.f64 (*.f64 2 (PI.f64)))
✓	3.2b	(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))

Compiler

Compiled 77 to 52 computations (32.5% saved)

series47.0ms (0.4%)

Counts

4 → 48

Calls

15 calls:

Time	Variable		Point	Expression
19.0ms	n	@	0	(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
12.0ms	n	@	-inf	(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
6.0ms	n	@	inf	(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
3.0ms	k	@	inf	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))
2.0ms	k	@	0	(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 k))

rewrite80.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`prod-diff_binary64`
334×	`fma-def_binary64`
301×	`expm1-udef_binary64`
301×	`log1p-udef_binary64`
264×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	64
1	344	56
2	4524	52

Stop Event

1×	node limit

Counts

4 → 140

Calls

Call 1

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

Outputs
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2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (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 n (.f64 2 (PI.f64))) (.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 n (.f64 2 (PI.f64))) (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 n (.f64 2 (PI.f64))) (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 n (.f64 2 (PI.f64))) (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 n (.f64 2 (PI.f64))) (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 n (.f64 2 (PI.f64))) (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 n (.f64 2 (PI.f64))) (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 n (.f64 2 (PI.f64))) (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 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 1))))))

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

895×	`times-frac_binary64`
297×	`log-prod_binary64`
231×	`associate-r_binary64`
217×	`exp-prod_binary64`
208×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	3830
1	891	3578
2	3682	3515

Stop Event

1×	node limit

Counts

188 → 232

Calls

Call 1

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

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

eval499.0ms (4.4%)

Compiler: Compiled 26418 to 18153 computations (31.3% saved)

prune271.0ms (2.4%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	1160	14	1174
Fresh	15	4	19
Picked	1	0	1
Done	3	3	6
Total	1179	21	1200

Error

Counts

1200 → 21

Alt Table

Click to see full alt table

Status	Error	Program
▶	10.7b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) 2)
	10.5b	(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
✓	0.4b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.4b	(/.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2))
	22.7b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	22.6b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
▶	22.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
▶	10.6b	(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) 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)))
	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (pow.f64 k -1/2) (/.f64 1 (pow.f64 (pow.f64 (.f64 (*.f64 2 n) (PI.f64)) (-.f64 1 k)) -1/2)))
✓	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	10.4b	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 n (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k))) (*.f64 k (pow.f64 n k))))
	32.8b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
	12.6b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	33.0b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
▶	32.7b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	12.5b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))

Compiler

Compiled 600 to 487 computations (18.8% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 57 to 40 computations (29.8% saved)

series130.0ms (1.2%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
58.0ms	n	@	0	(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
18.0ms	n	@	-inf	(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
18.0ms	k	@	inf	(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
16.0ms	n	@	inf	(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)
15.0ms	k	@	-inf	(pow.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) -1/2)

rewrite67.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`log-prod_binary64`
399×	`pow2_binary64`
266×	`pow1/3_binary64`
263×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	310	39
2	3956	39

Stop Event

1×	node limit

Counts

2 → 66

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) (cbrt.f64 (*.f64 (pow.f64 k -1) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 k -1) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) (cbrt.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1)) (*.f64 (cbrt.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/4))) (/.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 (-.f64 1 k) -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (*.f64 (pow.f64 k -1/4) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) 1) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 -1/2 (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k -1/4) 1) (/.f64 (pow.f64 k -1/4) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 -1/2 (-.f64 1 k)))))))) (#(struct:change #<rule 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simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
760×	`times-frac_binary64`
363×	`associate-/l*_binary64`
308×	`unswap-sqr_binary64`
293×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	3025
1	681	2599
2	2569	2498

