Details

analyze108.0ms (1.1%)

Algorithm

1×

Search

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample2.5s (26.6%)

Results

1.2s	8256×	body	256	valid
709.0ms	1351×	body	1024	invalid
218.0ms	689×	body	512	invalid
195.0ms	1630×	body	256	invalid
88.0ms	520×	body	256	infinite
54.0ms	230×	body	256	unsamplable

Bogosity

preprocess54.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 20 to 17 computations (15% saved)

simplify38.0ms (0.4%)

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

0.6b

Counts

8 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.6b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize26.0ms (0.3%)

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))
✓	0.5b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 56 to 38 computations (32.1% saved)

series63.0ms (0.7%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
25.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
18.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
8.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
2.0ms	k	@	0	(/.f64 1 (sqrt.f64 k))
2.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite68.0ms (0.7%)

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))))))

simplify86.0ms (0.9%)

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))

localize23.0ms (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)
✓	0.5b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))

Compiler

Compiled 50 to 30 computations (40% saved)

series8.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

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

rewrite62.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 92

Calls

Call 1

Inputs
(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 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 (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))

eval137.0ms (1.4%)

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

prune76.0ms (0.8%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	326	20	346
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	326	22	348

Error

0.0b

Counts

348 → 22

Alt Table

Click to see full alt table

Status	Error	Program
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
	11.0b	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))) 3)
▶	0.7b	(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.6b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	3.5b	(/.f64 (pow.f64 (.f64 2 (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
▶	0.6b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
▶	0.5b	(/.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))
	20.6b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
	0.9b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)))))
	0.8b	(.f64 (pow.f64 (pow.f64 (sqrt.f64 k) -1/2) 2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.7b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	1.0b	(.f64 (/.f64 (cbrt.f64 (pow.f64 k -1/2)) (cbrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	0.7b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (exp.f64 1/2) (.f64 (-.f64 1 k) (log.f64 (.f64 n (.f64 2 (PI.f64)))))))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 1/2 k))))
▶	20.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	3.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))))
	0.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	3.7b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	10.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	12.8b	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k)) k))))

Compiler

Compiled 766 to 632 computations (17.5% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 70 to 46 computations (34.3% saved)

series19.0ms (0.2%)

Counts

4 → 36

Calls

18 calls:

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

rewrite73.0ms (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	61
1	302	52
2	4000	52

Stop Event

1×	node limit

Counts

4 → 126

Calls

Call 1

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

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

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-def_binary64`
525×	`associate-*l/_binary64`
438×	`associate-*r/_binary64`
436×	`associate-/r*_binary64`
256×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	348	3213
1	792	2872
2	2902	2763

Stop Event

1×	node limit

Counts

162 → 215

Calls

Call 1

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

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

localize21.0ms (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	(pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	9.7b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))

Compiler

Compiled 50 to 33 computations (34% saved)

series14.0ms (0.2%)

Counts

3 → 60

Calls

18 calls:

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

rewrite66.0ms (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)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 n (PI.f64))
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
✓	0.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))

Compiler

Compiled 41 to 21 computations (48.8% saved)

series7.0ms (0.1%)

Counts

3 → 0

Calls

12 calls:

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

rewrite57.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 85

Calls

Call 1

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

Outputs

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

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

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

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

85 → 104

Calls

Call 1

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

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

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))
✓	0.2b	(/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2))))
✓	0.3b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
✓	0.7b	(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))

Compiler

Compiled 66 to 46 computations (30.3% saved)

series83.0ms (0.9%)

Counts

4 → 60

Calls

21 calls:

Time	Variable		Point	Expression
33.0ms	n	@	0	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
21.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
9.0ms	n	@	inf	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
5.0ms	k	@	0	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
2.0ms	n	@	0	(/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2))))

rewrite79.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 140

Calls

Call 1

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

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

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

200 → 249

Calls

Call 1

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

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

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
	0.2b	(*.f64 (PI.f64) n)
✓	0.5b	(pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 (PI.f64) n)) 2)) (-.f64 1/2 (/.f64 k 2)))
✓	0.5b	(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)

Compiler

Compiled 69 to 39 computations (43.5% saved)

series23.0ms (0.2%)

Counts

3 → 36

Calls

15 calls:

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

rewrite72.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

785×	`log-prod_binary64`
399×	`pow2_binary64`
272×	`pow1/3_binary64`
271×	`expm1-udef_binary64`
271×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	339	44
2	4128	40

Stop Event

1×	node limit

Counts

3 → 104

Calls

Call 1

Inputs

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

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

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 2 (fma.f64 k -1/2 1/2)))) (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 1/2 k))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 2 (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))) (sqrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 (fma.f64 k -1/2 1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) n) 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)) (pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (fma.f64 k -1/2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 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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simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
646×	`distribute-rgt-in_binary64`
630×	`distribute-lft-in_binary64`
433×	`unswap-sqr_binary64`
380×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	3235
1	766	2816
2	2424	2765

Stop Event

1×	node limit

Counts

140 → 191

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

eval716.0ms (7.5%)

Compiler: Compiled 23740 to 15747 computations (33.7% saved)

prune245.0ms (2.6%)

Pruning

25 alts after pruning (21 fresh and 4 done)

	Pruned	Kept	Total
New	1052	18	1070
Fresh	12	3	15
Picked	1	0	1
Done	2	4	6
Total	1067	25	1092

Error

Counts

1092 → 25

Alt Table

Click to see full alt table

Status	Error	Program
	21.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
✓	0.6b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.6b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
▶	0.5b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2)))))
	20.7b	(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	0.9b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
	20.8b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
	10.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.7b	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
▶	20.5b	(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))
	20.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4) 2))
✓	20.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
▶	20.8b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
	23.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 1/2)))
	0.7b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
✓	10.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 n (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k))) (*.f64 k (pow.f64 n k))))
	12.7b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	30.4b	(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
	30.4b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
	30.4b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
▶	30.4b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	12.8b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))

