Details

analyze161.0ms (1.5%)

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 (25.3%)

Results

1.3s	8256×	body	256	valid
721.0ms	1294×	body	1024	invalid
227.0ms	710×	body	512	invalid
185.0ms	1591×	body	256	invalid
78.0ms	474×	body	256	infinite
55.0ms	242×	body	256	unsamplable

Bogosity

preprocess54.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 20 to 17 computations (15% saved)

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 7

Calls

Call 1

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

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

eval2.0ms (0%)

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

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.4b

Counts

8 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.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)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series72.0ms (0.7%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
23.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
21.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
16.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
2.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite111.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 105

Calls

Call 1

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

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

simplify100.0ms (1%)

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	6620	2466

Stop Event

1×	node limit

Counts

153 → 184

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

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

localize21.0ms (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)

series10.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	n	@	-inf	(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	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))

rewrite63.0ms (0.6%)

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))))))
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Outputs

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simplify68.0ms (0.7%)

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

eval130.0ms (1.2%)

Compiler: Compiled 7471 to 5049 computations (32.4% saved)

prune77.0ms (0.7%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	321	25	346
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	322	26	348

Error

0.0b

Counts

348 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	19.7b	(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3) 1/3)
	0.7b	(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
	13.3b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
	0.5b	(/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1 n) -1) (.f64 (PI.f64) -2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	28.4b	(/.f64 (pow.f64 (.f64 2 (pow.f64 (pow.f64 (.f64 (PI.f64) n) 3) 1/3)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	3.1b	(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.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)))))
▶	0.6b	(/.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))
▶	0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (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))
	24.7b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
	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 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)))
	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)))
	3.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k))))
	24.8b	(.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)))
▶	12.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	14.5b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
	18.3b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3))

Compiler

Compiled 936 to 769 computations (17.8% saved)

localize28.0ms (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 1/2 k)))
✓	0.1b	(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 1/2 k))) (sqrt.f64 k))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))

Compiler

Compiled 70 to 46 computations (34.3% saved)

series22.0ms (0.2%)

Counts

4 → 24

Calls

18 calls:

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

rewrite79.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`log-prod_binary64`
386×	`pow2_binary64`
265×	`pow1/3_binary64`
261×	`log-pow_binary64`
261×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	73
1	302	55
2	4000	55

Stop Event

1×	node limit

Counts

4 → 147

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 1/2 k))) (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 1/2 k)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2 (.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (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 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 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 2) 1/2)))) (#(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 (.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 2 (.f64 (PI.f64) n)) 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 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 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 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (/.f64 1 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) 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(.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 2) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2))) (/.f64 1 (neg.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 k -1/2) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 n) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 k)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 1) (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 k)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 k)) (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) 2) (cbrt.f64 k)) (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k))) (cbrt.f64 k)) (/.f64 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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (-.f64 1 k)) 3) (pow.f64 k 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 1/2 k -1/2)) (sqrt.f64 k)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) k) (sqrt.f64 k)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (fma.f64 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simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

366×	`associate-/r/_binary64`
321×	`log-prod_binary64`
283×	`associate-r_binary64`
246×	`associate-l_binary64`
233×	`sqr-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	3873
1	917	3618
2	4144	3536

Stop Event

1×	node limit

Counts

171 → 289

Calls

Call 1

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

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

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
✓	11.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 50 to 33 computations (34% saved)

series13.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

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

rewrite68.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	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))))))

simplify79.0ms (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)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	4.7b	(exp.f64 (*.f64 -1/2 (log.f64 k)))

Compiler

Compiled 63 to 43 computations (31.7% saved)

series51.0ms (0.5%)

Counts

2 → 24

Calls

9 calls:

Time	Variable		Point	Expression
25.0ms	k	@	-inf	(exp.f64 (*.f64 -1/2 (log.f64 k)))
11.0ms	k	@	inf	(exp.f64 (*.f64 -1/2 (log.f64 k)))
9.0ms	k	@	0	(exp.f64 (*.f64 -1/2 (log.f64 k)))
2.0ms	k	@	inf	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms	k	@	-inf	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite62.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

807×	`log-prod_binary64`
422×	`pow2_binary64`
292×	`pow1/3_binary64`
288×	`expm1-udef_binary64`
287×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	336	27
2	4115	26

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

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

Outputs

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

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

534×	`unswap-sqr_binary64`
478×	`fma-def_binary64`
402×	`log-prod_binary64`
374×	`distribute-rgt-in_binary64`
366×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1170
1	342	1124
2	1199	1022
3	5738	1022

Stop Event

1×	node limit

Counts

70 → 68

Calls

Call 1

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

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

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 65 to 32 computations (50.8% saved)

series5.0ms (0%)

Counts

3 → 48

Calls

15 calls:

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

rewrite65.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 105

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	319	3155
1	733	2811
2	2443	2760

Stop Event

1×	node limit

Counts

153 → 176

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

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

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 73 to 45 computations (38.4% saved)

series43.0ms (0.4%)

Counts

3 → 60

Calls

18 calls:

Time	Variable		Point	Expression
18.0ms	n	@	0	(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4))
9.0ms	k	@	inf	(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4))
9.0ms	k	@	-inf	(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4))
2.0ms	k	@	0	(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4))
1.0ms	n	@	inf	(/.f64 (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) (pow.f64 k 1/4))

rewrite74.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

815×	`log-prod_binary64`
276×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`
257×	`pow3_binary64`
253×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	329	54
2	4261	54