Stop Event

1×	node limit

Counts

102 → 128

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))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(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 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))
(+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (/.f64 1 (*.f64 n (PI.f64)))) (sqrt.f64 1/2)))
(+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 -1/4 (+.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)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2))))
(+.f64 (.f64 (.f64 (pow.f64 k 3) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/12 (+.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 -1/8 (.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 1/48 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64))))) (+.f64 (.f64 1/2 (.f64 (.f64 k (.f64 (sqrt.f64 1/2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))))) (+.f64 (.f64 (.f64 (pow.f64 k 2) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 -1/4 (+.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)))))) (sqrt.f64 (/.f64 1 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 (/.f64 1 (.f64 n (PI.f64)))) (sqrt.f64 1/2)))))
(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))))
(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))))
(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))))
(sqrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k)))))
(+.f64 0 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))) 1)
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))
(.f64 1 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))) 1)
(.f64 (cbrt.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))) (cbrt.f64 (.f64 (pow.f64 k -1) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))
(.f64 (cbrt.f64 (.f64 (pow.f64 k -1) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))) (cbrt.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))
(.f64 (cbrt.f64 (pow.f64 k -1)) (.f64 (cbrt.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/4))) (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/4))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (pow.f64 k -1/2))
(.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))))
(.f64 (pow.f64 k -1/4) (.f64 (pow.f64 k -1/4) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) 1) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))
(.f64 (/.f64 (pow.f64 k -1/4) 1) (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))) (/.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))) (cbrt.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))))
(.f64 (/.f64 (pow.f64 k -1/4) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))) (/.f64 (pow.f64 k -1/4) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))))
(.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/4))) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/4))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/4))) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/4))))
(pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 1)
(pow.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 3) 1/3)
(pow.f64 (cbrt.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 3)
(pow.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/4))) 2)
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) (pow.f64 k -1/2)) -1)
(pow.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) (pow.f64 k -1/2)) 1) -1)
(neg.f64 (/.f64 (pow.f64 k -1/2) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))))
(sqrt.f64 (.f64 (pow.f64 k -1) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) 3)))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))
(exp.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))))
(exp.f64 (.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 1))
(+.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))) 1)
(.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))) 1)
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1)))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1)) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/4)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/4)))
(.f64 (pow.f64 n (.f64 -1/2 (-.f64 1 k))) (pow.f64 (.f64 2 (PI.f64)) (.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 -1/2 (-.f64 1 k))) (pow.f64 n (.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 1 (.f64 -1/2 (-.f64 1 k))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (.f64 -1/2 (-.f64 1 k))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 -1/2 (-.f64 1 k))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 (.f64 n 2) (.f64 -1/2 (-.f64 1 k))) (pow.f64 (PI.f64) (.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 1 -1/2) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) (-.f64 1 k))) -1/2) (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) -1/2))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))) -1/2) (pow.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) -1/2))
(.f64 (pow.f64 (/.f64 n (pow.f64 n k)) -1/2) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) -1/2))
(sqrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k)))))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) 3))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k)))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k)))))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (.f64 n 2))))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (*.f64 n 2))))) 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 2 (.f64 n (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 2 (.f64 n (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 2 (.f64 n (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 2 (.f64 n (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 2 (.f64 n (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 2 (.f64 n (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 2 (.f64 n (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 2 (.f64 n (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))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -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)))))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -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)))))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -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)))))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -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)))))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -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)))))
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(pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) -1/2)
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(.f64 (cbrt.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) (/.f64 (cbrt.f64 (/.f64 1 k)) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (neg.f64 (-.f64 1 k))))))
(.f64 (/.f64 (pow.f64 k -1/4) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))) (/.f64 (pow.f64 k -1/4) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))) (/.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2)))))
(/.f64 (/.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2)))) (cbrt.f64 (/.f64 1 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k)))))
(/.f64 (/.f64 (pow.f64 k -1/2) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (neg.f64 (-.f64 1 k))))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))))
(.f64 (/.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/4))) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/4))))
(pow.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/4))) 2)
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 k -1)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/4))) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/4))))
(.f64 (cbrt.f64 (/.f64 1 k)) (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2))))
(pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 1)
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(pow.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 3) 1/3)
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(pow.f64 (cbrt.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 3)
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(pow.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/4))) 2)
(pow.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/4))) 2)
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) (pow.f64 k -1/2)) -1)
(pow.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/4))) 2)
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(pow.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) 3)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) 3)))
(cbrt.f64 (/.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) 3)))
(cbrt.f64 (/.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2)) 3) k)))
(pow.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) (pow.f64 k -1/2)) 1) -1)
(pow.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/4))) 2)
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(neg.f64 (/.f64 (pow.f64 k -1/2) (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))))
(pow.f64 (/.f64 (pow.f64 k -1/4) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/4))) 2)
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(sqrt.f64 (.f64 (pow.f64 k -1) (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 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 2 (.f64 n (PI.f64))) (-.f64 1 k)) k))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))) 3))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) 3)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 k -1/2) 3) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) 3)))
(cbrt.f64 (/.f64 (/.f64 (pow.f64 k -1/2) k) (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)) 3)))
(cbrt.f64 (/.f64 (pow.f64 k -1/2) (.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2)) 3) k)))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(exp.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))))))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(exp.f64 (.f64 (fma.f64 -1/2 (log.f64 k) (log.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))))) 1))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))))
(+.f64 0 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2))))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))) 1)
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(.f64 1 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))) 1)
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1)))
(.f64 (cbrt.f64 (/.f64 1 (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) -1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (neg.f64 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2))))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1)) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k)))))
(.f64 (cbrt.f64 (/.f64 1 (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) -1/2))))
(.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (neg.f64 (-.f64 1 k)))) (cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 (-.f64 1 k) -1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (-.f64 1 k) -1/4)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 (-.f64 1 k) -1/4)))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(.f64 (pow.f64 n (.f64 -1/2 (-.f64 1 k))) (pow.f64 (.f64 2 (PI.f64)) (.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 n (.f64 (-.f64 1 k) -1/2)) (pow.f64 (.f64 2 (PI.f64)) (.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 -1/2 (-.f64 1 k))) (pow.f64 n (.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 n (.f64 (-.f64 1 k) -1/2)) (pow.f64 (.f64 2 (PI.f64)) (.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 1 (.f64 -1/2 (-.f64 1 k))) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) 2) (.f64 -1/2 (-.f64 1 k))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 (-.f64 1 k) -1/2)) (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 -1/2 (-.f64 1 k))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (*.f64 -1/2 (-.f64 1 k))))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (.f64 2 (.f64 (-.f64 1 k) -1/2)))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (*.f64 -1 (-.f64 1 k)))
(pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (neg.f64 (-.f64 1 k)))
(.f64 (pow.f64 (.f64 n 2) (.f64 -1/2 (-.f64 1 k))) (pow.f64 (PI.f64) (.f64 -1/2 (-.f64 1 k))))
(.f64 (pow.f64 (.f64 n 2) (.f64 (-.f64 1 k) -1/2)) (pow.f64 (PI.f64) (.f64 (-.f64 1 k) -1/2)))
(.f64 (pow.f64 1 -1/2) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) 2) (-.f64 1 k))) -1/2) (pow.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) -1/2))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 2) (-.f64 1 k))) -1/2) (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) -1/2))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))) -1/2) (pow.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) -1/2))
(pow.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))) -1)
(/.f64 1 (sqrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1 k))))
(.f64 (pow.f64 (/.f64 n (pow.f64 n k)) -1/2) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k)) -1/2))
(sqrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) -1))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k))) 3))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (*.f64 -1/2 (-.f64 1 k)))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(exp.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (.f64 n 2))))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 -1/2 (-.f64 1 k))))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
(exp.f64 (.f64 (.f64 -1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 (PI.f64) (*.f64 n 2))))) 1))
(exp.f64 (.f64 (.f64 (-.f64 1 k) -1/2) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (PI.f64) (/.f64 k n))
✓	9.8b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