Compiler

Compiled 702 to 576 computations (17.9% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2)))
✓	0.2b	(/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2))))
✓	0.3b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2)))))
	0.7b	(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))

Compiler

Compiled 80 to 50 computations (37.5% saved)

series25.0ms (0.3%)

Counts

3 → 12

Calls

18 calls:

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

rewrite74.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

324×	`expm1-udef_binary64`
324×	`log1p-udef_binary64`
311×	`log-pow_binary64`
259×	`prod-diff_binary64`
238×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	62
1	404	56
2	5609	48

Stop Event

1×	node limit

Counts

3 → 107

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

583×	`associate-/r/_binary64`
341×	`distribute-rgt-in_binary64`
335×	`distribute-lft-in_binary64`
239×	`associate-r_binary64`
204×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	2787
1	738	2700
2	3207	2567

Stop Event

1×	node limit

Counts

119 → 181

Calls

Call 1

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

Outputs
(sqrt.f64 n)
(+.f64 (.f64 -1/2 (.f64 (*.f64 k (log.f64 n)) (sqrt.f64 n))) (sqrt.f64 n))
(fma.f64 -1/2 (.f64 (sqrt.f64 n) (.f64 k (log.f64 n))) (sqrt.f64 n))
(.f64 (fma.f64 (log.f64 n) (.f64 -1/2 k) 1) (sqrt.f64 n))
(+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (.f64 1/8 (.f64 (.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n)))
(fma.f64 -1/2 (.f64 (sqrt.f64 n) (.f64 k (log.f64 n))) (fma.f64 1/8 (.f64 (sqrt.f64 n) (.f64 (*.f64 k k) (pow.f64 (log.f64 n) 2))) (sqrt.f64 n)))
(+.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (+.f64 (.f64 -1/2 (.f64 k (log.f64 n))) (.f64 1/8 (.f64 k (.f64 k (pow.f64 (log.f64 n) 2)))))))
(.f64 (sqrt.f64 n) (+.f64 (.f64 (log.f64 n) (.f64 -1/2 k)) (fma.f64 (.f64 1/8 (*.f64 k k)) (pow.f64 (log.f64 n) 2) 1)))
(+.f64 (.f64 -1/48 (.f64 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3)) (sqrt.f64 n))) (+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 n))) (+.f64 (.f64 1/8 (.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 n))) (sqrt.f64 n))))
(fma.f64 -1/48 (.f64 (sqrt.f64 n) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3))) (fma.f64 -1/2 (.f64 (sqrt.f64 n) (.f64 k (log.f64 n))) (fma.f64 1/8 (.f64 (sqrt.f64 n) (.f64 (*.f64 k k) (pow.f64 (log.f64 n) 2))) (sqrt.f64 n))))
(+.f64 (.f64 (+.f64 (.f64 1/8 (.f64 k (.f64 k (pow.f64 (log.f64 n) 2)))) 1) (sqrt.f64 n)) (.f64 (sqrt.f64 n) (+.f64 (.f64 (.f64 -1/48 (pow.f64 k 3)) (pow.f64 (log.f64 n) 3)) (.f64 -1/2 (*.f64 k (log.f64 n))))))
(fma.f64 (sqrt.f64 n) (fma.f64 -1/48 (.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3)) (.f64 (log.f64 n) (.f64 -1/2 k))) (.f64 (fma.f64 (.f64 1/8 (.f64 k k)) (pow.f64 (log.f64 n) 2) 1) (sqrt.f64 n)))
(.f64 (sqrt.f64 n) (exp.f64 (.f64 -1/2 (*.f64 k (log.f64 n)))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 -1/2) (.f64 k (log.f64 n))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 (.f64 k (log.f64 n))) -1/2))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 -1/2 k)))
(.f64 (sqrt.f64 n) (exp.f64 (.f64 -1/2 (*.f64 k (log.f64 n)))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 -1/2) (.f64 k (log.f64 n))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 (.f64 k (log.f64 n))) -1/2))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 -1/2 k)))
(.f64 (sqrt.f64 n) (exp.f64 (.f64 -1/2 (*.f64 k (log.f64 n)))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 -1/2) (.f64 k (log.f64 n))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 (.f64 k (log.f64 n))) -1/2))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 -1/2 k)))
(.f64 (sqrt.f64 n) (exp.f64 (.f64 -1/2 (*.f64 k (log.f64 n)))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 -1/2) (.f64 k (log.f64 n))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 (.f64 k (log.f64 n))) -1/2))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 -1/2 k)))
(.f64 (sqrt.f64 n) (exp.f64 (.f64 -1/2 (*.f64 k (log.f64 n)))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 -1/2) (.f64 k (log.f64 n))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 (.f64 k (log.f64 n))) -1/2))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 -1/2 k)))
(.f64 (sqrt.f64 n) (exp.f64 (.f64 -1/2 (*.f64 k (log.f64 n)))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 -1/2) (.f64 k (log.f64 n))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 (.f64 k (log.f64 n))) -1/2))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 -1/2 k)))
(.f64 (sqrt.f64 n) (exp.f64 (.f64 -1/2 (*.f64 k (log.f64 n)))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 -1/2) (.f64 k (log.f64 n))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 (.f64 k (log.f64 n))) -1/2))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 -1/2 k)))
(.f64 (sqrt.f64 n) (exp.f64 (.f64 -1/2 (*.f64 k (log.f64 n)))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 -1/2) (.f64 k (log.f64 n))))
(.f64 (sqrt.f64 n) (pow.f64 (exp.f64 (.f64 k (log.f64 n))) -1/2))
(.f64 (sqrt.f64 n) (pow.f64 n (.f64 -1/2 k)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k))))) 1)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 k 1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 k 1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 k))
(.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 k 1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k))) 1)