Stop Event

1×	node limit

Counts

3 → 118

Calls

Call 1

Inputs

(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))) (pow.f64 k 1/4))

(/.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))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))))) (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (sqrt.f64 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)) (sqrt.f64 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) (sqrt.f64 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)) (sqrt.f64 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x 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simplify100.0ms (1%)

Algorithm

1×	egg-herbie

Rules

550×	`distribute-rgt-in_binary64`
546×	`distribute-lft-in_binary64`
491×	`unswap-sqr_binary64`
243×	`associate-r_binary64`
198×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	395	5375
1	973	4918
2	3647	4730

Stop Event

1×	node limit

Counts

178 → 259

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

eval498.0ms (4.8%)

Compiler: Compiled 28022 to 18705 computations (33.2% saved)

prune269.0ms (2.6%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	1174	12	1186
Fresh	15	5	20
Picked	1	0	1
Done	3	2	5
Total	1193	19	1212

Error

Counts

1212 → 19

Alt Table

Click to see full alt table

Status	Error	Program
▶	19.7b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.7b	(/.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)))))
▶	0.5b	(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
	24.8b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.5b	(/.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k 1/2 -1/2)))
	24.7b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	12.4b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
▶	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 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	12.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	12.6b	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)) k))
	37.0b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
▶	14.6b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	37.2b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
▶	37.0b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	14.5b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
	18.3b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2))

Compiler

Compiled 564 to 456 computations (19.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 49 to 32 computations (34.7% saved)

series18.0ms (0.2%)

Counts

4 → 24

Calls

18 calls:

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

rewrite66.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

674×	`log-prod_binary64`
420×	`pow-unpow_binary64`
344×	`pow2_binary64`
237×	`pow1/3_binary64`
232×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	277	53
2	3508	53

Stop Event

1×	node limit

Counts

4 → 125

Calls

Call 1

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

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

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

522×	`log-prod_binary64`
408×	`associate-/r*_binary64`
358×	`fma-neg_binary64`
224×	`sqr-pow_binary64`
185×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	2954
1	667	2810
2	2674	2754
3	7309	2754

Stop Event

1×	node limit

Counts

149 → 172

Calls

Call 1

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

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

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (PI.f64) (/.f64 k n))
✓	11.9b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series9.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite53.0ms (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)))))))

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

123 → 134

Calls

Call 1

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

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 k -1/2)
✓	0.2b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 53 to 38 computations (28.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

9 calls:

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

rewrite58.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	307	27
2	3794	26

Stop Event

1×	node limit

Counts

2 → 41

Calls

Call 1

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

Outputs

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

((#(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 (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 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 (pow.f64 k -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 k -1)) (cbrt.f64 (pow.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 k -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 k k)) -1/2) (pow.f64 (cbrt.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 sqrt.f64 (pow.f64 k -1))))) (#(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 (*.f64 -1/2 (log.f64 k)) 1))))))

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

910×	`log-prod_binary64`
803×	`associate-l_binary64`
748×	`associate-r_binary64`
459×	`unswap-sqr_binary64`
317×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1227
1	320	1173
2	1034	1030
3	6923	1030

Stop Event

1×	node limit

Counts

65 → 71

Calls

Call 1

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

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

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	3.8b	(exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64))))))
✓	11.8b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))

Compiler

Compiled 72 to 50 computations (30.6% saved)

series11.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	k	@	0	(.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))
1.0ms	k	@	-inf	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
1.0ms	k	@	0	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
0.0ms	k	@	inf	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
0.0ms	k	@	-inf	(.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))

rewrite69.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log-prod_binary64`
351×	`pow2_binary64`
263×	`pow-unpow_binary64`
248×	`pow1/3_binary64`
242×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	285	49
2	3531	49

Stop Event

1×	node limit

Counts

3 → 159

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Rules

540×	`sqr-pow_binary64`
517×	`unswap-sqr_binary64`
334×	`times-frac_binary64`
270×	`associate-/l*_binary64`
230×	`log-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	432	5379
1	1074	5242
2	3265	5127

Stop Event

1×	node limit

Counts

219 → 329

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

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

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2)
	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.3b	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
✓	18.8b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)

Compiler

Compiled 68 to 47 computations (30.9% saved)

series133.0ms (1.3%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
56.0ms	n	@	-inf	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
21.0ms	n	@	inf	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
18.0ms	k	@	inf	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
16.0ms	n	@	0	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
15.0ms	k	@	-inf	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)

rewrite72.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

740×	`log-prod_binary64`
397×	`pow2_binary64`
266×	`pow1/3_binary64`
264×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	334	39
2	4097	39

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

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

Outputs

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

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

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

363×	`fma-neg_binary64`
340×	`exp-sum_binary64`
299×	`associate-+l+_binary64`
249×	`associate-+r+_binary64`
208×	`exp-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	289	4305
1	765	3853
2	2559	3064
3	6702	3056