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

rewrite54.0ms (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))))))
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(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)))
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(-.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)
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(*.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)))
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(*.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))
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(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) 2)
(pow.f64 (/.f64 k (*.f64 (PI.f64) n)) -1)
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(log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))
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(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
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(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)
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(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
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(/.f64 (*.f64 n (PI.f64)) k)
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(/.f64 (*.f64 n (PI.f64)) k)
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(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (*.f64 n (PI.f64)) k)
(*.f64 (PI.f64) (/.f64 n k))
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(/.f64 (*.f64 n (PI.f64)) k)
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(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))))
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(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
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(sqrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k))))
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(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
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(*.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))

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 43 to 27 computations (37.2% saved)

series13.0ms (0.1%)

Counts

2 → 0

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	k	@	-inf	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
1.0ms	k	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
1.0ms	n	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
1.0ms	n	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))
1.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))

rewrite57.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`log-prod_binary64`
375×	`pow-prod-down_binary64`
289×	`pow2_binary64`
244×	`pow-unpow_binary64`
205×	`pow-to-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	249	26
2	3094	26

Stop Event

1×	node limit

Counts

2 → 114

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)) 1)))) (#(struct:change #<rule 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4)) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 k -1/2) (sqrt.f64 n)) (sqrt.f64 (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 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k))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) 3/2) (pow.f64 k 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 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simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

540×	`associate-l_binary64`
458×	`associate-r_binary64`
436×	`associate-/l*_binary64`
400×	`log-prod_binary64`
355×	`exp-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	2008
1	601	1881
2	1690	1861
3	6555	1861

Stop Event

1×	node limit

Counts

114 → 191

Calls

Call 1

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

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

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.2b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
	9.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 80 to 55 computations (31.3% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

6 calls:

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

rewrite52.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`log-prod_binary64`
483×	`pow-unpow_binary64`
359×	`pow2_binary64`
244×	`pow1/3_binary64`
241×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	285	19
2	3751	19

Stop Event

1×	node limit

Counts

1 → 29

Calls

Call 1

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

Outputs

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

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

416×	`associate-l_binary64`
375×	`associate-r_binary64`
318×	`log-prod_binary64`
304×	`associate-+r+_binary64`
286×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	1081
1	218	1036
2	705	1036
3	4314	838

Stop Event

1×	node limit

Counts

41 → 51

Calls

Call 1

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

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

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.2b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
✓	0.3b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) 2)
✓	9.9b	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4)

Compiler

Compiled 67 to 46 computations (31.3% saved)

series88.0ms (0.8%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
21.0ms	k	@	-inf	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4)
18.0ms	n	@	-inf	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4)
17.0ms	n	@	0	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4)
15.0ms	n	@	inf	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4)
9.0ms	k	@	inf	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4)

rewrite60.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

722×	`log-prod_binary64`
498×	`pow-unpow_binary64`
374×	`pow2_binary64`
250×	`pow1/3_binary64`
248×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	310	39
2	3885	39

