Metrics for Migdal et al, Equation (51)

analyze105.0ms (0.8%)

Memory

-22.7MiB live, 224.5MiB allocated

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
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	51.5%	0%	7
52.5%	25%	22.6%	0.1%	0%	52.3%	0%	8
53.8%	25%	21.5%	0.1%	0%	53.5%	0%	9
54.5%	25%	20.9%	0.1%	0%	54%	0%	10
55.3%	25%	20.2%	0.1%	0%	54.7%	0%	11
55.7%	25%	19.9%	0.1%	0%	55.1%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.2s (23.6%)

Memory

58.2MiB live, 6 691.3MiB allocated

Samples

1.1s	5 533×	1	invalid
1.0s	8 256×	0	valid
125.0ms	469×	2	invalid
34.0ms	450×	0	invalid
27.0ms	225×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 1.8s

ival-pow: 590.0ms (32.1% of total)

ival-mult: 371.0ms (20.2% of total)

ival-div: 326.0ms (17.7% of total)

ival-pi: 161.0ms (8.8% of total)

ival-sqrt: 153.0ms (8.3% of total)

ival-sub: 107.0ms (5.8% of total)

adjust: 97.0ms (5.3% of total)

...in/eval/compile.rkt:110:19: 15.0ms (0.8% of total)

ival-true: 12.0ms (0.7% of total)

ival-assert: 6.0ms (0.3% of total)

Bogosity

preprocess133.0ms (1%)

Memory

1.1MiB live, 122.9MiB allocated

Algorithm

1×	egg-herbie

Rules

465×	`fma-define`
240×	`fmm-def`
123×	`associate-r`
80×	`associate-l`
74×	`sub-neg`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	39	438
1	96	380
2	211	380
3	410	364
4	686	352
5	1171	352
6	1433	352
7	1696	352
8	2015	352
9	2058	352
10	2086	352
11	2097	352
12	2099	352

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64)))))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 (-.f64 #s(literal 1 binary64) n) #s(literal 2 binary64))))

Outputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (neg.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal -2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal -2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 k))) (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 k)) #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (/.f64 (+.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (neg.f64 k))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (neg.f64 k))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (neg.f64 k))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (neg.f64 k))))
(neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))))
(.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 #s(literal -2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal -2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal -2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) (/.f64 (-.f64 #s(literal 1 binary64) n) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 n)) (pow.f64 (.f64 k (*.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 n #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 k (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 n #s(literal 2 binary64)))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (/.f64 n #s(literal -2 binary64)))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 n #s(literal -1/2 binary64)))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 k (.f64 #s(literal 2 binary64) (PI.f64))) (fma.f64 n #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 n))

explain153.0ms (1.1%)

Memory

6.0MiB live, 321.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
3	72	(4.5311094342093284e-181 1.7479758844725045e+117)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`k`
0	0	-	-	`n`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	-	`(PI.f64)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	sensitivity	75	35

Confusion

	Predicted +	Predicted -
+	3	0
-	72	181

Precision

0.04

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	3	0	0
-	72	35	146

Precision?

0.02727272727272727

Recall?

1.0

Freqs

test

number	freq
0	181
1	75

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

56.0ms

512×

valid

Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-pow: 10.0ms (27.7% of total)

ival-div: 9.0ms (25% of total)

ival-mult: 8.0ms (22.2% of total)

ival-sqrt: 4.0ms (11.1% of total)

ival-sub: 3.0ms (8.3% of total)

ival-pi: 2.0ms (5.5% of total)

ival-true: 1.0ms (2.8% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

eval1.0ms (0%)

Memory: 1.5MiB live, 1.5MiB allocated
Compiler: Compiled 59 to 23 computations (61% saved)

prune1.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Status

Accuracy

Program

▶

99.7%

(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))

▶

99.6%

(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify24.0ms (0.2%)

Memory

-14.7MiB live, 22.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 k #s(literal 2 binary64))
✓	cost-diff	(PI.f64)
✓	cost-diff	(*.f64 (PI.f64) n)
✓	cost-diff	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	(*.f64 #s(literal 2 binary64) (PI.f64))
✓	cost-diff	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	cost-diff	(sqrt.f64 k)
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Rules

16×	`sub-neg`
15×	`fma-define`
13×	`*-commutative`
8×	`+-commutative`
6×	`associate-r`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	359
1	45	347
2	65	347
3	86	347
4	106	323
5	129	323
6	156	323
7	184	323
8	192	323
9	193	323

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) k)
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(/.f64 k #s(literal 2 binary64))
k
(sqrt.f64 k)

Outputs
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
(*.f64 #s(literal 2 binary64) (PI.f64))
#s(literal 2 binary64)
(PI.f64)
n
(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) k)
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(pow.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 k #s(literal 2 binary64))
k
(sqrt.f64 k)

localize75.0ms (0.6%)

Memory

-10.0MiB live, 108.6MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	accuracy	99.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.8%	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓	accuracy	99.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	accuracy	99.6%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Samples

40.0ms

256×

valid

Compiler

Compiled 104 to 22 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-pow: 8.0ms (29.4% of total)

ival-mult: 7.0ms (25.7% of total)

ival-div: 6.0ms (22% of total)

ival-sub: 2.0ms (7.3% of total)

ival-sqrt: 2.0ms (7.3% of total)

ival-pi: 1.0ms (3.7% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series93.0ms (0.7%)

Memory

17.7MiB live, 134.8MiB allocated

Counts

12 → 160

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 k))>
#<alt (sqrt.f64 k)>
#<alt (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)>
#<alt (*.f64 #s(literal 2 binary64) (PI.f64))>
#<alt (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))>
#<alt (*.f64 (PI.f64) n)>
#<alt (PI.f64)>
#<alt (/.f64 k #s(literal 2 binary64))>
#<alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))>
#<alt (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))>
#<alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))>
#<alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))>

Outputs
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) k))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 n (PI.f64))>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (*.f64 #s(literal 1/2 binary64) k)>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1/48 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1/48 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))>
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#<alt (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
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#<alt (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k))))>
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#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k))))>
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#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k))))>
#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k))))>

Calls

42 calls:

Time	Variable		Point	Expression
33.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
20.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
11.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
7.0ms	n	@	0	(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
2.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite313.0ms (2.3%)

Memory

-7.7MiB live, 368.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 096×	`log1p-expm1-u`
523×	`expm1-log1p-u`
292×	`prod-diff`
148×	`add-exp-log`
148×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	274
1	427	270
2	4798	270