Stop Event

1×	node limit

Counts

99 → 116

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 7)) 1/9))))
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(.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4)) (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4))
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3))
(log.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2))))
(cbrt.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))
(log1p.f64 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))
(exp.f64 (.f64 3/2 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (fma.f64 -1 (log.f64 (/.f64 -1 n)) (log.f64 (*.f64 (PI.f64) -2)))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (-.f64 (log.f64 (*.f64 (PI.f64) -2)) (log.f64 (/.f64 -1 n)))) k))
(sqrt.f64 (/.f64 (/.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))
(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))
(pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(cbrt.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))))
(cbrt.f64 (pow.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k) 3/2))
(+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 7)) 1/9))))
(+.f64 (cbrt.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 7) 1/18) (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 7) 1/18)))))
(fma.f64 -1/2 (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) 7) 1/18) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) 7) 1/18) (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (cbrt.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) (log.f64 k)))))
(fma.f64 -1/2 (.f64 (pow.f64 (pow.f64 (pow.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k) 3/2) 7) 1/18) (.f64 (pow.f64 (pow.f64 (pow.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k) 3/2) 7) 1/18) (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (cbrt.f64 (pow.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k) 3/2)))
(+.f64 (.f64 1/3 (.f64 (.f64 (pow.f64 k 2) (-.f64 (.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (+.f64 (.f64 3/4 (+.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 9/8 (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2)))) (.f64 3/4 (.f64 (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 17)) 1/9) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))))) (pow.f64 (/.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)) 1/3))) (+.f64 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 1/3) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))) (pow.f64 (.f64 1 (pow.f64 (exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 7)) 1/9)))))
(fma.f64 1/3 (.f64 (.f64 (.f64 k k) (-.f64 (.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) (fma.f64 3/4 (.f64 0 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2)) (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 9/8))) (.f64 3/4 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 17) 1/18) (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 17) 1/18)))))) (cbrt.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 2)))) (+.f64 (cbrt.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))) 7) 1/18) (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 k) (log.f64 (.f64 2 (*.f64 (PI.f64) n))))) 7) 1/18))))))
(fma.f64 1/3 (.f64 (.f64 k k) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) 2))) (fma.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) (fma.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) 9/8 0) (.f64 (.f64 (pow.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) 2) -3/4) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) 17) 1/18) (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) 17) 1/18)))))) (fma.f64 -1/2 (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) 7) 1/18) (.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (log.f64 k))) 7) 1/18) (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))) (cbrt.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 (.f64 2 (*.f64 (PI.f64) n))) (log.f64 k))))))
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(.f64 (pow.f64 1 3/2) (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (pow.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) 3/2) (pow.f64 (/.f64 1 k) 3/2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 2)) 3/2) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3/2))
(.f64 (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3/2) (pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k)) 3/2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(.f64 (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4)) (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 1/4))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(log.f64 (exp.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(cbrt.f64 (pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2) 3))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(expm1.f64 (log1p.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(log1p.f64 (expm1.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(exp.f64 (.f64 3/2 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k)) k))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)
(exp.f64 (.f64 (.f64 3/2 (log.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 1))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))) 3) (pow.f64 k 3)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 1 k)) (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 3) (pow.f64 k 3)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k) 3/2)

eval509.0ms (4.9%)

Compiler: Compiled 24845 to 16893 computations (32% saved)

prune277.0ms (2.6%)

Pruning

32 alts after pruning (25 fresh and 7 done)

	Pruned	Kept	Total
New	1012	17	1029
Fresh	4	8	12
Picked	0	1	1
Done	0	6	6
Total	1016	32	1048

Error

Counts

1048 → 32

Alt Table

Click to see full alt table

Status	Error	Program
✓	19.7b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	41.3b	(pow.f64 (pow.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k) 3/2) 1/3)
	46.2b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/6)
▶	39.0b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
	37.2b	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
	37.5b	(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
	0.6b	(/.f64 (pow.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (*.f64 2 (-.f64 1 k))) (sqrt.f64 k))
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.5b	(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
▶	24.8b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	0.5b	(/.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (fma.f64 k 1/2 -1/2)))
	24.7b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	36.6b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
	12.4b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
✓	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 2 (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
▶	0.5b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	37.1b	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
✓	12.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	12.6b	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)) k))
	37.0b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
✓	14.6b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	37.2b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
▶	37.0b	(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
✓	37.0b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	37.0b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
	37.0b	(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
	14.5b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))
	38.7b	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
	18.3b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
	40.0b	(cbrt.f64 (pow.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k) 3/2))
	40.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))

Compiler

Compiled 801 to 657 computations (18% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 57 to 41 computations (28.1% saved)

series4.0ms (0%)

Counts

2 → 12

Calls

9 calls:

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

rewrite63.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

734×	`log-prod_binary64`
518×	`pow-unpow_binary64`
380×	`pow2_binary64`
262×	`pow1/3_binary64`
258×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	306	26
2	3861	25

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

simplify51.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-l_binary64`
490×	`associate-r_binary64`
314×	`log-prod_binary64`
287×	`exp-prod_binary64`
247×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1098
1	336	1041
2	1064	1005
3	5792	1005

Stop Event

1×	node limit

Counts

66 → 72

Calls

Call 1

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

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

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (PI.f64) (.f64 2 (/.f64 n k)))
✓	11.9b	(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))

Compiler

Compiled 29 to 14 computations (51.7% saved)

series5.0ms (0%)

Counts

2 → 24

Calls

12 calls:

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

rewrite49.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

946×	`pow1_binary64`
875×	`add-log-exp_binary64`
875×	`log1p-expm1-u_binary64`
875×	`expm1-log1p-u_binary64`
856×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	189	24
2	2375	24