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

Inputs
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 1/4) 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/8) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/4) (pow.f64 (/.f64 1 k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 2) 1/4) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/4) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/4 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.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 2)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.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 2)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.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 2)) (-.f64 1 k)) k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) (*.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/8) (*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/8) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/8) 3) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.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 2)) (-.f64 1 k)) k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.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 2)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.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 2)) (-.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 2)) (-.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 2)) (-.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 2)) (-.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 2)) (-.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 2)) (-.f64 1 k)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (-.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 2)) (-.f64 1 k)) k))) 1))))))

simplify89.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

415×	`*-commutative_binary64`
331×	`associate-+l+_binary64`
300×	`exp-sum_binary64`
291×	`associate-+r+_binary64`
231×	`exp-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	266	3976
1	685	3384
2	2287	2815
3	5551	2696

Stop Event

1×	node limit

Counts

100 → 157

Calls

Call 1

Inputs
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k) 1/4)
(pow.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k) 1/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/4 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
(+.f64 (.f64 -1/4 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))))) (+.f64 (.f64 (pow.f64 k 2) (.f64 (+.f64 (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 1/8 (+.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)))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))))
(+.f64 (.f64 -1/4 (.f64 k (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))))) (+.f64 (.f64 (pow.f64 k 2) (.f64 (+.f64 (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)) (.f64 1/8 (+.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)))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))) (+.f64 (.f64 (pow.f64 k 3) (.f64 (+.f64 (.f64 -1/32 (.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 (.f64 1/24 (+.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 -1/384 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k)))))
(exp.f64 (.f64 1/4 (+.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 1/4 (+.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 1/4 (+.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 1/4 (+.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 (.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))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (.f64 k (+.f64 (.f64 -1/4 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/4 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 2))))))
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (+.f64 (.f64 k (+.f64 (.f64 -1/4 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/4 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2))))) (.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 2 (.f64 (+.f64 (.f64 1/8 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 2)))) (pow.f64 k 2))))
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (+.f64 (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/4 (.f64 (+.f64 (.f64 1/8 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 -1/4 (.f64 (+.f64 (.f64 1/8 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)))) (.f64 2 (.f64 (+.f64 (.f64 1/24 (+.f64 (.f64 3 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (+.f64 (.f64 -2 (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 -1/384 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3)) (.f64 -1/32 (.f64 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)))))) (+.f64 (.f64 k (+.f64 (.f64 -1/4 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (.f64 -1/4 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2))))) (.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (.f64 2 (.f64 (+.f64 (.f64 1/8 (+.f64 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2) (.f64 -1 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 1/32 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)))) (pow.f64 k 2)))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) (-.f64 1 k))) (log.f64 (/.f64 1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1 (*.f64 -1 k))))) (log.f64 (/.f64 -1 k))))) 2)
(+.f64 0 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4))) 1)
(.f64 1 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4) 1)
(.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/8) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/8))
(.f64 (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))))
(.f64 (pow.f64 1 1/4) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) 1/4) (pow.f64 (/.f64 1 k) 1/4))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)) 2) 1/4) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/4))
(.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)) 1/4) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/4))
(sqrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)))
(fabs.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4))
(log.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/4))
(expm1.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)))
(log1p.f64 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)))
(exp.f64 (.f64 1/4 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))) 1))
(+.f64 0 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)))) 1)
(.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/4))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1)
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))) (.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k))) (sqrt.f64 (/.f64 1 k)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/8) (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/8) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)))
(.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/8) 3) (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k) 1/8))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)))
(.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)))) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 1/4)))
(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))) (sqrt.f64 (neg.f64 k)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k)) 3))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k))) 1))

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

eval957.0ms (8.5%)

Compiler: Compiled 23052 to 16227 computations (29.6% saved)

prune269.0ms (2.4%)

Pruning

41 alts after pruning (36 fresh and 5 done)

	Pruned	Kept	Total
New	1026	31	1057
Fresh	8	5	13
Picked	1	0	1
Done	2	5	7
Total	1037	41	1078