Stop Event

1×	node limit

Counts

12 → 299

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
(sqrt.f64 k)
(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
(*.f64 #s(literal 2 binary64) (PI.f64))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(PI.f64)
(/.f64 k #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))

Outputs
(-.f64 (exp.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(*.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) (cbrt.f64 (/.f64 #s(literal 1 binary64) k)))
(*.f64 (cbrt.f64 (/.f64 #s(literal 1 binary64) k)) (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 k) #s(literal -1 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(pow.f64 k #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal -1 binary64))
(pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (pow.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 k)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(log.f64 (exp.f64 (pow.f64 k #s(literal -1/2 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 k #s(literal -1/2 binary64)))))
(cbrt.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64))))
(log1p.f64 (expm1.f64 (pow.f64 k #s(literal -1/2 binary64))))
(exp.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 k)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 k))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 k))
(*.f64 (sqrt.f64 k) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 k))
(*.f64 (cbrt.f64 k) (cbrt.f64 (sqrt.f64 k)))
(*.f64 (cbrt.f64 k) (/.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal 1 binary64)))
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(*.f64 (pow.f64 k #s(literal 1/4 binary64)) (/.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 1 binary64)))
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(exp.f64 (log.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))) (pow.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) #s(literal 2 binary64)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))))
(log.f64 (exp.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
(exp.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)))

simplify234.0ms (1.8%)

Memory

24.6MiB live, 250.7MiB allocated

Algorithm

1×	egg-herbie

Rules

718×	`fma-define`
421×	`associate-r`
353×	`associate-l`
344×	`exp-prod`
253×	`distribute-lft-neg-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	600	19256
1	1218	17586
2	4112	16578

Stop Event

1×	node limit

Counts

459 → 408

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.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 n (PI.f64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 #s(literal 1/2 binary64) k)
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1/48 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))))
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(.f64 (pow.f64 n (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))) (pow.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))) #s(literal 2 binary64)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))))
(sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))))
(log.f64 (exp.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
(exp.f64 (.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)))) #s(literal 1 binary64)))

Outputs
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 k)
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 k)
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 k)
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 k)
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.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 n (PI.f64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) k)
(*.f64 k #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))))))) k)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) k))))) k)
(/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 (.f64 k (.f64 n (PI.f64))))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (.f64 n (PI.f64)))))) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))) #s(literal 1/8 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (fma.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))))) (.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 n (.f64 (PI.f64) k)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) k))))) k)
(/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1/48 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (sqrt.f64 (.f64 k (.f64 n (PI.f64))))) (.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (fma.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))) #s(literal 1/8 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 k (.f64 n (PI.f64)))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (fma.f64 k (fma.f64 #s(literal -1/48 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) (pow.f64 k #s(literal 3 binary64))))))) (.f64 (.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))) (.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 (.f64 n (.f64 (PI.f64) k)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) k))))) k)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (+.f64 #s(literal 1 binary64) k))))
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(exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
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eval63.0ms (0.5%)

Memory: -23.8MiB live, 89.9MiB allocated
Compiler: Compiled 9 568 to 1 524 computations (84.1% saved)

prune87.0ms (0.6%)

Memory

14.5MiB live, 135.9MiB allocated

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	443	16	459
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	443	18	461

Accuracy

100.0%

Counts

461 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
	74.9%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
✓	99.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	99.5%	(/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
	99.8%	(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
▶	99.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
	96.5%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
	99.6%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	99.5%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (sqrt.f64 k)))
	99.5%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))
✓	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
▶	47.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
▶	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
	96.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
	36.3%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	36.3%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	88.7%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Compiler

Compiled 642 to 451 computations (29.8% saved)

simplify60.0ms (0.4%)

Memory

13.5MiB live, 51.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))))
	cost-diff	0	(sqrt.f64 k)
	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
	cost-diff	0	(PI.f64)
	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	256	(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	cost-diff	0	(sqrt.f64 k)
	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 (PI.f64) k)
✓	cost-diff	0	(*.f64 n (/.f64 (PI.f64) k))
✓	cost-diff	0	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	0	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))

Rules

133×	`associate-r`
107×	`associate-l`
102×	`fma-define`
71×	`associate-*r/`
50×	`*-commutative`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	42	987
1	75	975
2	132	975
3	200	959
4	254	957
5	312	955
6	429	951
7	638	951
8	897	951
9	1014	951
10	1015	951

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
(sqrt.f64 k)
k
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (/.f64 (PI.f64) k))
n
(/.f64 (PI.f64) k)
(PI.f64)
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
n
(PI.f64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
#s(literal 1/4 binary64)
(pow.f64 k #s(literal 1/4 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

Outputs
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
(sqrt.f64 k)
k
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64)))
(*.f64 k #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
n
(/.f64 (PI.f64) k)
(PI.f64)
k
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) n))) (sqrt.f64 k))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 n (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) n))
(*.f64 n (PI.f64))
(*.f64 (PI.f64) n)
n
(PI.f64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) k))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) k)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))
(+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/4 binary64) k))
(fma.f64 #s(literal -1/4 binary64) k #s(literal 1/4 binary64))
(fma.f64 k #s(literal -1/4 binary64) #s(literal 1/4 binary64))
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
#s(literal 1/4 binary64)
(pow.f64 k #s(literal 1/4 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
#s(literal 1 binary64)
(sqrt.f64 k)
k
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))
(*.f64 k #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

localize150.0ms (1.1%)

Memory

3.0MiB live, 193.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
	accuracy	99.7%	(*.f64 (PI.f64) n)
	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
	accuracy	73.1%	(PI.f64)
	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
✓	accuracy	99.6%	(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
	accuracy	73.1%	(PI.f64)
	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	accuracy	73.1%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (PI.f64) k)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	88.8%	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
	accuracy	73.1%	(PI.f64)
✓	accuracy	99.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	accuracy	99.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
	accuracy	99.7%	(*.f64 (PI.f64) n)
	accuracy	73.1%	(PI.f64)

Samples

58.0ms	185×	0	valid
23.0ms	71×	0	exit

Compiler

Compiled 277 to 38 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-pow: 19.0ms (33.8% of total)

ival-mult: 17.0ms (30.3% of total)

ival-sqrt: 8.0ms (14.2% of total)

ival-div: 6.0ms (10.7% of total)

ival-pow2: 2.0ms (3.6% of total)

ival-pi: 1.0ms (1.8% of total)

ival-sub: 1.0ms (1.8% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series132.0ms (1%)