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 k 1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 k))
(.f64 1 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))
(/.f64 (exp.f64 (.f64 (fma.f64 k 1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 k))
(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 1/2 k 1/2))) (/.f64 k (.f64 n (pow.f64 (pow.f64 n k) -1))))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 1/2 k 1/2))) (/.f64 k (.f64 n (/.f64 1 (pow.f64 n k)))))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 1/2 k 1/2))) (.f64 (/.f64 (/.f64 k n) 1) (pow.f64 n k)))))
(.f64 (cbrt.f64 (/.f64 (exp.f64 (.f64 (fma.f64 k 1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k 1/2 1/2))) (.f64 (/.f64 k n) (pow.f64 n k)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 1/2 k 1/2))) (/.f64 k (.f64 n (pow.f64 (pow.f64 n k) -1))))) (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 1/2 k 1/2))) (/.f64 k (.f64 n (/.f64 1 (pow.f64 n k)))))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2)) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 1/2 k 1/2))) (.f64 (/.f64 (/.f64 k n) 1) (pow.f64 n k)))))
(.f64 (cbrt.f64 (/.f64 (exp.f64 (.f64 (fma.f64 k 1/2 1/2) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 2 (fma.f64 k 1/2 1/2))) (.f64 (/.f64 k n) (pow.f64 n k)))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2))) 2) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (PI.f64)) (fma.f64 1/2 k 1/2))) (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k))))
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(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(*.f64 (/.f64 (cbrt.f64 k) (sqrt.f64 (pow.f64 n (fma.f64 1/2 k 1/2)))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (sqrt.f64 (pow.f64 n (fma.f64 1/2 k 1/2)))))
(.f64 (cbrt.f64 k) (.f64 (/.f64 1 (pow.f64 n (fma.f64 1/2 k 1/2))) (cbrt.f64 (sqrt.f64 k))))
(*.f64 (cbrt.f64 k) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 1/2 k 1/2))))
(*.f64 (cbrt.f64 k) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 n (fma.f64 k 1/2 1/2))))
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2))) 1)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2))) 3) 1/3)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))) 3)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))) 2)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(pow.f64 (/.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) (sqrt.f64 k)) -1)
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(neg.f64 (/.f64 (sqrt.f64 k) (neg.f64 (pow.f64 n (fma.f64 1/2 k 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(sqrt.f64 (/.f64 k (*.f64 n (pow.f64 (pow.f64 n k) -1))))
(sqrt.f64 (/.f64 k (*.f64 n (/.f64 1 (pow.f64 n k)))))
(sqrt.f64 (*.f64 (/.f64 (/.f64 k n) 1) (pow.f64 n k)))
(sqrt.f64 (*.f64 (/.f64 k n) (pow.f64 n k)))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2))))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2))) 3))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) 3)))
(cbrt.f64 (/.f64 (pow.f64 k 3/2) (pow.f64 (pow.f64 n (fma.f64 k 1/2 1/2)) 3)))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))) 1))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 1/2 k 1/2)))
(/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k 1/2 1/2)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 n (fma.f64 1/2 k 1/2)))) 1)
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(pow.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) 1)
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(pow.f64 (pow.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) 3) 1/3)
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(pow.f64 (cbrt.f64 (pow.f64 n (fma.f64 1/2 k 1/2))) 3)
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(pow.f64 (sqrt.f64 (pow.f64 n (fma.f64 1/2 k 1/2))) 2)
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(sqrt.f64 (*.f64 n (pow.f64 (pow.f64 n k) -1)))
(sqrt.f64 (*.f64 n (/.f64 1 (pow.f64 n k))))
(sqrt.f64 (/.f64 n (pow.f64 n k)))
(log.f64 (exp.f64 (pow.f64 n (fma.f64 1/2 k 1/2))))
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 n (fma.f64 1/2 k 1/2)))))
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(cbrt.f64 (pow.f64 (pow.f64 n (fma.f64 1/2 k 1/2)) 3))
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(cbrt.f64 (*.f64 (pow.f64 n 3/2) (pow.f64 (pow.f64 (pow.f64 n k) -1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 n 3/2) (pow.f64 (pow.f64 (pow.f64 n k) -1/4) 6)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (pow.f64 n k) -1/2) 3) (pow.f64 n 3/2)))
(cbrt.f64 (*.f64 (pow.f64 n 3/2) (pow.f64 (pow.f64 (pow.f64 n k) -1/2) 3)))
(cbrt.f64 (*.f64 (pow.f64 n 3/2) (pow.f64 (pow.f64 (pow.f64 n k) -1/4) 6)))
(expm1.f64 (log1p.f64 (pow.f64 n (fma.f64 1/2 k 1/2))))
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(log1p.f64 (expm1.f64 (pow.f64 n (fma.f64 1/2 k 1/2))))
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(exp.f64 (*.f64 (fma.f64 1/2 k 1/2) (log.f64 n)))
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))
(exp.f64 (.f64 (.f64 (fma.f64 1/2 k 1/2) (log.f64 n)) 1))
(pow.f64 n (fma.f64 1/2 k 1/2))
(pow.f64 n (fma.f64 k 1/2 1/2))

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (PI.f64) (/.f64 k n))
✓	9.5b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Compiler

Compiled 29 to 11 computations (62.1% saved)

series7.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite53.0ms (0.6%)