Error

Counts

1078 → 41

Alt Table

Click to see full alt table

Status	Error	Program
▶	39.9b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)
	35.1b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/6) -3)
	35.1b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/6) 3)
	40.1b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
	35.2b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
	32.6b	(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
	10.5b	(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
	46.9b	(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
▶	33.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
	33.3b	(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))
	22.6b	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2))
▶	0.4b	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
	22.6b	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 k))
	32.8b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
	32.8b	(/.f64 1 (pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/4) 2))
	22.8b	(/.f64 1 (/.f64 (.f64 (sqrt.f64 k) (pow.f64 n -1/2)) (sqrt.f64 (.f64 2 (PI.f64)))))
✓	22.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
✓	10.6b	(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
	32.8b	(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))))
	22.7b	(/.f64 1 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) -1/2) (sqrt.f64 k)))
	32.7b	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 (/.f64 k n) (PI.f64)) 2)))
	22.7b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
	22.7b	(.f64 (/.f64 1 (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	32.8b	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
	0.5b	(.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))))
✓	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	10.4b	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 n (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k))) (*.f64 k (pow.f64 n k))))
	32.8b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
	12.6b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	32.8b	(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
	32.8b	(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
	32.8b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
✓	32.7b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
▶	32.7b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
▶	32.8b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
	32.8b	(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
	12.5b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))
	34.6b	(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 k (.f64 2 (PI.f64))) n)) -1/2))
	38.4b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2))

Compiler

Compiled 1033 to 854 computations (17.3% saved)

localize27.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 53 to 34 computations (35.8% saved)

series19.0ms (0.2%)

Counts

3 → 36

Calls

15 calls:

Time	Variable		Point	Expression
4.0ms	k	@	-inf	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))
3.0ms	k	@	0	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
2.0ms	k	@	-inf	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
1.0ms	n	@	0	(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
1.0ms	n	@	inf	(pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2))

rewrite65.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`log-prod_binary64`
393×	`pow2_binary64`
266×	`pow1/3_binary64`
263×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	45
1	305	45
2	3867	45

Stop Event

1×	node limit

Counts

3 → 85

Calls

Call 1

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

Outputs

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

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 2 n)) (-.f64 1 k)) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 k -1/2) (pow.f64 (pow.f64 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simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

764×	`times-frac_binary64`
668×	`fma-def_binary64`
564×	`unswap-sqr_binary64`
455×	`associate-/l*_binary64`
340×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	282	3402
1	689	2791
2	2515	2630

Stop Event

1×	node limit

Counts

121 → 153

Calls

Call 1

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

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

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 (PI.f64) k) n)
✓	0.2b	(/.f64 (PI.f64) k)
✓	9.8b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series5.0ms (0%)

Counts

3 → 24

Calls

15 calls:

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

rewrite57.0ms (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	26
1	189	26
2	2390	26

Stop Event

1×	node limit

Counts

3 → 78

Calls

Call 1

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

Outputs

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

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

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

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
480×	`associate-*l/_binary64`
427×	`unswap-sqr_binary64`
406×	`associate-/l*_binary64`
369×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	1242
1	393	1110
2	1426	984
3	7755	984

Stop Event

1×	node limit

Counts

102 → 105

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

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

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))
✓	0.4b	(/.f64 (PI.f64) (/.f64 1 n))
✓	9.8b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))

Compiler

Compiled 50 to 35 computations (30% saved)

series5.0ms (0%)

Counts

3 → 36

Calls

15 calls:

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

rewrite60.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`log-prod_binary64`
426×	`pow-prod-down_binary64`
305×	`pow2_binary64`
290×	`pow-unpow_binary64`
216×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	257	26
2	3374	26

Stop Event

1×	node limit

Counts

3 → 133

Calls

Call 1

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

Outputs

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

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

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
375×	`distribute-rgt-in_binary64`
361×	`log-prod_binary64`
234×	`cube-prod_binary64`
192×	`div-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	1593
1	747	1517
2	2717	1481

Stop Event

1×	node limit

Counts

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

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

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 2 (PI.f64)) (/.f64 n k))
✓	0.4b	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
✓	10.3b	(cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))

Compiler

Compiled 38 to 21 computations (44.7% saved)

series14.0ms (0.1%)

Counts

3 → 24

Calls

18 calls:

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

rewrite60.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`log-prod_binary64`
412×	`exp-prod_binary64`
335×	`pow-prod-down_binary64`
282×	`pow2_binary64`
233×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	233	37
2	2866	37

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

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

Outputs

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

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

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

simplify54.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
523×	`distribute-rgt-in_binary64`
490×	`distribute-lft-in_binary64`
293×	`times-frac_binary64`
277×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	264	1987
1	558	1926
2	1677	1926

Stop Event

1×	node limit

Counts

140 → 145

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

Outputs
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
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(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
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(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
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(*.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 2)))
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(*.f64 (cbrt.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))) (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 2)))
(.f64 (cbrt.f64 (/.f64 n k)) (cbrt.f64 (.f64 2 (PI.f64))))
(.f64 (cbrt.f64 (.f64 2 (PI.f64))) (cbrt.f64 (/.f64 n k)))
(.f64 (cbrt.f64 (/.f64 n k)) (cbrt.f64 (.f64 2 (PI.f64))))
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(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2/3)
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(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 2) 1/6)
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(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 3) 1/9)
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(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))) 2)) 3/2)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/6) 2)
(cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
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(pow.f64 (exp.f64 1) (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))
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(cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(pow.f64 (exp.f64 1/3) (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))
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(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))) 2)) (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))))) 2)) (cbrt.f64 (log.f64 (cbrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))))) (sqrt.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))))))
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(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 2))
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(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1) 1))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k)))) 1/3) 3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 3))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))) 1) 2))
(.f64 2 (.f64 (PI.f64) (/.f64 n k)))
(/.f64 2 (/.f64 (/.f64 k n) (PI.f64)))