Stop Event

1×	node limit

Counts

2 → 44

Calls

Call 1

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

Outputs

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

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

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-def_binary64`
494×	`log-prod_binary64`
352×	`unswap-sqr_binary64`
309×	`log-div_binary64`
271×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	924
1	231	864
2	887	804
3	4392	804

Stop Event

1×	node limit

Counts

68 → 52

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

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

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
✓	1.0b	(sqrt.f64 (*.f64 (PI.f64) 2))
✓	11.4b	(sqrt.f64 (/.f64 k n))

Compiler

Compiled 29 to 15 computations (48.3% saved)

series9.0ms (0.1%)

Counts

3 → 0

Calls

12 calls:

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

rewrite62.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

561×	`log-prod_binary64`
419×	`exp-prod_binary64`
314×	`pow-prod-down_binary64`
264×	`pow2_binary64`
189×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	213	26
2	2808	26

Stop Event

1×	node limit

Counts

3 → 136

Calls

Call 1

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

Outputs

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

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

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

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

568×	`associate-/r*_binary64`
446×	`fma-neg_binary64`
381×	`log-prod_binary64`
265×	`*-commutative_binary64`
231×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	1570
1	674	1520
2	1914	1508
3	6688	1508

Stop Event

1×	node limit

Counts

136 → 176

Calls

Call 1

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

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

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 2 (PI.f64)) (/.f64 n k))
✓	0.8b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
✓	15.1b	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6)

Compiler

Compiled 41 to 24 computations (41.5% saved)

series83.0ms (0.8%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
23.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6)
13.0ms	k	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6)
12.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6)
12.0ms	k	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6)
11.0ms	k	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6)

rewrite64.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

612×	`log-prod_binary64`
369×	`pow-prod-down_binary64`
314×	`pow2_binary64`
278×	`pow-unpow_binary64`
229×	`pow-to-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	268	38
2	3206	38

Stop Event

1×	node limit

Counts

3 → 97

Calls

Call 1

Inputs
(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
(.f64 (.f64 2 (PI.f64)) (/.f64 n k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18) (cbrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/6) (pow.f64 (/.f64 n k) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 n k) 1/6) (pow.f64 (*.f64 2 (PI.f64)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/6) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/6 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/6 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/12 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) 3/2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6) (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) (*.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18) (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))))) (#(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 2 (PI.f64)) 1/6) (*.f64 (pow.f64 (/.f64 n k) 1/6) (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 5/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/4) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 5/12) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) (cbrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) (pow.f64 (*.f64 2 (PI.f64)) 1/6)) (pow.f64 (/.f64 n k) 1/6))))) (#(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 2 (/.f64 (PI.f64) (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 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 2 (/.f64 (PI.f64) (/.f64 k n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 2) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18) 18)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12) 12)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/4) 4)))) (#(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 sqrt.f64 (*.f64 4 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/6 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 3))))))

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

438×	`fma-def_binary64`
393×	`distribute-rgt-in_binary64`
380×	`distribute-lft-in_binary64`
370×	`associate-*l/_binary64`
336×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	3013
1	655	2667
2	1894	2619

Stop Event

1×	node limit

Counts

169 → 185

Calls

Call 1

Inputs
(exp.f64 (.f64 1/6 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 3)
(pow.f64 (exp.f64 (.f64 1/6 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 3)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
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(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
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(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
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(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
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(.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 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))) 1)
(.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6) 1)
(.f64 1 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))
(.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18) (cbrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18))
(.f64 (pow.f64 (.f64 2 (PI.f64)) 1/6) (pow.f64 (/.f64 n k) 1/6))
(.f64 (pow.f64 (/.f64 n k) 1/6) (pow.f64 (.f64 2 (PI.f64)) 1/6))
(.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12))
(*.f64 (pow.f64 2 1/6) (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 1/6))
(sqrt.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(log.f64 (exp.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))))
(cbrt.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6)))
(exp.f64 (.f64 1/6 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(exp.f64 (.f64 (.f64 1/6 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/3))
(exp.f64 (.f64 (.f64 2 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/12))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18)) 3))
(exp.f64 (.f64 (.f64 1/12 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) 3/2))
(+.f64 0 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) 1)
(.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6) (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1)
(.f64 1 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) (.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18) (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
(.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 2 (PI.f64)) 1/6) (.f64 (pow.f64 (/.f64 n k) 1/6) (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 5/12))
(.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/4) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/4))
(.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 5/12) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12))
(.f64 (.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1) (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6))
(.f64 (.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) (cbrt.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))) (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18))
(.f64 (.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) (pow.f64 (.f64 2 (PI.f64)) 1/6)) (pow.f64 (/.f64 n k) 1/6))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(fabs.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))))
(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2)) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 3/2))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2))
(+.f64 0 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n))))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 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 2 (/.f64 (PI.f64) (/.f64 k n))) 1)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/6) 6)
(pow.f64 (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 2)
(pow.f64 (*.f64 4 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 2)) 1/2)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3) 1/3)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3/2) 2/3)
(pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 3)
(pow.f64 (pow.f64 (cbrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 2) 3/2)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/18) 18)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/12) 12)
(pow.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 1/4) 4)
(pow.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))) -1)
(sqrt.f64 (*.f64 4 (pow.f64 (/.f64 (PI.f64) (/.f64 k n)) 2)))
(log.f64 (pow.f64 (exp.f64 2) (/.f64 (PI.f64) (/.f64 k n))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))))
(cbrt.f64 (pow.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))) 3))
(expm1.f64 (log1p.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(log1p.f64 (expm1.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(exp.f64 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n)))))
(exp.f64 (.f64 (log.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n)))) 1))
(exp.f64 (.f64 (.f64 1/6 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 6))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 2))
(exp.f64 (.f64 (.f64 2 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/2))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 2 (/.f64 (PI.f64) (/.f64 k n))))) 3))