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 (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

123 → 134

Calls

Call 1

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

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

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 38 to 20 computations (47.4% saved)

series4.0ms (0%)

Counts

2 → 0

Calls

9 calls:

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

rewrite53.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	240	23
2	2777	23

Stop Event

1×	node limit

Counts

2 → 77

Calls

Call 1

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

Outputs

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

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

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

623×	`times-frac_binary64`
567×	`associate-l_binary64`
515×	`associate-r_binary64`
359×	`associate-/l*_binary64`
322×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	184	1120
1	386	1081
2	1242	1081

Stop Event

1×	node limit

Counts

77 → 99

Calls

Call 1

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

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

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 32 to 16 computations (50% saved)

series6.0ms (0.1%)

Counts

3 → 0

Calls

12 calls:

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

rewrite56.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

550×	`log-prod_binary64`
400×	`exp-prod_binary64`
380×	`pow-prod-down_binary64`
274×	`pow2_binary64`
226×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	227	26
2	2753	26

Stop Event

1×	node limit

Counts

3 → 121

Calls

Call 1

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

Outputs

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

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

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

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

414×	`log-prod_binary64`
398×	`times-frac_binary64`
368×	`unswap-sqr_binary64`
354×	`associate-/l*_binary64`
318×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	1412
1	614	1344
2	1774	1317
3	7078	1317

Stop Event

1×	node limit

Counts

121 → 158

Calls

Call 1

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

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

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
	0.2b	(.f64 n (.f64 2 (PI.f64)))
✓	0.2b	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
✓	0.6b	(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))

Compiler

Compiled 67 to 44 computations (34.3% saved)

series19.0ms (0.2%)

Counts

3 → 48

Calls

18 calls:

Time	Variable		Point	Expression
5.0ms	k	@	-inf	(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
2.0ms	k	@	0	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
1.0ms	k	@	0	(sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))
1.0ms	k	@	-inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))
1.0ms	k	@	inf	(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k))))

rewrite67.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	307	54
2	4022	54

Stop Event

1×	node limit

Counts

3 → 124

Calls

Call 1

Inputs

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

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

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

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) 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simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

770×	`times-frac_binary64`
710×	`fma-def_binary64`
514×	`unswap-sqr_binary64`
228×	`log-prod_binary64`
222×	`sqr-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	377	4887
1	854	4189
2	3057	4161

Stop Event

1×	node limit

Counts

172 → 199

Calls

Call 1

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

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

eval330.0ms (3.5%)

Compiler: Compiled 18351 to 11684 computations (36.3% saved)

prune226.0ms (2.4%)

Pruning

38 alts after pruning (32 fresh and 6 done)

	Pruned	Kept	Total
New	918	22	940
Fresh	6	10	16
Picked	1	0	1
Done	2	6	8
Total	927	38	965

Error

Counts

965 → 38

Alt Table

Click to see full alt table

Status	Error	Program
	21.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	46.7b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/6)
	39.8b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
▶	30.5b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
	32.9b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
	10.2b	(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
	30.7b	(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
✓	0.6b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.6b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
	10.2b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 (*.f64 (/.f64 k n) (pow.f64 n k))))
	30.2b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
	20.7b	(/.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) 2))) (sqrt.f64 k))
▶	20.5b	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2)))
▶	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))))
	10.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	20.8b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
✓	20.5b	(.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 k)) (sqrt.f64 (.f64 n (PI.f64))))
▶	20.9b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/4) 2))
✓	20.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	23.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 1/2)))
	20.5b	(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
	30.4b	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 2))
	23.8b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
✓	10.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 n (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k))) (*.f64 k (pow.f64 n k))))
	12.7b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	30.4b	(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
	30.4b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
	30.3b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)))
▶	30.4b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
✓	30.4b	(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))
	30.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 1 k) (/.f64 (PI.f64) (/.f64 1 n)))))
	30.4b	(sqrt.f64 (.f64 2 (.f64 (neg.f64 (PI.f64)) (/.f64 1 (/.f64 (neg.f64 k) n)))))
	12.8b	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)) 1/2))
	32.6b	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2))
	38.2b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))

Compiler

Compiled 978 to 806 computations (17.6% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))))
✓	0.2b	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))))
	0.2b	(*.f64 (PI.f64) n)
	0.5b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))

Compiler

Compiled 67 to 41 computations (38.8% saved)

series13.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite67.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

833×	`log-prod_binary64`
285×	`expm1-udef_binary64`
285×	`log1p-udef_binary64`
265×	`pow3_binary64`
259×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	336	44
2	4412	40

Stop Event

1×	node limit

Counts

2 → 87

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 k) (*.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (/.f64 k (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 4) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 k (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) n) 2) 4) (fma.f64 k -1/2 1/2)))) (cbrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 k 1/4) (*.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 k)) (/.f64 1 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (neg.f64 (fma.f64 k -1/2 1/2))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 k) 1) (/.f64 (cbrt.f64 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 k 1/4) 1) (/.f64 (pow.f64 k 1/4) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 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simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

628×	`associate-/l*_binary64`
567×	`associate-*r/_binary64`
397×	`associate-/r*_binary64`
387×	`unswap-sqr_binary64`
339×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	3369
1	600	3122
2	2057	2790

Stop Event

1×	node limit

Counts

111 → 161

Calls

Call 1

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

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

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(*.f64 n (PI.f64))
✓	0.3b	(.f64 (/.f64 2 k) (.f64 n (PI.f64)))
✓	9.5b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))

Compiler

Compiled 27 to 14 computations (48.1% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

12 calls:

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

rewrite49.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

917×	`pow1_binary64`
849×	`add-log-exp_binary64`
849×	`log1p-expm1-u_binary64`
849×	`expm1-log1p-u_binary64`
830×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	190	24
2	2336	24

Stop Event

1×	node limit

Counts

2 → 49

Calls

Call 1

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

Outputs

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

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

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

717×	`log-div_binary64`
651×	`fma-def_binary64`
435×	`fma-neg_binary64`
376×	`times-frac_binary64`
358×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	1031
1	273	983
2	1009	937
3	5973	937

Stop Event

1×	node limit

Counts

73 → 66

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

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 29 to 15 computations (48.3% saved)

series6.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

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

rewrite51.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

538×	`log-prod_binary64`
395×	`exp-prod_binary64`
329×	`pow-prod-down_binary64`
258×	`pow2_binary64`
192×	`div-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	214	13
2	2736	13

Stop Event

1×	node limit

Counts

1 → 61

Calls

Call 1

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

Outputs

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

simplify51.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-*l/_binary64`
494×	`associate-/r/_binary64`
492×	`associate-*r/_binary64`
330×	`fma-def_binary64`
276×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	1145
1	418	1074
2	1054	1041
3	3247	1001

Stop Event

1×	node limit

Counts

61 → 92

Calls

Call 1

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

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

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 2 (PI.f64)) (/.f64 n k))
✓	0.5b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 2)
✓	9.7b	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)

Compiler

Compiled 40 to 23 computations (42.5% saved)

series117.0ms (1.2%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
53.0ms	n	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)
16.0ms	k	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)
13.0ms	n	@	0	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)
13.0ms	k	@	-inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)
8.0ms	n	@	inf	(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)

rewrite65.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

584×	`log-prod_binary64`
426×	`exp-prod_binary64`
356×	`pow-prod-down_binary64`
292×	`pow2_binary64`
252×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	243	38
2	2981	38

Stop Event

1×	node limit

Counts

3 → 113

Calls

Call 1

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

Outputs

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((#(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 (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 (*.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 (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)) 1/4) (pow.f64 (*.f64 (/.f64 n k) (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/8) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/8) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 5/6) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) (*.f64 2 (PI.f64))) 1/4) (pow.f64 (/.f64 n k) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.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 (*.f64 4 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))) 1/4))))) (#(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 (*.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 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 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 (*.f64 2 (PI.f64)) (/.f64 n k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (PI.f64)) (/.f64 k n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (PI.f64) n)) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1) k)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 2 (*.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 n) (*.f64 2 (PI.f64))) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (PI.f64)) (neg.f64 n)) (neg.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/4) 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/12) 12)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))) -1)))) (#(struct:change #<rule egg-rr> 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(*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 4 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 1) 4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1) 2))))))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-def_binary64`
661×	`times-frac_binary64`
509×	`unswap-sqr_binary64`
343×	`associate-/l*_binary64`
262×	`log-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	3420
1	728	3347
2	2316	2647

Stop Event

1×	node limit

Counts

185 → 178

Calls

Call 1

Inputs
(exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64)))))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (/.f64 (PI.f64) k)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 k)) (log.f64 (.f64 2 (.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (/.f64 -1 k)) (log.f64 (.f64 -2 (*.f64 n (PI.f64))))))) 2)
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(.f64 2 (/.f64 (.f64 n (PI.f64)) k))
(+.f64 0 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)))))
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(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4))) 1)
(.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 1)
(.f64 1 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/12) (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) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/12))
(.f64 (pow.f64 (.f64 2 (PI.f64)) 1/4) (pow.f64 (/.f64 n k) 1/4))
(.f64 (pow.f64 (/.f64 n k) 1/4) (pow.f64 (.f64 2 (PI.f64)) 1/4))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/8) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/8))
(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 1/4))
(sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(fabs.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4))
(log.f64 (exp.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4))))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/4))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)))
(exp.f64 (log.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 4 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))) 1/8))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/4)) 1/3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/12)) 3))
(exp.f64 (.f64 (.f64 1/8 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))) 2))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1) 1/4))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1/2) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.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))) 1/8) 2))
(+.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 (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 (*.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 (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)) 1/4) (pow.f64 (.f64 (/.f64 n k) (.f64 (*.f64 2 (PI.f64)) (/.f64 n k))) 1/4))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/8) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3/8))
(.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/8) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/8))
(.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 5/6) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/12))
(.f64 (pow.f64 (.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) (*.f64 2 (PI.f64))) 1/4) (pow.f64 (/.f64 n k) 1/4))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (sqrt.f64 k))
(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 (.f64 4 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))) 1/4))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/6)) 3))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 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 (.f64 2 (PI.f64)) (/.f64 n k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 2) (.f64 (PI.f64) (/.f64 n k))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))) 1)
(/.f64 (*.f64 2 (PI.f64)) (/.f64 k n))
(/.f64 1 (/.f64 k (.f64 2 (.f64 (PI.f64) n))))
(/.f64 (.f64 2 (.f64 (PI.f64) n)) k)
(/.f64 (neg.f64 (.f64 2 (.f64 (PI.f64) n))) (neg.f64 k))
(/.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) 1) k)
(/.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (pow.f64 (cbrt.f64 k) 2)) (cbrt.f64 k))
(/.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) (sqrt.f64 k)) (sqrt.f64 k))
(/.f64 (.f64 (neg.f64 n) (.f64 2 (PI.f64))) (neg.f64 k))
(/.f64 (.f64 (.f64 2 (PI.f64)) (neg.f64 n)) (neg.f64 k))
(pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) 4)
(pow.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 2/3)
(pow.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)) 1/2)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3) 1/3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/4) 4/3)
(pow.f64 (cbrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 3)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/12) 12)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 6)
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/8) 8)
(pow.f64 (exp.f64 1) (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 4) 1/4)
(pow.f64 (/.f64 k (.f64 2 (.f64 (PI.f64) n))) -1)
(pow.f64 (.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4) (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 1/12)) 3)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))) 2)) (cbrt.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))) (sqrt.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(sqrt.f64 (.f64 4 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) 2)))
(log.f64 (pow.f64 (exp.f64 2) (*.f64 (PI.f64) (/.f64 n k))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))))
(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3))
(expm1.f64 (log1p.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(log1p.f64 (expm1.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(exp.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))))
(exp.f64 (.f64 (log.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)) 1/4)) 4))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 2))
(exp.f64 (.f64 (log.f64 (.f64 4 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) 2))) 1/2))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (*.f64 2 (PI.f64)) (/.f64 n k)))) 3))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1) 1))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/4)) 1) 4))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k))) 1/2) 2))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)))) 1) 2))