Memory

5.4MiB live, 202.9MiB allocated

Counts

13 → 244

Calls

Call 1

Inputs
#<alt (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))>
#<alt (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))>
#<alt (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))>
#<alt (*.f64 n (/.f64 (PI.f64) k))>
#<alt (/.f64 (PI.f64) k)>
#<alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))>
#<alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))>
#<alt (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))))>
#<alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))>

Outputs
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (+.f64 (.f64 #s(literal -1/16 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/48 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
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#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
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#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
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#<alt (/.f64 (*.f64 n (PI.f64)) k)>
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#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
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#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
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#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1/48 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64))>
#<alt (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) #s(literal 1/4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))) (.f64 #s(literal 1/32 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) #s(literal 1/4 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))))) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))) (.f64 k (+.f64 (.f64 #s(literal -1/384 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) #s(literal 1/4 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)))) (.f64 #s(literal 1/32 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))))))) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>

Calls

66 calls:

Time	Variable		Point	Expression
40.0ms	n	@	0	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
20.0ms	k	@	-inf	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
13.0ms	k	@	inf	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
7.0ms	k	@	inf	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
4.0ms	k	@	inf	(* (/ 1 (sqrt k)) (* (sqrt (* 2 (* (PI) n))) (pow (* 2 (* (PI) n)) (* k -1/2))))

rewrite134.0ms (1%)

Memory

11.5MiB live, 127.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

339×	`associate-r`
297×	`log1p-expm1-u`
297×	`expm1-log1p-u`
293×	`pow1`
289×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	506
1	724	442

Stop Event

1×	node limit

Counts

13 → 343

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
(*.f64 n (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))

Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) k)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k))))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))) k)))
(.f64 (cbrt.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(.f64 (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k)))) (sqrt.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) k)))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) n)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) k)))
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(pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (sqrt.f64 k)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (pow.f64 k #s(literal 1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 k #s(literal 1/4 binary64)))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(fabs.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(exp.f64 (log.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 1 binary64)))

simplify427.0ms (3.2%)

Memory

-25.1MiB live, 525.2MiB allocated

Algorithm

1×	egg-herbie

Rules

753×	`associate-l`
271×	`*-commutative`
259×	`associate-/l*`
252×	`associate-*r/`
252×	`exp-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	975	32765
1	2307	31401
2	6414	30892

Stop Event

1×	node limit

Counts

587 → 658

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (+.f64 (.f64 #s(literal -1/16 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/48 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
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(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/8 binary64)) (pow.f64 k #s(literal 1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 k #s(literal 1/4 binary64)))))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(fabs.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(exp.f64 (log.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 1 binary64)))

Outputs
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 n) (log.f64 (.f64 (PI.f64) #s(literal 2 binary64)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (exp.f64 k) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(neg.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(neg.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(neg.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(neg.f64 (.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (+.f64 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n))))))))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 k (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (pow.f64 (exp.f64 k) (-.f64 (log.f64 (.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n))))))) (neg.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))))) k)
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(pow.f64 (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 k #s(literal 1/4 binary64)) (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)))
(neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 k #s(literal 1/4 binary64)))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (neg.f64 (pow.f64 k #s(literal 1/4 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (neg.f64 (neg.f64 (pow.f64 k #s(literal 1/4 binary64)))))
(/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64)))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/2 binary64)) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(sqrt.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(fabs.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))
(fabs.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64))))
(fabs.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64))))
(fabs.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64))))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)))) (pow.f64 k #s(literal -1/4 binary64))))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))))))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64))) #s(literal 3 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(exp.f64 (log.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/4 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/4 binary64)))

eval157.0ms (1.2%)

Memory: 37.3MiB live, 261.6MiB allocated
Compiler: Compiled 26 216 to 3 550 computations (86.5% saved)

prune262.0ms (2%)

Memory

16.6MiB live, 332.2MiB allocated

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	1 165	13	1 178
Fresh	8	3	11
Picked	4	1	5
Done	2	0	2
Total	1 179	17	1 196

Accuracy

100.0%

Counts

1 196 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	36.2%	(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
▶	36.2%	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	99.5%	(/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
	99.6%	(/.f64 (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))) (pow.f64 k #s(literal 1/4 binary64)))
▶	47.4%	(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
	47.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
▶	99.6%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	47.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
▶	47.2%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	36.3%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
	36.3%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
✓	36.3%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	36.3%	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
	88.7%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	36.4%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
▶	36.4%	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
	75.6%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))

Compiler

Compiled 457 to 357 computations (21.9% saved)

simplify18.0ms (0.1%)

Memory

-22.9MiB live, 21.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
	cost-diff	0	(/.f64 (PI.f64) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 (PI.f64) k))
✓	cost-diff	0	(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
✓	cost-diff	0	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	cost-diff	0	(/.f64 (PI.f64) k)
✓	cost-diff	0	(.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))
✓	cost-diff	0	(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))
✓	cost-diff	6528	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (PI.f64) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
✓	cost-diff	0	(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
✓	cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
	cost-diff	0	(PI.f64)
	cost-diff	0	(/.f64 (PI.f64) k)
✓	cost-diff	0	(.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
✓	cost-diff	0	(*.f64 k #s(literal -1/2 binary64))
	cost-diff	0	(PI.f64)
	cost-diff	0	(*.f64 (PI.f64) n)
	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))

Rules

21×	`*-commutative`
15×	`associate-l`
12×	`associate-r`
9×	`associate-/l*`
3×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	616
1	58	604
2	87	604
3	102	604
4	114	604

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(pow.f64 k #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))
(/.f64 (PI.f64) k)
(PI.f64)
k
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
n
(sqrt.f64 k)
k
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))
(.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))
(/.f64 (PI.f64) k)
(PI.f64)
k
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(PI.f64)
k
(sqrt.f64 n)
n
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
#s(literal 2 binary64)
(*.f64 (PI.f64) n)
(PI.f64)
n
(+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(*.f64 k #s(literal -1/2 binary64))
k
#s(literal -1/2 binary64)
(pow.f64 k #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
(.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))
(.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))
(.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))
(/.f64 (PI.f64) k)
(PI.f64)
k
(*.f64 n #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) n)
n
#s(literal 2 binary64)
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
(*.f64 (PI.f64) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (PI.f64))
(PI.f64)
#s(literal 2 binary64)
n
(sqrt.f64 k)
k
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n)) #s(literal 1/4 binary64))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k))) #s(literal 1/4 binary64))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 1/4 binary64))
(.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))
(.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))
(.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k)))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))
(/.f64 (PI.f64) k)
(PI.f64)
k
(*.f64 n #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) n)
n
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (.f64 (sqrt.f64 n) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (PI.f64) k)
(PI.f64)
k
(sqrt.f64 n)
n
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

localize218.0ms (1.6%)