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

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.3b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))
✓	0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))

Compiler

Compiled 48 to 33 computations (31.3% saved)

series16.0ms (0.1%)

Counts

2 → 12

Calls

12 calls:

Time	Variable		Point	Expression
9.0ms	k	@	0	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))
1.0ms	n	@	0	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))
1.0ms	n	@	-inf	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))
1.0ms	n	@	0	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
1.0ms	n	@	inf	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))

rewrite65.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

656×	`log-prod_binary64`
392×	`pow-prod-down_binary64`
314×	`pow2_binary64`
250×	`pow-unpow_binary64`
219×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	258	28
2	3259	28

Stop Event

1×	node limit

Counts

2 → 97

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 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(*.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1 (neg.f64 (pow.f64 k 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/4) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) 1) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 k 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) 1) (sqrt.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 k 1/12) -2) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 k 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k -1/8) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/8)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 n) (pow.f64 k 1/8)) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 k 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 k 1/4) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) (pow.f64 k 3/4)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (pow.f64 k 1/4) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 (pow.f64 k 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 3/2) (pow.f64 k 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (sqrt.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 k 1/4) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))))) -1))))))

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/r*_binary64`
562×	`unswap-sqr_binary64`
471×	`associate-*l/_binary64`
402×	`fma-def_binary64`
381×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	2343
1	610	2262
2	2298	2173

Stop Event

1×	node limit

Counts

109 → 205

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 0 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 1)
(.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) (pow.f64 k -1/4))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k)) 1)
(.f64 1 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))
(.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)) (pow.f64 k -1/4)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))) (cbrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))
(.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (pow.f64 k -1/4)))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))
(.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) (/.f64 1 (neg.f64 (pow.f64 k 1/4))))
(.f64 (pow.f64 k -1/4) (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(.f64 (pow.f64 (pow.f64 k 1/12) -2) (/.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) (pow.f64 k 1/12)))
(.f64 (pow.f64 k -1/8) (/.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) (pow.f64 k 1/8)))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/8)) (pow.f64 k -3/8))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (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 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) 1) (pow.f64 k -1/2))
(.f64 (/.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 1) (/.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)) (pow.f64 k 1/4)))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) 1) (/.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (pow.f64 k 1/4)))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 k -1/4) (pow.f64 k 1/12)))
(.f64 (/.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (cbrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (pow.f64 k 1/12)))
(.f64 (/.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) (pow.f64 k 1/8)) (/.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)) (pow.f64 k 1/8)))
(pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 1)
(pow.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))) 2)
(pow.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) -1/2) (sqrt.f64 k)) -1)
(pow.f64 (/.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 3) (pow.f64 k 3/4)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) -1)
(pow.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) -1/2) (sqrt.f64 k)) 1) -1)
(neg.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) (neg.f64 (pow.f64 k 1/4))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 3) (pow.f64 k 3/4)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k))) 1))
(exp.f64 (.f64 (.f64 3 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))) 2))
(exp.f64 (.f64 (neg.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))) -1))
(+.f64 0 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))))) 1)
(.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/4))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 1)
(.f64 1 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)) (cbrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)))
(.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/6) (pow.f64 k -1/4)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 k -1/4)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k -1/4)))
(.f64 (neg.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n)))) (/.f64 1 (neg.f64 (pow.f64 k 1/4))))
(.f64 (pow.f64 k -1/4) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) 1) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/4)))
(.f64 (/.f64 (sqrt.f64 n) 1) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/4)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) 1) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))
(.f64 (pow.f64 (pow.f64 k 1/12) -2) (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/12)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)))
(.f64 (/.f64 (sqrt.f64 n) (cbrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/12)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/12)))
(.f64 (pow.f64 k -1/8) (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/8)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/8)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/8)))
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 k 1/8)) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/8)))
(pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 1)
(pow.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 3) 1/3)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)) 3)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) 2)
(pow.f64 (/.f64 (pow.f64 k 1/4) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) -1)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (pow.f64 k 3/4)) 1/3)
(pow.f64 (/.f64 (/.f64 (pow.f64 k 1/4) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) 1) -1)
(neg.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (pow.f64 k 1/4))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (pow.f64 k 3/4)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12))) 3))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8))) 2))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 k 1/4) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))) -1))