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 k (*.f64 2 (PI.f64))) n)
✓	0.2b	(/.f64 k (*.f64 2 (PI.f64)))
✓	0.3b	(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2)
✓	21.3b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)

Compiler

Compiled 43 to 29 computations (32.6% saved)

series282.0ms (2.5%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
130.0ms	k	@	0	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)
35.0ms	k	@	-inf	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)
35.0ms	n	@	0	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)
29.0ms	n	@	-inf	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)
25.0ms	k	@	inf	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)

rewrite83.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`log-prod_binary64`
365×	`pow-prod-down_binary64`
332×	`pow2_binary64`
228×	`pow1/3_binary64`
227×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	269	47
2	3474	46

Stop Event

1×	node limit

Counts

4 → 135

Calls

Call 1

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

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

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

769×	`fma-def_binary64`
456×	`unswap-sqr_binary64`
352×	`distribute-rgt-in_binary64`
277×	`log-prod_binary64`
221×	`exp-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	368	4294970519
1	900	3087
2	3072	2941

Stop Event

1×	node limit

Counts

219 → 249

Calls

Call 1

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

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

eval278.0ms (2.5%)

Compiler: Compiled 13085 to 8904 computations (32% saved)

prune196.0ms (1.7%)

Pruning

42 alts after pruning (34 fresh and 8 done)

	Pruned	Kept	Total
New	799	17	816
Fresh	14	17	31
Picked	0	1	1
Done	2	7	9
Total	815	42	857

Error

Counts

857 → 42

Alt Table

Click to see full alt table

Status	Error	Program
✓	39.9b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)
	35.1b	(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/6) -3)
	35.2b	(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
	35.2b	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 3/2)
	32.7b	(pow.f64 (/.f64 (/.f64 (/.f64 k (PI.f64)) n) 2) -1/2)
	10.5b	(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
	32.7b	(pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) 2))) -1/2)
	32.8b	(pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/2)
	33.1b	(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) 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 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
	22.6b	(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 k))
	32.8b	(/.f64 1 (pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/4) 2))
✓	10.6b	(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))))
	32.7b	(/.f64 1 (sqrt.f64 (/.f64 (/.f64 (/.f64 k n) (PI.f64)) 2)))
	22.7b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
	22.7b	(.f64 (/.f64 1 (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	22.9b	(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k 2))) (sqrt.f64 n))
	33.0b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
	22.7b	(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
	32.8b	(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
	22.9b	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k))))
	0.5b	(.f64 (neg.f64 (pow.f64 k -1/2)) (/.f64 1 (neg.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 -1/2 (-.f64 1 k))))))
✓	10.6b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	10.4b	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 n (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k))) (*.f64 k (pow.f64 n k))))
	32.8b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
	12.6b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	32.8b	(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
	32.8b	(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
	32.8b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
	32.8b	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
	32.7b	(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
	32.8b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
	32.8b	(sqrt.f64 (.f64 2 (/.f64 (neg.f64 (PI.f64)) (.f64 k (/.f64 -1 n)))))
✓	32.7b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
✓	32.7b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
✓	32.8b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
	12.7b	(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
	12.5b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))
	34.6b	(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 k (.f64 2 (PI.f64))) n)) -1/2))
	38.4b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 (/.f64 k (PI.f64)) n) 2) -3/2))

Compiler

Compiled 550 to 452 computations (17.8% saved)

regimes261.0ms (2.3%)

Counts

88 → 1

Calls

Call 1

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

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

Calls

5 calls:

95.0ms	k
38.0ms	n
37.0ms	(.f64 (.f64 2 (PI.f64)) n)
36.0ms	(.f64 (.f64 2 (PI.f64)) n)
20.0ms	(.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)`
0.3b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1154 to 781 computations (32.3% saved)

regimes402.0ms (3.6%)

Counts

86 → 1

Calls

Call 1

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

Calls

5 calls:

110.0ms	n
100.0ms	(.f64 (.f64 2 (PI.f64)) n)
54.0ms	(.f64 (.f64 2 (PI.f64)) n)
53.0ms	k
34.0ms	(.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)`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 1114 to 755 computations (32.2% saved)

regimes201.0ms (1.8%)