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

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4)
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) 2)) 1/4) 2))
✓	0.5b	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/4) 2)

Compiler

Compiled 52 to 36 computations (30.8% saved)

series7.0ms (0.1%)

Counts

3 → 24

Calls

12 calls:

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

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

643×	`log-prod_binary64`
401×	`pow-prod-down_binary64`
328×	`pow2_binary64`
274×	`pow-unpow_binary64`
246×	`pow-to-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	294	34
2	3357	34

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.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 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 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/6) (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 n 1/4) (pow.f64 (*.f64 (*.f64 (PI.f64) 2) (*.f64 2 (*.f64 n (PI.f64)))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/8) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) 5/6) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 2 (*.f64 n (PI.f64))) n) 1/4) (pow.f64 (*.f64 (PI.f64) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))))) (#(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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) 1/6)) 3))))))

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

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

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

397×	`log-prod_binary64`
375×	`times-frac_binary64`
374×	`exp-prod_binary64`
356×	`unswap-sqr_binary64`
326×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	2203
1	505	1506
2	1550	1482
3	6535	1478

Stop Event

1×	node limit

Counts

113 → 143

Calls

Call 1

Inputs
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))) 2)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))
(+.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 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4))
(.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) 1)
(.f64 1 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (cbrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
(.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6))
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) 2)))
(.f64 (pow.f64 n 1/4) (pow.f64 (.f64 (.f64 (PI.f64) 2) (.f64 2 (*.f64 n (PI.f64)))) 1/4))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/8) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 3/8))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/8) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/8))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 2))
(.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 5/6) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/12))
(.f64 (pow.f64 (.f64 (.f64 2 (.f64 n (PI.f64))) n) 1/4) (pow.f64 (*.f64 (PI.f64) 2) 1/4))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(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))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 3/2)) 1/3))
(exp.f64 (.f64 (.f64 2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 1/4))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6)) 3))
(+.f64 0 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))
(/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))
(/.f64 (cbrt.f64 (.f64 2 (.f64 n (PI.f64)))) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (pow.f64 k 1/4)) (pow.f64 k 1/4))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) 1) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))) (cbrt.f64 k)) (pow.f64 k 1/6))
(/.f64 (.f64 -1 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))) -1) (neg.f64 (sqrt.f64 k)))
(pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 1)
(pow.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k) 1/2)
(pow.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3) 1/3)
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))) 2)
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)) 1/3)
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) -1)
(sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k)) 3))
(cbrt.f64 (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/2) (pow.f64 k 3/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (.f64 n (PI.f64))) k))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k))) 1))
(exp.f64 (.f64 (log.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sqrt.f64 (/.f64 (.f64 2 (*.f64 n (PI.f64))) k)))) 2))
(+.f64 0 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4))) 1)
(.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4) 1)
(.f64 1 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/4))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/12) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/6))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/6) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/12))
(.f64 (pow.f64 n 1/4) (pow.f64 (.f64 (PI.f64) 2) 1/4))
(.f64 (pow.f64 (.f64 (PI.f64) 2) 1/4) (pow.f64 n 1/4))
(.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/8) (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/8))
(.f64 (pow.f64 (.f64 n (PI.f64)) 1/4) (pow.f64 2 1/4))
(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
(fabs.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4))
(log.f64 (exp.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4))))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 3/4))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) 1/4)))
(exp.f64 (.f64 1/4 (log.f64 (.f64 2 (*.f64 n (PI.f64))))))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 1))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 (*.f64 n (PI.f64))))) 1/2))
(exp.f64 (.f64 (.f64 3/4 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 1/3))
(exp.f64 (.f64 (.f64 2 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 1/8))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 2 (*.f64 n (PI.f64))) 1/12)) 3))
(exp.f64 (.f64 (.f64 1/8 (log.f64 (.f64 2 (.f64 n (PI.f64))))) 2))

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

eval290.0ms (3%)

Compiler: Compiled 14604 to 9519 computations (34.8% saved)

prune198.0ms (2.1%)

Pruning

43 alts after pruning (36 fresh and 7 done)

	Pruned	Kept	Total
New	842	16	858
Fresh	7	20	27
Picked	1	0	1
Done	3	7	10
Total	853	43	896