Outputs
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (/.f64 1 k) 1/4) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (pow.f64 (/.f64 1 k) 1/4) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))))
(.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 k) 1/4)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))))
(.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 k) 1/4)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))))
(.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 k) 1/4)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 1/4 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))))) (sqrt.f64 (.f64 n (PI.f64))))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k)))) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 k))))))
(.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2)) (.f64 (pow.f64 -1 1/4) (pow.f64 (/.f64 -1 k) 1/4)))
(+.f64 0 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64))))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64)))))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64)))))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)))) 1)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) (pow.f64 k -1/4))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) (sqrt.f64 k))) (pow.f64 k -1/4))
(.f64 (sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 n (PI.f64)))) (pow.f64 k -1/4))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n))) (pow.f64 k -1/4))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k)) 1)
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))
(.f64 1 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))
(.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)) (pow.f64 k -1/4)))
(.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k))) (/.f64 (.f64 (pow.f64 k -1/4) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6)) (pow.f64 k 1/12)))
(.f64 (cbrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64)))) (/.f64 (pow.f64 k -1/4) (/.f64 (pow.f64 k 1/12) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6))))
(.f64 (pow.f64 k -1/4) (.f64 (/.f64 (cbrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n))) (pow.f64 k 1/12)) (pow.f64 (.f64 n (*.f64 2 (PI.f64))) 1/6)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))) (cbrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k)))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64)))))) (cbrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))) (cbrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))) (cbrt.f64 (*.f64 (/.f64 2 (/.f64 k n)) (PI.f64))))
(.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64)))))) (cbrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64))))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))) (cbrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))) (cbrt.f64 (*.f64 (/.f64 2 (/.f64 k n)) (PI.f64))))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (pow.f64 k -1/4)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 k 1/8)) 2) (pow.f64 k -1/4))
(.f64 (pow.f64 k -1/4) (pow.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4) (pow.f64 k 1/8)) 2))
(.f64 (pow.f64 k -1/4) (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (pow.f64 k 1/4)))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k))) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))
(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)))
(sqrt.f64 (*.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))
(.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) (/.f64 1 (neg.f64 (pow.f64 k 1/4))))
(.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) (sqrt.f64 k)))) (/.f64 1 (neg.f64 (pow.f64 k 1/4))))
(.f64 1 (/.f64 (sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 n (PI.f64)))) (pow.f64 k 1/4)))
(/.f64 (sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n))) (pow.f64 k 1/4))
(.f64 (pow.f64 k -1/4) (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) (sqrt.f64 k))) (pow.f64 k -1/4))
(.f64 (sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 n (PI.f64)))) (pow.f64 k -1/4))
(.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n))) (pow.f64 k -1/4))
(.f64 (pow.f64 (pow.f64 k 1/12) -2) (/.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) (pow.f64 k 1/12)))
(.f64 (pow.f64 (pow.f64 k 1/12) -2) (/.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) (sqrt.f64 k))) (pow.f64 k 1/12)))
(.f64 (pow.f64 (pow.f64 k 1/12) -2) (/.f64 (sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 n (PI.f64)))) (pow.f64 k 1/12)))
(.f64 (pow.f64 (pow.f64 k 1/12) -2) (/.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n))) (pow.f64 k 1/12)))
(.f64 (pow.f64 k -1/8) (/.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) (pow.f64 k 1/8)))
(.f64 (pow.f64 k -1/8) (/.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) (sqrt.f64 k))) (pow.f64 k 1/8)))
(.f64 (pow.f64 k -1/8) (/.f64 (sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 n (PI.f64)))) (pow.f64 k 1/8)))
(.f64 (pow.f64 k -1/8) (/.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n))) (pow.f64 k 1/8)))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/8)) (pow.f64 k -3/8))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -3/8)) (pow.f64 k 1/8))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (pow.f64 k 1/8) (pow.f64 k -3/8)))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 (pow.f64 k 1/8) (pow.f64 k -3/8)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/4)))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6) (pow.f64 k 1/4)))
(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/6) (cbrt.f64 (.f64 n (*.f64 2 (PI.f64))))) (pow.f64 k 1/2))
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 k 1/4)) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/4)))
(/.f64 (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 2 (PI.f64)))) (pow.f64 k 1/2))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) 1) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/2))
(.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (pow.f64 k -1/2))
(.f64 (/.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 1) (/.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)) (pow.f64 k 1/4)))
(.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (.f64 (pow.f64 k 1/4) (pow.f64 k 1/12))))
(/.f64 (.f64 (cbrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6)) (.f64 (pow.f64 k 1/12) (pow.f64 k 1/4)))
(/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/6) (.f64 (pow.f64 k 1/4) (/.f64 (pow.f64 k 1/12) (cbrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n))))))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) 1) (/.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (pow.f64 k 1/4)))
(/.f64 (pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 k 1/8)) 2) (pow.f64 k 1/4))
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/2))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 k -1/4) (pow.f64 k 1/12)))
(.f64 (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 k -1/4) (pow.f64 k 1/12)))
(.f64 (/.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 k -1/4) (pow.f64 k 1/12)))
(.f64 (/.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) (cbrt.f64 (sqrt.f64 k))) (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 2 (/.f64 k (.f64 n (PI.f64)))))) (/.f64 (cbrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (PI.f64)) (/.f64 k n)))) (/.f64 (cbrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))) (/.f64 (cbrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (cbrt.f64 (sqrt.f64 k))) (/.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) (pow.f64 k 1/12)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 k 1/8))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (*.f64 (pow.f64 k 1/12) (pow.f64 k 1/8))))
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(.f64 (pow.f64 k -1/8) (/.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/8)))
(.f64 (pow.f64 k -1/8) (/.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/8)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k -1/8)) (pow.f64 k 1/8))
(.f64 (/.f64 (pow.f64 k -1/8) (pow.f64 k 1/8)) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))))
(.f64 (/.f64 (cbrt.f64 (.f64 2 (.f64 (PI.f64) n))) (pow.f64 k 1/8)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/8)))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6) (pow.f64 k 1/4)))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (/.f64 (cbrt.f64 (.f64 2 (*.f64 n (PI.f64)))) (pow.f64 k 1/4)))
(.f64 (cbrt.f64 (.f64 n (.f64 2 (PI.f64)))) (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) 1/6) (pow.f64 k 1/4)))
(.f64 (/.f64 (sqrt.f64 n) (pow.f64 k 1/8)) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/8)))
(.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 k 1/4)))
(pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 1)
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(pow.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)) 1/2)
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 3) 1/3)
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12)) 3)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (pow.f64 k 1/12)) 3)
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/6) (pow.f64 k 1/12)) 3)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8)) 2)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 k 1/8)) 2)
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))
(pow.f64 (/.f64 (pow.f64 k 1/4) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) -1)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 k 1/8)) 2)
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (pow.f64 k 3/4)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/4)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 k 3/4)))
(pow.f64 (/.f64 (/.f64 (pow.f64 k 1/4) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) 1) -1)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 k 1/8)) 2)
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))
(neg.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 (pow.f64 k 1/4))))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 k 1/8)) 2)
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))
(sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k))) 3))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 3/2) (pow.f64 k 3/4)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/4)))
(cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 3/2) (pow.f64 k 3/4)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)))))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)))) 1))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(exp.f64 (.f64 (log.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k))) 3)) 1/3))
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) (sqrt.f64 k)))
(sqrt.f64 (.f64 (/.f64 2 (sqrt.f64 k)) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 (sqrt.f64 k) n)))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/6) (pow.f64 k 1/12))) 3))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (pow.f64 k 1/12)) 3)
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) 1/6) (pow.f64 k 1/12)) 3)
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/4) (pow.f64 k 1/8))) 2))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 k 1/8)) 2)
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 k 1/4) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))) -1))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 k 1/8)) 2)
(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4))