Memory

-34.9MiB live, 209.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(sqrt.f64 (/.f64 (PI.f64) k))
	accuracy	99.6%	(/.f64 (PI.f64) k)
✓	accuracy	99.5%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
✓	accuracy	99.3%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.6%	(.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))
	accuracy	99.6%	(/.f64 (PI.f64) k)
✓	accuracy	99.2%	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	accuracy	75.4%	(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))
	accuracy	100.0%	(PI.f64)
✓	accuracy	99.8%	(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
✓	accuracy	99.6%	(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
✓	accuracy	99.5%	(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
	accuracy	100.0%	(PI.f64)
✓	accuracy	99.6%	(.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))
	accuracy	99.6%	(/.f64 (PI.f64) k)
✓	accuracy	75.8%	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
	accuracy	100.0%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
✓	accuracy	99.8%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	accuracy	99.6%	(*.f64 (PI.f64) n)

Samples

149.0ms

256×

valid

Compiler

Compiled 177 to 32 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

ival-sqrt: 73.0ms (56.6% of total)

ival-pow: 32.0ms (24.8% of total)

ival-mult: 14.0ms (10.9% of total)

ival-div: 3.0ms (2.3% of total)

ival-add: 3.0ms (2.3% of total)

ival-pow2: 2.0ms (1.6% of total)

ival-pi: 1.0ms (0.8% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series249.0ms (1.9%)

Memory

6.1MiB live, 277.2MiB allocated

Counts

14 → 256

Calls

Call 1

Inputs
#<alt (*.f64 k #s(literal -1/2 binary64))>
#<alt (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))>
#<alt (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))>
#<alt (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))>
#<alt (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))>
#<alt (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)>
#<alt (*.f64 (PI.f64) #s(literal 2 binary64))>
#<alt (pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))>
#<alt (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))>
#<alt (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))>
#<alt (sqrt.f64 (/.f64 (PI.f64) k))>
#<alt (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))>
#<alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))>

Outputs
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
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#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
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#<alt (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))>
#<alt (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))>
#<alt (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))>
#<alt (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))>
#<alt (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))>
#<alt (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))>
#<alt (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 k (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1/48 binary64) (.f64 (.f64 k (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k))))>
#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k))))>
#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k))))>
#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k))))>
#<alt (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k))))>

Calls

66 calls:

Time	Variable		Point	Expression
88.0ms	n	@	0	(pow (pow (* (/ (PI) k) (* n 2)) 1/4) 2)
66.0ms	n	@	0	(pow (* (/ (PI) k) (* n 2)) 1/4)
17.0ms	n	@	-inf	(pow (* (/ (PI) k) (* n 2)) 1/4)
16.0ms	k	@	-inf	(pow (* (/ (PI) k) (* n 2)) 1/4)
16.0ms	k	@	0	(pow (* (/ (PI) k) (* n 2)) 1/4)

rewrite286.0ms (2.1%)

Memory

-7.2MiB live, 148.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

536×	`log1p-expm1-u`
264×	`associate-r`
229×	`expm1-log1p-u`
226×	`pow1`
223×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	377
1	581	369
2	6994	369

Stop Event

1×	node limit

Counts

14 → 489

Calls

Call 1

Inputs
(*.f64 k #s(literal -1/2 binary64))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))
(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
(*.f64 (PI.f64) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64))
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
(sqrt.f64 (/.f64 (PI.f64) k))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))

Outputs
(-.f64 (exp.f64 (log1p.f64 (*.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 k #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal -1/8 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 k #s(literal -1/2 binary64))) #s(literal 2 binary64))
(sqrt.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 k #s(literal 2 binary64))))
(log.f64 (pow.f64 (exp.f64 k) #s(literal -1/2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 k #s(literal -1/2 binary64)))))
(cbrt.f64 (*.f64 (pow.f64 k #s(literal 3 binary64)) #s(literal -1/8 binary64)))
(expm1.f64 (log1p.f64 (*.f64 k #s(literal -1/2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 k #s(literal -1/2 binary64))))
(exp.f64 (log.f64 (*.f64 k #s(literal -1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (pow.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))) (cbrt.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))) (.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64))) (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64))))
(.f64 (cbrt.f64 #s(literal 2 binary64)) (.f64 (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
(.f64 (cbrt.f64 (/.f64 (PI.f64) k)) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(.f64 (cbrt.f64 (.f64 (/.f64 (PI.f64) k) n)) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (pow.f64 k #s(literal -1/2 binary64))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (sqrt.f64 n) (pow.f64 k #s(literal -1/2 binary64))))
(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) (.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) (.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 k #s(literal -1/2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
(.f64 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/8 binary64)) (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/8 binary64))) (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/8 binary64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k)))))
(.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (sqrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 n) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (cbrt.f64 k)) (/.f64 (sqrt.f64 n) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 n) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 k))))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64))) (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64))))
(.f64 (.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (cbrt.f64 #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 n))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (.f64 (/.f64 (PI.f64) k) n))) (cbrt.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n)))) (sqrt.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) #s(literal 1 binary64)))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 k)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
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(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
(exp.f64 (.f64 (.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) #s(literal 1 binary64)))

simplify581.0ms (4.4%)

Memory

9.9MiB live, 480.6MiB allocated

Algorithm

1×	egg-herbie

Rules

738×	`fma-define`
493×	`associate-r`
449×	`associate-l`
360×	`exp-prod`
323×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	791	29237
1	1581	28829
2	5012	28503

Stop Event

1×	node limit

Counts

745 → 523

Calls

Call 1

Inputs
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 #s(literal -1 binary64) (log.f64 k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 #s(literal -1 binary64) (log.f64 k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 #s(literal -1 binary64) (log.f64 k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 #s(literal -1 binary64) (log.f64 k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (*.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))
(exp.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))
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(cbrt.f64 (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 k))
(pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (PI.f64) k) n) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))
(log.f64 (exp.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)))))
(cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64)) (pow.f64 n #s(literal 3/2 binary64))))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3/2 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64))))
(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
(log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
(exp.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 (PI.f64) k) n))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (/.f64 (PI.f64) k) n))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (PI.f64) k)))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))) (cbrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (cbrt.f64 (/.f64 (PI.f64) k)) (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (/.f64 (PI.f64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (PI.f64))))
(/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 1 binary64)) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))
(/.f64 (/.f64 (sqrt.f64 (PI.f64)) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(pow.f64 (/.f64 (PI.f64) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (PI.f64) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (PI.f64) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (/.f64 (PI.f64) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) k)))))
(cbrt.f64 (pow.f64 (/.f64 (PI.f64) k) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) k))))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (PI.f64) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))) #s(literal 1 binary64))
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 2 binary64))
(sqrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) k)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))))))
(cbrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64))) #s(literal 3 binary64)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64))))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
(log1p.f64 (expm1.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
(exp.f64 (log.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 k #s(literal -1/2 binary64)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (sqrt.f64 n) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)))))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
(exp.f64 (.f64 (.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) #s(literal 1 binary64)))