Counts

53 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) 2))) -1/2)
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(pow.f64 (/.f64 (/.f64 (/.f64 k (PI.f64)) n) 2) -1/2)
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 (/.f64 k n) (PI.f64)) 2)))
(sqrt.f64 (.f64 2 (/.f64 (neg.f64 (PI.f64)) (.f64 k (/.f64 -1 n)))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k 2))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (/.f64 k (PI.f64)) n) 2) -3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 k (.f64 2 (PI.f64))) n)) -1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 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)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/6) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/6) -3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(/.f64 1 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) -1/2) (sqrt.f64 k)))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/4) 2))
(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)
(/.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 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

Calls

4 calls:

68.0ms	(.f64 (.f64 2 (PI.f64)) n)
43.0ms	(.f64 (.f64 2 (PI.f64)) n)
40.0ms	k
34.0ms	n

Results

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

Compiler

Compiled 568 to 371 computations (34.7% saved)

regimes179.0ms (1.6%)

Counts

51 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) 2))) -1/2)
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(pow.f64 (/.f64 (/.f64 (/.f64 k (PI.f64)) n) 2) -1/2)
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 (/.f64 k n) (PI.f64)) 2)))
(sqrt.f64 (.f64 2 (/.f64 (neg.f64 (PI.f64)) (.f64 k (/.f64 -1 n)))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k 2))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (/.f64 k (PI.f64)) n) 2) -3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 k (.f64 2 (PI.f64))) n)) -1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 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)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/6) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/6) -3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
(/.f64 1 (.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) -1/2) (sqrt.f64 k)))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
(/.f64 1 (pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/4) 2))
(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 2 n) (PI.f64)) (-.f64 1 k))) -1/2)

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

Calls

3 calls:

62.0ms	(.f64 (.f64 2 (PI.f64)) n)
60.0ms	n
41.0ms	k

Results

Error	Segments	Branch
0.4b	2	`k`
9.2b	3	`n`
9.2b	3	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 532 to 346 computations (35% saved)

bsearch19.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
18.0ms	8.229574691627475e-19	1.5540466285221788e-16

Results

17.0ms

112×

body

256

valid

Compiler

Compiled 226 to 187 computations (17.3% saved)

regimes235.0ms (2.1%)

Counts

46 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
(sqrt.f64 (/.f64 2 (/.f64 (/.f64 k n) (PI.f64))))
(sqrt.f64 (/.f64 n (/.f64 k (*.f64 2 (PI.f64)))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) 2))) -1/2)
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(pow.f64 (/.f64 (/.f64 (/.f64 k (PI.f64)) n) 2) -1/2)
(sqrt.f64 (*.f64 2 (/.f64 (/.f64 (PI.f64) k) (/.f64 1 n))))
(/.f64 1 (sqrt.f64 (/.f64 (/.f64 (/.f64 k n) (PI.f64)) 2)))
(sqrt.f64 (.f64 2 (/.f64 (neg.f64 (PI.f64)) (.f64 k (/.f64 -1 n)))))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
(/.f64 1 (/.f64 1 (sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))))
(sqrt.f64 (.f64 2 (/.f64 (.f64 (/.f64 1 k) (neg.f64 (PI.f64))) (/.f64 -1 n))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k 2))) (sqrt.f64 n))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) n)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -3/2))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 (/.f64 k (PI.f64)) n) 2) -3/2))
(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
(pow.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3/2)
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 k (.f64 2 (PI.f64))) n)) -1/2))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64))))))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2))
(pow.f64 (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) 3) 8) 1/6)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))) 1/3) 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)) 3/2) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (/.f64 2 k)) 1/6) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/6) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 1/6) -3)
(pow.f64 (pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) 3/2) -1/3)

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

Calls

3 calls:

95.0ms	(.f64 (.f64 2 (PI.f64)) n)
89.0ms	n
38.0ms	k

Results

Error	Segments	Branch
2.6b	2	`k`
10.3b	5	`n`
10.3b	5	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 469 to 302 computations (35.6% saved)

bsearch13.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
13.0ms	1.0231225833862382e-19	3.053526616682645e-19

Results

12.0ms

80×

body

256

valid

Compiler

Compiled 168 to 144 computations (14.3% saved)

regimes188.0ms (1.7%)

Counts

37 → 2

Calls

Call 1

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

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

Calls

3 calls:

74.0ms	(.f64 (.f64 2 (PI.f64)) n)
70.0ms	n
32.0ms	k

Results

Error	Segments	Branch
2.6b	2	`k`
10.3b	5	`n`
10.3b	5	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 370 to 235 computations (36.5% saved)

bsearch13.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
13.0ms	1.0231225833862382e-19	3.053526616682645e-19

Results

12.0ms

80×

body

256

valid

Compiler

Compiled 158 to 134 computations (15.2% saved)

regimes236.0ms (2.1%)