Error

Counts

896 → 43

Alt Table

Click to see full alt table

Status	Error	Program
	21.1b	(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k) 3/2) 1/3)
	30.5b	(pow.f64 (pow.f64 (/.f64 (.f64 2 (.f64 (PI.f64) n)) k) 1/4) 2)
	32.9b	(pow.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) (/.f64 2 k)) 1/6) 3)
	39.8b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2) 1/3)
	32.9b	(pow.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 1/6) 3)
	39.8b	(pow.f64 (pow.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)) 3/2) 1/3)
	10.2b	(pow.f64 (/.f64 k (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1 k))) -1/2)
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 3)
	30.7b	(pow.f64 (cbrt.f64 (.f64 n (.f64 2 (/.f64 (PI.f64) k)))) 3/2)
✓	0.6b	(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
✓	0.6b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 k 1/2)))))
	10.2b	(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (sqrt.f64 (*.f64 (/.f64 k n) (pow.f64 n k))))
	20.6b	(/.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 (/.f64 k 2)))
	20.7b	(/.f64 (sqrt.f64 (/.f64 n (/.f64 1/2 (PI.f64)))) (sqrt.f64 k))
	30.2b	(/.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 k n)))
✓	20.5b	(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2)))
	23.7b	(/.f64 (exp.f64 (.f64 (.f64 3/2 (log.f64 (*.f64 n (PI.f64)))) 1/3)) (sqrt.f64 (/.f64 k 2)))
✓	0.7b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2)))))
	10.2b	(/.f64 1 (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)))))
	30.1b	(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
	32.5b	(-.f64 (+.f64 1 (sqrt.f64 (.f64 2 (/.f64 (.f64 n (PI.f64)) k)))) 1)
	1.3b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 k -1/2)) 3) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	20.8b	(.f64 (pow.f64 k -1/2) (sqrt.f64 (.f64 2 (*.f64 n (PI.f64)))))
✓	20.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	23.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (.f64 (log.f64 (.f64 n (.f64 (PI.f64) 2))) 1/2)))
	30.6b	(.f64 (sqrt.f64 (/.f64 n k)) (sqrt.f64 (.f64 2 (PI.f64))))
	20.5b	(.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64))))
	30.5b	(.f64 (sqrt.f64 (.f64 (/.f64 2 k) n)) (sqrt.f64 (PI.f64)))
	23.8b	(.f64 (exp.f64 (.f64 -1/2 (log.f64 k))) (sqrt.f64 (.f64 2 (.f64 n (PI.f64)))))
✓	10.5b	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (-.f64 1 k)) k))
	10.4b	(sqrt.f64 (/.f64 (.f64 n (pow.f64 (.f64 2 (PI.f64)) (-.f64 1 k))) (*.f64 k (pow.f64 n k))))
	12.7b	(sqrt.f64 (/.f64 (exp.f64 (.f64 (-.f64 1 k) (log.f64 (.f64 n (*.f64 2 (PI.f64)))))) k))
	30.4b	(sqrt.f64 (/.f64 2 (/.f64 k (*.f64 n (PI.f64)))))
	31.4b	(sqrt.f64 (-.f64 (+.f64 1 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 1))
	30.4b	(sqrt.f64 (.f64 (/.f64 (.f64 2 (PI.f64)) k) n))
	30.3b	(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)))
	30.4b	(sqrt.f64 (*.f64 (/.f64 2 (/.f64 k (PI.f64))) n))
✓	30.4b	(sqrt.f64 (.f64 (/.f64 2 k) (.f64 n (PI.f64))))
	32.4b	(sqrt.f64 (.f64 (/.f64 2 k) (exp.f64 (log.f64 (.f64 n (PI.f64))))))
	30.4b	(sqrt.f64 (*.f64 (PI.f64) (/.f64 2 (/.f64 k n))))
	30.4b	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 2 k))))
	32.6b	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 n (PI.f64)) (/.f64 2 k))) 1/2))
	38.2b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) (/.f64 n k)) 3/2))

Compiler

Compiled 584 to 481 computations (17.6% saved)

regimes144.0ms (1.5%)

Counts

78 → 1

Calls

Call 1

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

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

Calls

4 calls:

34.0ms	n
33.0ms	(.f64 (.f64 2 (PI.f64)) n)
33.0ms	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
0.5b	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)`

Compiler

Compiled 1028 to 667 computations (35.1% saved)

regimes146.0ms (1.5%)

Counts

75 → 1

Calls

Call 1

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

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

4 calls:

36.0ms	k
35.0ms	(.f64 (.f64 2 (PI.f64)) n)
33.0ms	n
19.0ms	(.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)`

Compiler

Compiled 975 to 632 computations (35.2% saved)

regimes263.0ms (2.8%)

Counts

73 → 1

Calls

Call 1

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

Outputs
(/.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)))))

Calls

4 calls:

155.0ms	(.f64 (.f64 2 (PI.f64)) n)
34.0ms	k
32.0ms	n
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
0.6b	1	`k`
0.6b	1	`n`
0.6b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.6b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 935 to 606 computations (35.2% saved)

regimes142.0ms (1.5%)

Counts

64 → 1

Calls

Call 1

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

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

Calls

4 calls:

48.0ms	k
29.0ms	(.f64 (.f64 2 (PI.f64)) n)
28.0ms	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
0.6b	1	`k`
0.6b	1	`n`
0.6b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.6b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 780 to 498 computations (36.2% saved)

regimes212.0ms (2.2%)

Counts

39 → 2

Calls

Call 1

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

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

Calls

2 calls:

125.0ms	n
51.0ms	k

Results

Error	Segments	Branch
0.7b	2	`k`
7.7b	5	`n`

Compiler

Compiled 401 to 249 computations (37.9% saved)

bsearch16.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	1.1700923593418915e-17	1.6980011332655785e-16

Results

15.0ms

96×

body

256

valid

Compiler

Compiled 191 to 157 computations (17.8% saved)

regimes118.0ms (1.2%)

Counts

37 → 2

Calls

Call 1

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

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

Calls

2 calls:

76.0ms	n
31.0ms	k

Results

Error	Segments	Branch
0.7b	2	`k`
8.0b	5	`n`

Compiler

Compiled 374 to 231 computations (38.2% saved)

bsearch17.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
17.0ms	1.1700923593418915e-17	1.6980011332655785e-16