Outputs
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(*.f64 #s(literal -1/2 binary64) k)
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 n (PI.f64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (.f64 n (PI.f64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (sqrt.f64 n) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 (sqrt.f64 n) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) k))))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) k))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 k #s(literal -1/2 binary64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (pow.f64 (PI.f64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 n #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (PI.f64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (.f64 n #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 n (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 (exp.f64 (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (exp.f64 (log.f64 n))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(literal 1 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(fabs.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64))))
(log.f64 (exp.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(cbrt.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64)))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))))
(log1p.f64 (expm1.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))) #s(literal 1 binary64)))
(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) k #s(literal 1/2 binary64)))

eval267.0ms (2%)

Memory: 8.3MiB live, 232.1MiB allocated
Compiler: Compiled 12 852 to 2 507 computations (80.5% saved)

prune247.0ms (1.9%)

Memory

7.7MiB live, 333.9MiB allocated

Pruning

24 alts after pruning (19 fresh and 5 done)

	Pruned	Kept	Total
New	796	14	810
Fresh	6	5	11
Picked	1	4	5
Done	0	1	1
Total	803	24	827

Accuracy

100.0%

Counts

827 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	36.2%	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	24.2%	(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
	26.8%	(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
✓	47.4%	(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
	47.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
	37.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	47.4%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	47.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓	47.2%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	47.3%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	36.3%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
✓	36.3%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
▶	88.7%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	36.4%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
	36.4%	(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
▶	36.4%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
▶	39.1%	(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
✓	36.4%	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
	75.6%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
	36.4%	(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
▶	36.4%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
	34.2%	(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
	28.3%	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)))
▶	28.3%	(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))

Compiler

Compiled 521 to 422 computations (19% saved)

simplify371.0ms (2.8%)

Memory

2.3MiB live, 120.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
✓	cost-diff	0	(fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
✓	cost-diff	6528	(+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))
✓	cost-diff	6528	(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
✓	cost-diff	0	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
✓	cost-diff	0	(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
✓	cost-diff	0	(pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64))
✓	cost-diff	0	(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
✓	cost-diff	0	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
✓	cost-diff	128	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	cost-diff	0	(PI.f64)
✓	cost-diff	0	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
✓	cost-diff	0	(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
✓	cost-diff	0	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
✓	cost-diff	0	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Rules

3 373×	`associate-+r+`
1 559×	`fma-define`
486×	`distribute-rgt-in`
484×	`distribute-lft-in`
423×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	665
1	59	665
2	105	665
3	204	665
4	408	665
5	575	665
6	865	665
7	1183	665
8	1339	665
9	1354	665
10	1354	665
11	1796	665
12	2494	665
13	2604	665
14	2610	665
15	2610	665
16	2610	665
17	3894	665
18	4802	665
19	4814	665
20	4818	665
21	4818	665
22	4818	665
23	5914	665
24	5914	665
25	5914	665
26	5914	665

Stop Event

1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
n
(PI.f64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
n
(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
(PI.f64)
(/.f64 #s(literal 2 binary64) k)
#s(literal 2 binary64)
k
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
#s(literal 1 binary64)
(/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
k
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(PI.f64)
(*.f64 n #s(literal 2 binary64))
n
#s(literal 2 binary64)
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64))
(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
n
(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
(PI.f64)
(/.f64 #s(literal 2 binary64) k)
#s(literal 2 binary64)
k
#s(literal 3/2 binary64)
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))
#s(literal -1 binary64)
(fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
n
(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
(PI.f64)
(/.f64 #s(literal 2 binary64) k)
#s(literal 2 binary64)
k
#s(literal 1 binary64)

Outputs
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
#s(literal 2 binary64)
(*.f64 n (PI.f64))
n
(PI.f64)
(-.f64 #s(literal 1 binary64) k)
#s(literal 1 binary64)
k
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))
n
(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
(*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(PI.f64)
(/.f64 #s(literal 2 binary64) k)
#s(literal 2 binary64)
k
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
(/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))
#s(literal 1 binary64)
(/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
(/.f64 k (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
(/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n))
k
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(PI.f64)
(*.f64 n #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) n)
n
#s(literal 2 binary64)
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64))
(pow.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)) #s(literal 3/2 binary64))
(pow.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)) #s(literal 3/2 binary64))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64))
(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))
n
(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
(*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(PI.f64)
(/.f64 #s(literal 2 binary64) k)
#s(literal 2 binary64)
k
#s(literal 3/2 binary64)
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
(+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))
(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 n (/.f64 (.f64 #s(literal 2 binary64) (PI.f64)) k))
(.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))
#s(literal -1 binary64)
(fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal 1 binary64))
(fma.f64 #s(literal 2 binary64) (/.f64 (*.f64 n (PI.f64)) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k) #s(literal 1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)) #s(literal 1 binary64))
n
(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
(*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) k)
(PI.f64)
(/.f64 #s(literal 2 binary64) k)
#s(literal 2 binary64)
k
#s(literal 1 binary64)

localize175.0ms (1.3%)

Memory

9.3MiB live, 331.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
✓	accuracy	99.5%	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
✓	accuracy	75.8%	(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
✓	accuracy	65.9%	(+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))
✓	accuracy	99.7%	(pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64))
✓	accuracy	99.6%	(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
✓	accuracy	99.5%	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
✓	accuracy	57.0%	(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
✓	accuracy	99.7%	(/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	accuracy	99.6%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
✓	accuracy	75.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	accuracy	100.0%	(PI.f64)
✓	accuracy	99.6%	(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
✓	accuracy	99.5%	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
✓	accuracy	75.8%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
✓	accuracy	99.9%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
✓	accuracy	99.6%	(*.f64 n (PI.f64))
✓	accuracy	88.9%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Samples

42.0ms	63×	2	valid
40.0ms	63×	1	valid
33.0ms	127×	0	valid
2.0ms	3×	3	valid

Compiler

Compiled 198 to 29 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-mult: 18.0ms (22.7% of total)

ival-pow: 17.0ms (21.4% of total)

ival-sqrt: 16.0ms (20.2% of total)

ival-div: 11.0ms (13.9% of total)

adjust: 5.0ms (6.3% of total)

ival-add: 5.0ms (6.3% of total)

ival-cbrt: 3.0ms (3.8% of total)

ival-sub: 2.0ms (2.5% of total)

ival-pi: 2.0ms (2.5% of total)