eval396.0ms (3.8%)

Compiler: Compiled 14293 to 9281 computations (35.1% saved)

prune261.0ms (2.5%)

Pruning

47 alts after pruning (36 fresh and 11 done)

	Pruned	Kept	Total
New	829	23	852
Fresh	7	13	20
Picked	0	1	1
Done	1	10	11
Total	837	47	884

Error

Counts

884 → 47

Alt Table

Click to see full alt table

Status	Error	Program
✓	19.7b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	41.3b	(pow.f64 (pow.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)) 3/2) 1/3)
	41.3b	(pow.f64 (pow.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k) 3/2) 1/3)
	39.0b	(pow.f64 (pow.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k) 1/6) 3)
	39.0b	(pow.f64 (pow.f64 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n)) 1/6) 3)
	46.2b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/6)
✓	39.0b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
	37.2b	(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3/2)
	37.5b	(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
✓	0.5b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.5b	(/.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
✓	24.8b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
	24.7b	(/.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 n (.f64 2 (PI.f64))) -1/2))
	37.2b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 (/.f64 n k) -1/2))
	24.8b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 n)))
✓	36.6b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
	38.1b	(/.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (exp.f64 (.f64 (log.f64 (/.f64 k n)) 1/2)))
	24.7b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k))
	24.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
	24.7b	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) -1/2)))
	12.4b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)))))
	36.6b	(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 2 (PI.f64)) n))))
	38.3b	(-.f64 (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n)))) 1)
✓	0.5b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	24.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	37.2b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 (PI.f64) 2)))
	37.1b	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
	24.7b	(.f64 (sqrt.f64 (.f64 n (*.f64 2 (PI.f64)))) (pow.f64 k -1/2))
	37.1b	(.f64 (sqrt.f64 (.f64 2 (/.f64 n k))) (sqrt.f64 (PI.f64)))
	37.1b	(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))))
	15.5b	(.f64 (cbrt.f64 (/.f64 (pow.f64 k -1/2) k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	12.8b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	12.6b	(sqrt.f64 (/.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) k)) k))
	37.0b	(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) 2) n) k))
✓	14.6b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	37.0b	(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
	37.6b	(sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1))
	37.2b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
	37.0b	(sqrt.f64 (*.f64 (/.f64 2 (/.f64 k n)) (PI.f64)))
✓	37.0b	(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
	37.3b	(sqrt.f64 (*.f64 n (/.f64 2 (/.f64 k (PI.f64)))))
✓	37.0b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	37.0b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
	14.5b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 2)) (-.f64 1 k)) k)) 1/2))
	38.7b	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
	18.3b	(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1 k)) k) 3/2))
	40.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))

Compiler

Compiled 619 to 510 computations (17.6% saved)

regimes199.0ms (1.9%)

Counts

79 → 1

Calls

Call 1

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

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

Calls

5 calls:

43.0ms	(.f64 (.f64 2 (PI.f64)) n)
39.0ms	(.f64 (.f64 2 (PI.f64)) n)
34.0ms	n
34.0ms	k
18.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

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

Compiler

Compiled 1068 to 711 computations (33.4% saved)

regimes245.0ms (2.3%)

Counts

75 → 1

Calls

Call 1

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

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:

68.0ms	(.f64 (.f64 2 (PI.f64)) n)
67.0ms	n
33.0ms	k
32.0ms	(.f64 (.f64 2 (PI.f64)) n)
16.0ms	(.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 994 to 663 computations (33.3% saved)

regimes211.0ms (2%)

Counts

74 → 1

Calls

Call 1

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

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

Calls

5 calls:

46.0ms	(.f64 (.f64 2 (PI.f64)) n)
43.0ms	n
42.0ms	(.f64 (.f64 2 (PI.f64)) n)
37.0ms	k
14.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.5b	1	`k`
0.5b	1	`n`
0.5b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 975 to 651 computations (33.2% saved)

regimes181.0ms (1.7%)