Results

15.0ms

96×

body

256

valid

Compiler

Compiled 185 to 151 computations (18.4% saved)

regimes143.0ms (1.5%)

Counts

36 → 2

Calls

Call 1

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

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

Calls

2 calls:

88.0ms	n
45.0ms	k

Results

Error	Segments	Branch
11.6b	2	`k`
15.6b	3	`n`

Compiler

Compiled 362 to 223 computations (38.4% saved)

bsearch6.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
5.0ms	5339042.813884057	3521916392928.6167

Results

2.0ms	16×	body	256	valid
2.0ms	10×	body	256	infinite

Compiler

Compiled 50 to 42 computations (16% saved)

regimes98.0ms (1%)

Counts

18 → 2

Calls

Call 1

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

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

Calls

2 calls:

77.0ms	n
17.0ms	k

Results

Error	Segments	Branch
11.6b	2	`k`
15.6b	3	`n`

Compiler

Compiled 175 to 110 computations (37.1% saved)

bsearch20.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
20.0ms	5339042.813884057	3521916392928.6167

Results

17.0ms	10×	body	256	infinite
2.0ms	16×	body	256	valid

Compiler

Compiled 50 to 42 computations (16% saved)

regimes39.0ms (0.4%)

Counts

15 → 2

Calls

Call 1

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

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

Calls

2 calls:

20.0ms	n
15.0ms	k

Results

Error	Segments	Branch
21.1b	2	`k`
21.4b	2	`n`

Compiler

Compiled 148 to 95 computations (35.8% saved)

bsearch5.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
5.0ms	5339042.813884057	3521916392928.6167

Results

2.0ms	16×	body	256	valid
2.0ms	9×	body	256	infinite

Compiler

Compiled 51 to 43 computations (15.7% saved)

regimes17.0ms (0.2%)

Counts

11 → 1

Calls

Call 1

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

Calls

2 calls:

7.0ms	k
6.0ms	n

Results

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

Compiler

Compiled 106 to 69 computations (34.9% saved)

regimes13.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	n
5.0ms	k

Results

Error	Segments	Branch
30.3b	1	`k`
30.3b	1	`n`

Compiler

Compiled 72 to 45 computations (37.5% saved)

regimes10.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.4%)

Threshold costs -0.1b (-0.4%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	k
4.0ms	n

Results

Error	Segments	Branch
30.4b	1	`k`
30.4b	1	`n`

Compiler

Compiled 48 to 31 computations (35.4% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	361
1	105	361
2	120	361
3	126	361
4	129	361

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2)))))
(/.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 (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 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 2515018790852807/40564819207303340847894502572032) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2))) (pow.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 2758407706096627/81129638414606681695789005144064) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 10000000) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2))) (sqrt.f64 (-.f64 (+.f64 1 (.f64 2 (/.f64 (*.f64 n (PI.f64)) k))) 1)))
(if (<=.f64 k 10000000) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (-.f64 (+.f64 1 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 1)))
(if (<=.f64 k 10000000) (/.f64 1 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) (sqrt.f64 (-.f64 (+.f64 1 (.f64 2 (/.f64 (*.f64 n (PI.f64)) k))) 1)))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Outputs
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (sqrt.f64 k) (.f64 (sqrt.f64 n) (pow.f64 n (.f64 k -1/2)))))
(/.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 (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 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))) (/.f64 (sqrt.f64 k) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(if (<=.f64 k 2515018790852807/40564819207303340847894502572032) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2))) (pow.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 2515018790852807/40564819207303340847894502572032) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 k 2))) (pow.f64 (/.f64 k (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1 k))) -1/2))
(if (<=.f64 k 2758407706096627/81129638414606681695789005144064) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 2758407706096627/81129638414606681695789005144064) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 k 2))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 2 (PI.f64))) (-.f64 1 k)) k)))
(if (<=.f64 k 10000000) (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 k 2))) (sqrt.f64 (-.f64 (+.f64 1 (.f64 2 (/.f64 (*.f64 n (PI.f64)) k))) 1)))
(if (<=.f64 k 10000000) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 k 2))) (sqrt.f64 (+.f64 (+.f64 1 (.f64 2 (/.f64 (*.f64 (PI.f64) n) k))) -1)))
(if (<=.f64 k 10000000) (.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 (-.f64 (+.f64 1 (.f64 2 (/.f64 (.f64 n (PI.f64)) k))) 1)))
(if (<=.f64 k 10000000) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 2 k))) (sqrt.f64 (+.f64 (+.f64 1 (.f64 2 (/.f64 (.f64 (PI.f64) n) k))) -1)))
(if (<=.f64 k 10000000) (/.f64 1 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) (sqrt.f64 (-.f64 (+.f64 1 (.f64 2 (/.f64 (*.f64 n (PI.f64)) k))) 1)))
(if (<=.f64 k 10000000) (/.f64 1 (sqrt.f64 (.f64 (/.f64 k n) (/.f64 1/2 (PI.f64))))) (sqrt.f64 (+.f64 (+.f64 1 (.f64 2 (/.f64 (*.f64 (PI.f64) n) k))) -1)))
(/.f64 1 (sqrt.f64 (*.f64 (/.f64 k n) (/.f64 1/2 (PI.f64)))))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) 2)))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 2 (PI.f64))))
(sqrt.f64 (*.f64 2 (/.f64 (PI.f64) (/.f64 k n))))

Compiler

Compiled 251 to 193 computations (23.1% saved)

soundness0.0ms (0%)

end112.0ms (1.2%)

Compiler: Compiled 229 to 145 computations (36.7% saved)