...in/eval/compile.rkt:110:19: 1.0ms (1.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series184.0ms (1.4%)

Memory

-19.3MiB live, 57.7MiB allocated

Counts

17 → 336

Calls

Call 1

Inputs
#<alt (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))>
#<alt (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)>
#<alt (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))>
#<alt (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))>
#<alt (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))>
#<alt (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))>
#<alt (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))>
#<alt (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))>
#<alt (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))>
#<alt (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64))>
#<alt (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))>
#<alt (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))>
#<alt (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))>
#<alt (*.f64 n (PI.f64))>

Outputs
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) k)>
#<alt (/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 (-.f64 (.f64 #s(literal -1/3 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))))) (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))) (.f64 k (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))) k)>
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#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal -1 binary64) (.f64 n (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 n (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 n (-.f64 (*.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k)) (/.f64 #s(literal 1 binary64) n))))>
#<alt (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))>
#<alt (/.f64 (+.f64 k (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) k)>
#<alt (/.f64 (+.f64 k (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) k)>
#<alt (/.f64 (+.f64 k (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) k)>
#<alt #s(literal 1 binary64)>
#<alt (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))>
#<alt (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))>
#<alt (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))>
#<alt #s(literal 1 binary64)>
#<alt (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))>
#<alt (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))>
#<alt (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))>

Calls

90 calls:

Time	Variable		Point	Expression
138.0ms	n	@	0	(cbrt (pow (* n (* (PI) (/ 2 k))) 3/2))
3.0ms	n	@	0	(pow (* n (* (PI) (/ 2 k))) 3/2)
2.0ms	n	@	-inf	(cbrt (pow (* n (* (PI) (/ 2 k))) 3/2))
2.0ms	k	@	0	(pow (* n (* (PI) (/ 2 k))) 3/2)
2.0ms	k	@	0	(sqrt (/ (pow (* 2 (* n (PI))) (- 1 k)) k))

rewrite331.0ms (2.5%)

Memory

27.4MiB live, 226.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

484×	`log1p-expm1-u`
262×	`prod-diff`
223×	`expm1-log1p-u`
220×	`associate-r`
216×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	497
1	546	493
2	7009	493

Stop Event

1×	node limit

Counts

17 → 588

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))
(/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))
(fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(*.f64 n (PI.f64))

Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64))
(.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))) (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 2 binary64)))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(log.f64 (exp.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(exp.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1 binary64))
(.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (-.f64 #s(literal 1 binary64) k)) k))
(.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)) (.f64 (pow.f64 (*.f64 n (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (/.f64 #s(literal 1 binary64) k)))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) k))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 2 binary64))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 2 binary64))) (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) k))
(.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) k)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) (.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(.f64 (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (/.f64 #s(literal 1 binary64) (neg.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) k) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)))
(.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64))) (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)) #s(literal 1 binary64)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (-.f64 #s(literal 1 binary64) k)) k))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (/.f64 (pow.f64 (.f64 n (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (cbrt.f64 k)))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (-.f64 #s(literal 1 binary64) k)) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) k))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) k))
(.f64 (/.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (/.f64 (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 k)))
(.f64 (.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) #s(literal -1 binary64))
(neg.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) (neg.f64 k)))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 2 binary64)))
(log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 3 binary64)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
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simplify694.0ms (5.2%)

Memory

-32.1MiB live, 693.6MiB allocated

Algorithm

1×	egg-herbie

Rules

547×	`fmm-def`
504×	`exp-prod`
479×	`cube-prod`
471×	`*-commutative`
320×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1067	8589971112
1	2255	8589969816
2	5912	8589969452

Stop Event

1×	node limit

Counts

924 → 680

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 (-.f64 (.f64 #s(literal -1/3 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))))) (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))) (.f64 k (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))) k)
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(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(.f64 (sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
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(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k)
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(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k)
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(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
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(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
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(.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 #s(literal -1 binary64) (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) (-.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal -1 binary64))))))
(pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))))))
(cbrt.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 3/2 binary64)))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))
(.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1 binary64))
(.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) (sqrt.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))))
(.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) (pow.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 2 binary64)))
(.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))) (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(.f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 2 binary64)) (cbrt.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))))
(.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) (-.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal -1 binary64))))))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1/4 binary64))) (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1/4 binary64)))
(.f64 (+.f64 (sqrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 1 binary64)) (-.f64 (sqrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) (cbrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) (-.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal -1 binary64)))) (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) (-.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal -1 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) (-.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal -1 binary64) (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 2 binary64)))
(log.f64 (exp.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)))))
(cbrt.f64 (pow.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))))
(log1p.f64 (expm1.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))))
(exp.f64 (log.f64 (+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 0 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 2 binary64)) (cbrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal -1 binary64))
(fma.f64 (sqrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal -1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
(+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 1 binary64))
(-.f64 (exp.f64 (log1p.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))
(.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (cbrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) (pow.f64 (cbrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 2 binary64)))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 2 binary64)) (cbrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))))
(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 1 binary64)))
(pow.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(log.f64 (exp.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(cbrt.f64 (pow.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(log1p.f64 (expm1.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
(exp.f64 (.f64 (log1p.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (PI.f64)))))
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(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))) #s(literal 1 binary64)))

Outputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))) (-.f64 #s(literal 1 binary64) k)) k))
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(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 2 binary64)) (cbrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal -1 binary64))
(.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(fma.f64 (sqrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal -1 binary64))
(.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
(+.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(+.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 1 binary64))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(-.f64 (exp.f64 (log1p.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(expm1.f64 (log1p.f64 (fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))))
(expm1.f64 (log1p.f64 (fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(.f64 #s(literal 1 binary64) (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (cbrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) (pow.f64 (cbrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 2 binary64)))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 2 binary64)) (cbrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (fma.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 8 binary64) (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal -2 binary64) k))) (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64)) #s(literal -1 binary64)) (fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal -1 binary64)))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (fma.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal -1 binary64)))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 2 binary64))) (fma.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(pow.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 3 binary64))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))) #s(literal 2 binary64))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(sqrt.f64 (pow.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (pow.f64 (fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fabs.f64 (fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64)))
(fabs.f64 (fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(log.f64 (exp.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(cbrt.f64 (pow.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)) #s(literal 3 binary64)))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(expm1.f64 (log1p.f64 (fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(expm1.f64 (log1p.f64 (fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))))
(expm1.f64 (log1p.f64 (fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(log1p.f64 (expm1.f64 (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(exp.f64 (.f64 (log1p.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))) #s(literal 1 binary64)))
(fma.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))
(fma.f64 (*.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k) #s(literal 1 binary64))
(fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))
(-.f64 (exp.f64 (log1p.f64 (*.f64 n (PI.f64)))) #s(literal 1 binary64))
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))
(pow.f64 (*.f64 n (PI.f64)) #s(literal 1 binary64))
(*.f64 n (PI.f64))
(pow.f64 (cbrt.f64 (*.f64 n (PI.f64))) #s(literal 3 binary64))
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 n (PI.f64))
(pow.f64 (sqrt.f64 (*.f64 n (PI.f64))) #s(literal 2 binary64))
(*.f64 n (PI.f64))
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (PI.f64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(*.f64 n (PI.f64))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 n (PI.f64)))))
(*.f64 n (PI.f64))
(cbrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(*.f64 n (PI.f64))
(expm1.f64 (log1p.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))) #s(literal 1 binary64)))
(*.f64 n (PI.f64))

eval182.0ms (1.4%)

Memory: 24.5MiB live, 176.8MiB allocated
Compiler: Compiled 14 468 to 2 737 computations (81.1% saved)

prune196.0ms (1.5%)

Memory

-20.2MiB live, 304.0MiB allocated

Pruning

27 alts after pruning (20 fresh and 7 done)

	Pruned	Kept	Total
New	863	11	874
Fresh	5	9	14
Picked	2	3	5
Done	1	4	5
Total	871	27	898

Accuracy

100.0%

Counts

898 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	36.2%	(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	24.2%	(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
	26.8%	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	37.1%	(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
	37.0%	(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
✓	47.4%	(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
	47.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
	37.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
	37.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
	47.4%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	47.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
	47.3%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	36.3%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	47.3%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
✓	36.3%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	47.3%	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	47.3%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
✓	88.7%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	88.8%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k))) k))
	36.4%	(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
	26.7%	(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
✓	36.4%	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
	36.4%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
	36.4%	(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
✓	36.4%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
	34.2%	(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
✓	28.3%	(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))

Compiler

Compiled 1 001 to 448 computations (55.2% saved)

regimes67.0ms (0.5%)

Memory

30.0MiB live, 146.2MiB allocated

Counts

56 → 1

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k))) k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
(/.f64 (.f64 (pow.f64 k #s(literal -1/4 binary64)) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) k))))) (pow.f64 k #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal -1/2 binary64))))

Outputs
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))

Calls

4 calls:

16.0ms	n
16.0ms	k
15.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
14.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.8%	1	`k`
99.8%	1	`n`
99.8%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.8%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes66.0ms (0.5%)

Memory

3.1MiB live, 154.4MiB allocated

Counts

49 → 1

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k))) k))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))

Outputs
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))

Calls

4 calls:

18.0ms	n
15.0ms	k
15.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
14.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.7%	1	`k`
99.7%	1	`n`
99.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes29.0ms (0.2%)

Memory

-5.9MiB live, 66.4MiB allocated

Counts

37 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Outputs
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Calls

2 calls:

13.0ms	n
13.0ms	k

Results

Accuracy	Segments	Branch
99.7%	2	`k`
88.7%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes31.0ms (0.2%)

Memory

13.4MiB live, 63.8MiB allocated

Counts

36 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)))
(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 (*.f64 n #s(literal 2 binary64)) k))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))))
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Outputs
(/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k))
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))

Calls

2 calls:

18.0ms	k
10.0ms	n

Results

Accuracy	Segments	Branch
57.6%	4	`n`
71.4%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

-12.8MiB live, 24.9MiB allocated

Counts

22 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))

Outputs
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
71.3%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes6.0ms (0%)

Memory

17.1MiB live, 17.1MiB allocated

Counts

14 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n))))

Outputs
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
61.1%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes6.0ms (0%)

Memory

-24.2MiB live, 12.8MiB allocated

Counts

9 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))

Outputs
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
61.1%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes4.0ms (0%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

8 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) k))
(sqrt.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))

Outputs
(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64))))
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
60.5%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes3.0ms (0%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))

Outputs
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
60.5%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes5.0ms (0%)

Memory

-27.9MiB live, 10.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))

Outputs
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))

Calls

2 calls:

1.0ms	n
1.0ms	k

Results

Accuracy	Segments	Branch
26.7%	1	`n`
26.7%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch28.0ms (0.2%)

Memory

13.8MiB live, 52.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
25.0ms	9.101299840647413e-18	3.5887613934255695e-11

Samples

20.0ms

144×

valid

Compiler

Compiled 264 to 216 computations (18.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-pow: 3.0ms (32.8% of total)

ival-div: 2.0ms (21.9% of total)

ival-mult: 2.0ms (21.9% of total)

ival-sub: 1.0ms (10.9% of total)

ival-sqrt: 1.0ms (10.9% of total)

ival-pi: 0.0ms (0% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

bsearch17.0ms (0.1%)

Memory

6.8MiB live, 44.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.697982818222525	21.502494391471984

Samples

12.0ms

112×

valid

Compiler

Compiled 154 to 137 computations (11% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 3.0ms (34.1% of total)

ival-mult: 2.0ms (22.7% of total)

ival-pow: 2.0ms (22.7% of total)

ival-sqrt: 1.0ms (11.4% of total)

ival-pi: 0.0ms (0% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

bsearch17.0ms (0.1%)

Memory

4.6MiB live, 41.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.697982818222525	21.502494391471984

Samples

12.0ms

112×

valid

Compiler

Compiled 154 to 137 computations (11% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 3.0ms (33.8% of total)

ival-mult: 2.0ms (22.5% of total)

ival-pow: 2.0ms (22.5% of total)

ival-sqrt: 1.0ms (11.3% of total)

ival-pi: 0.0ms (0% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

bsearch17.0ms (0.1%)

Memory

-0.5MiB live, 35.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.697982818222525	21.502494391471984

Samples

12.0ms

112×

valid

Compiler

Compiled 154 to 137 computations (11% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 3.0ms (33.6% of total)

ival-mult: 2.0ms (22.4% of total)

ival-pow: 2.0ms (22.4% of total)

ival-sqrt: 1.0ms (11.2% of total)

ival-pi: 0.0ms (0% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

bsearch24.0ms (0.2%)

Memory

18.9MiB live, 56.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	0.697982818222525	21.502494391471984