Counts

47 → 1

Calls

Call 1

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

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

Calls

5 calls:

56.0ms	n
41.0ms	k
37.0ms	(.f64 (.f64 2 (PI.f64)) n)
24.0ms	(.f64 (.f64 2 (PI.f64)) n)
11.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Results

Error	Segments	Branch
0.5b	1	`k`
0.5b	1	`n`
0.5b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`
0.5b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 544 to 355 computations (34.7% saved)

regimes284.0ms (2.7%)

Counts

39 → 2

Calls

Call 1

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

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

Calls

3 calls:

133.0ms	n
63.0ms	(.f64 (.f64 2 (PI.f64)) n)
48.0ms	k

Results

Error	Segments	Branch
0.5b	2	`k`
10.0b	3	`n`
10.0b	3	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 414 to 267 computations (35.5% saved)

bsearch26.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
25.0ms	7.862776698372485e-71	8.158264318748108e-65

Results

23.0ms

144×

body

256

valid

Compiler

Compiled 266 to 217 computations (18.4% saved)

regimes230.0ms (2.2%)

Counts

34 → 2

Calls

Call 1

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

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

Calls

3 calls:

105.0ms	(.f64 (.f64 2 (PI.f64)) n)
86.0ms	n
29.0ms	k

Results

Error	Segments	Branch
14.6b	2	`k`
18.4b	3	`n`
18.4b	3	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 350 to 224 computations (36% saved)

bsearch21.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
21.0ms	2.449659951471838e+33	8.929958323563444e+33

Results

13.0ms	80×	body	256	valid
7.0ms	45×	body	256	infinite

Compiler

Compiled 158 to 134 computations (15.2% saved)

regimes81.0ms (0.8%)

Counts

17 → 2

Calls

Call 1

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

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

Calls

3 calls:

41.0ms	n
18.0ms	k
17.0ms	(.f64 (.f64 2 (PI.f64)) n)

Results

Error	Segments	Branch
26.5b	2	`k`
26.9b	2	`n`
26.9b	2	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 173 to 112 computations (35.3% saved)

bsearch5.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
5.0ms	0.20374400760127842	25679.577174824975

Results

2.0ms	16×	body	256	valid
2.0ms	13×	body	256	infinite

Compiler

Compiled 51 to 43 computations (15.7% saved)

regimes24.0ms (0.2%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	(.f64 (.f64 2 (PI.f64)) n)
7.0ms	k
6.0ms	n

Results

Error	Segments	Branch
36.6b	1	`k`
36.6b	1	`n`
36.6b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 113 to 77 computations (31.9% saved)

regimes28.0ms (0.3%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

21.0ms	k
5.0ms	n

Results

Error	Segments	Branch
37.0b	1	`k`
37.0b	1	`n`

Compiler

Compiled 72 to 46 computations (36.1% saved)

regimes11.0ms (0.1%)

Accuracy

Total -0.3b remaining (-0.9%)

Threshold costs -0.3b (-0.9%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	n
4.0ms	k

Results

Error	Segments	Branch
37.0b	1	`k`
37.0b	1	`n`

Compiler

Compiled 56 to 36 computations (35.7% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-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	61	268
1	81	268
2	89	268
3	93	268
4	95	268

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 1/2 k))) (sqrt.f64 k))
(/.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 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 4742843975160471/59285549689505892056868344324448208820874232148807968788202283012051522375647232) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 2699999999999999910699198895357952) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(if (<=.f64 k 3602879701896397/9007199254740992) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 2 (PI.f64)) n)))) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 2 (PI.f64)) n))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Outputs
(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (*.f64 1/2 k))) (sqrt.f64 k))
(/.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 (sqrt.f64 (.f64 (.f64 2 n) (PI.f64))) (-.f64 1 k)) (sqrt.f64 k))
(/.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (-.f64 1 k)) (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 n (PI.f64))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 4742843975160471/59285549689505892056868344324448208820874232148807968788202283012051522375647232) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 2699999999999999910699198895357952) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(if (<=.f64 k 2699999999999999910699198895357952) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (+.f64 (+.f64 1 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))) -1)))
(if (<=.f64 k 3602879701896397/9007199254740992) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 2 (PI.f64)) n)))) (sqrt.f64 (-.f64 (+.f64 1 (/.f64 (*.f64 (PI.f64) 2) (/.f64 k n))) 1)))
(if (<=.f64 k 3602879701896397/9007199254740992) (/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64)))))) (sqrt.f64 (+.f64 (+.f64 1 (/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))) -1)))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 (.f64 2 (PI.f64)) n))))
(/.f64 1 (sqrt.f64 (/.f64 k (.f64 n (.f64 2 (PI.f64))))))
(sqrt.f64 (/.f64 (.f64 n (.f64 2 (PI.f64))) k))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Compiler

Compiled 187 to 146 computations (21.9% saved)

soundness137.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

732×	`fma-def_binary64`
667×	`associate-/l*_binary64`
561×	`associate-/r*_binary64`
539×	`distribute-rgt-in_binary64`
524×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	68	22
3	141	22
4	360	22
5	983	20
6	2213	20
7	5663	20
0	290	3006
1	668	2738
2	2308	2687

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 306 to 252 computations (17.6% saved)

end127.0ms (1.2%)

Compiler: Compiled 169 to 112 computations (33.7% saved)