Counts

26 → 2

Calls

Call 1

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

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

Calls

2 calls:

207.0ms	n
22.0ms	k

Results

Error	Segments	Branch
2.7b	2	`k`
10.3b	5	`n`

Compiler

Compiled 254 to 162 computations (36.2% saved)

bsearch22.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
22.0ms	1.5540466285221788e-16	2.295673519176761e-13

Results

20.0ms

128×

body

256

valid

Compiler

Compiled 239 to 203 computations (15.1% saved)

regimes75.0ms (0.7%)

Counts

23 → 2

Calls

Call 1

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

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

Calls

2 calls:

48.0ms	n
21.0ms	k

Results

Error	Segments	Branch
2.8b	2	`k`
10.3b	5	`n`

Compiler

Compiled 227 to 147 computations (35.2% saved)

bsearch14.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
14.0ms	1.0231225833862382e-19	3.053526616682645e-19

Results

12.0ms

80×

body

256

valid

Compiler

Compiled 158 to 134 computations (15.2% saved)

regimes27.0ms (0.2%)

Counts

20 → 1

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	n
9.0ms	k

Results

Error	Segments	Branch
12.7b	1	`k`
12.7b	1	`n`

Compiler

Compiled 200 to 132 computations (34% saved)

regimes45.0ms (0.4%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

32.0ms	k
8.0ms	n

Results

Error	Segments	Branch
32.6b	1	`k`
32.6b	1	`n`

Compiler

Compiled 151 to 97 computations (35.8% saved)

regimes14.0ms (0.1%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	n
5.0ms	k

Results

Error	Segments	Branch
32.7b	1	`k`
32.7b	1	`n`

Compiler

Compiled 90 to 58 computations (35.6% saved)

regimes31.0ms (0.3%)

Accuracy

Total -0.4b remaining (-1.2%)

Threshold costs -0.4b (-1.2%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

23.0ms	n
5.0ms	k

Results

Error	Segments	Branch
32.7b	1	`k`
32.7b	1	`n`

Compiler

Compiled 81 to 52 computations (35.8% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
6×	`+-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	76	340
1	100	340
2	108	340
3	112	340
4	114	340

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 1419768672255617/20282409603651670423947251286016) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 5399988732876221/20769187434139310514121985316880384) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2)) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 8515366847997117/41538374868278621028243970633760768) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 5942112188569825/39614081257132168796771975168) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 376441522243775/1298074214633706907132624082305024) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k)))) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) 2))) -1/2)
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))

Outputs
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 (-.f64 1 k) -1/2)))
(/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 2 (.f64 n (PI.f64))) (*.f64 -1/2 (-.f64 1 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 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 1419768672255617/20282409603651670423947251286016) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 5399988732876221/20769187434139310514121985316880384) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2)) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 5399988732876221/20769187434139310514121985316880384) (/.f64 (pow.f64 k -1/2) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2)) (sqrt.f64 (.f64 2 (.f64 n (+.f64 (+.f64 1 (/.f64 (PI.f64) k)) -1)))))
(if (<=.f64 k 8515366847997117/41538374868278621028243970633760768) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 8515366847997117/41538374868278621028243970633760768) (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 n (+.f64 (+.f64 1 (/.f64 (PI.f64) k)) -1)))))
(if (<=.f64 k 5942112188569825/39614081257132168796771975168) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 5942112188569825/39614081257132168796771975168) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (.f64 2 (.f64 n (+.f64 (+.f64 1 (/.f64 (PI.f64) k)) -1)))))
(if (<=.f64 k 376441522243775/1298074214633706907132624082305024) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k)))) (sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n))))
(if (<=.f64 k 376441522243775/1298074214633706907132624082305024) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k)))) (sqrt.f64 (.f64 2 (.f64 n (+.f64 (+.f64 1 (/.f64 (PI.f64) k)) -1)))))
(sqrt.f64 (.f64 2 (.f64 (-.f64 (+.f64 1 (/.f64 (PI.f64) k)) 1) n)))
(sqrt.f64 (.f64 2 (.f64 n (+.f64 (+.f64 1 (/.f64 (PI.f64) k)) -1))))
(pow.f64 (/.f64 (/.f64 k (*.f64 2 (PI.f64))) n) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 (PI.f64) 2))) -1/2)
(pow.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))) -1/2)
(sqrt.f64 (.f64 2 (.f64 (/.f64 (PI.f64) k) n)))
(sqrt.f64 (.f64 2 (.f64 n (/.f64 (PI.f64) k))))

Compiler

Compiled 239 to 189 computations (20.9% saved)

soundness81.0ms (0.7%)

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

Compiler

Compiled 248 to 206 computations (16.9% saved)

end180.0ms (1.6%)

Compiler: Compiled 217 to 146 computations (32.7% saved)