Samples

18.0ms

112×

valid

Compiler

Compiled 154 to 137 computations (11% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-pow: 10.0ms (64.6% of total)

ival-mult: 2.0ms (12.9% of total)

ival-div: 1.0ms (6.5% of total)

ival-sqrt: 1.0ms (6.5% of total)

ival-pi: 0.0ms (0% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

bsearch281.0ms (2.1%)

Memory

-234.9MiB live, 37.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
279.0ms	0.697982818222525	21.502494391471984

Samples

272.0ms

112×

valid

Compiler

Compiled 147 to 130 computations (11.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 269.0ms

ival-pi: 262.0ms (97.3% of total)

ival-mult: 2.0ms (0.7% of total)

ival-pow: 2.0ms (0.7% of total)

ival-div: 1.0ms (0.4% of total)

ival-sqrt: 1.0ms (0.4% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

bsearch17.0ms (0.1%)

Memory

-5.3MiB live, 38.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.697982818222525	21.502494391471984

Samples

12.0ms

112×

valid

Compiler

Compiled 147 to 130 computations (11.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 4.0ms (44.9% of total)

ival-pow: 2.0ms (22.5% of total)

ival-div: 1.0ms (11.2% of total)

ival-sqrt: 1.0ms (11.2% of total)

ival-pi: 0.0ms (0% of total)

...in/eval/compile.rkt:110:19: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

simplify11.0ms (0.1%)

Memory

-12.7MiB live, 26.8MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative`
5×	`sub-neg`
5×	`+-commutative`
3×	`1-exp`
3×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	523
1	101	523
2	110	523
3	116	523
4	120	523
5	121	523

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 2149935417987077/20282409603651670423947251286016 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 6980579422424269/2251799813685248 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 8106479329266893/2251799813685248 binary64)) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 7093169413108531/2251799813685248 binary64)) (pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 7093169413108531/2251799813685248 binary64)) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 7/2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))

Outputs
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 2149935417987077/20282409603651670423947251286016 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 2149935417987077/20282409603651670423947251286016 binary64)) (/.f64 (sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 6980579422424269/2251799813685248 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (sqrt.f64 k)) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 6980579422424269/2251799813685248 binary64)) (/.f64 (sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 k)) (sqrt.f64 #s(literal 0 binary64)))
(if (<=.f64 k #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 3602879701896397/1125899906842624 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (sqrt.f64 #s(literal 0 binary64)))
(if (<=.f64 k #s(literal 8106479329266893/2251799813685248 binary64)) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 8106479329266893/2251799813685248 binary64)) (pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(if (<=.f64 k #s(literal 7093169413108531/2251799813685248 binary64)) (pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 7093169413108531/2251799813685248 binary64)) (pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(if (<=.f64 k #s(literal 7093169413108531/2251799813685248 binary64)) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 7093169413108531/2251799813685248 binary64)) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) (.f64 #s(literal 2 binary64) n))) (sqrt.f64 #s(literal 0 binary64)))
(if (<=.f64 k #s(literal 7/2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64))))
(if (<=.f64 k #s(literal 7/2 binary64)) (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (sqrt.f64 #s(literal 0 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) #s(literal 1 binary64)))
(sqrt.f64 #s(literal 0 binary64))

soundness2.6s (19.5%)

Memory

19.5MiB live, 2 224.6MiB allocated

Rules

1 096×	`log1p-expm1-u`
753×	`associate-l`
738×	`fma-define`
718×	`fma-define`
547×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	438
1	96	380
2	211	380
3	410	364
4	686	352
5	1171	352
6	1433	352
7	1696	352
8	2015	352
9	2058	352
10	2086	352
11	2097	352
12	2099	352
0	34	497
1	546	493
2	7009	493
0	791	29237
1	1581	28829
2	5012	28503
0	42	506
1	724	442
0	975	32765
1	2307	31401
2	6414	30892
0	36	377
1	581	369
2	6994	369
0	1067	8589971112
1	2255	8589969816
2	5912	8589969452
0	26	274
1	427	270
2	4798	270
0	600	19256
1	1218	17586
2	4112	16578

Stop Event

1×	fuel
1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	node limit
1×	saturated

Compiler

Compiled 1 396 to 548 computations (60.7% saved)

preprocess357.0ms (2.7%)

Memory: -27.3MiB live, 126.8MiB allocated
Compiler: Compiled 336 to 158 computations (53% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	26	359
1	45	347
2	65	347
3	86	347
4	106	323
5	129	323
6	156	323
7	184	323
8	192	323
9	193	323

Iter	Nodes	Cost
0	26	359
1	45	347
2	65	347
3	86	347
4	106	323
5	129	323
6	156	323
7	184	323
8	192	323
9	193	323

analyze105.0ms (0.8%)

sample3.2s (23.6%)

preprocess133.0ms (1%)

explain153.0ms (1.1%)

eval1.0ms (0%)

prune1.0ms (0%)

simplify24.0ms (0.2%)

localize75.0ms (0.6%)

series93.0ms (0.7%)

rewrite313.0ms (2.3%)

simplify234.0ms (1.8%)

eval63.0ms (0.5%)

prune87.0ms (0.6%)

simplify60.0ms (0.4%)

localize150.0ms (1.1%)

series132.0ms (1%)

rewrite134.0ms (1%)

simplify427.0ms (3.2%)

eval157.0ms (1.2%)

prune262.0ms (2%)

simplify18.0ms (0.1%)

localize218.0ms (1.6%)

series249.0ms (1.9%)

rewrite286.0ms (2.1%)

simplify581.0ms (4.4%)

eval267.0ms (2%)

prune247.0ms (1.9%)

simplify371.0ms (2.8%)

localize175.0ms (1.3%)

series184.0ms (1.4%)

rewrite331.0ms (2.5%)

simplify694.0ms (5.2%)

eval182.0ms (1.4%)

prune196.0ms (1.5%)

regimes67.0ms (0.5%)

regimes66.0ms (0.5%)

regimes29.0ms (0.2%)

regimes31.0ms (0.2%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes6.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes5.0ms (0%)

bsearch28.0ms (0.2%)

bsearch17.0ms (0.1%)

bsearch17.0ms (0.1%)

bsearch17.0ms (0.1%)

bsearch24.0ms (0.2%)

bsearch281.0ms (2.1%)

bsearch17.0ms (0.1%)

simplify11.0ms (0.1%)

soundness2.6s (19.5%)

preprocess357.0ms (2.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	26	359
1	45	347
2	65	347
3	86	347
4	106	323
5	129	323
6	156	323
7	184	323
8	192	323
9	193	323