Metrics for Migdal et al, Equation (51)

analyze193.0ms (1.6%)

Memory

-36.5MiB live, 130.9MiB 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)

sample3.8s (31.5%)

Memory

54.7MiB live, 5 606.5MiB allocated

Samples

1.8s	5 545×	1	invalid
1.0s	8 256×	0	valid
218.0ms	467×	2	invalid
33.0ms	391×	0	invalid
28.0ms	230×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 2.5s

ival-mult: 851.0ms (33.7% of total)

ival-pow: 767.0ms (30.4% of total)

ival-div: 364.0ms (14.4% of total)

ival-sqrt: 155.0ms (6.1% of total)

ival-pi: 134.0ms (5.3% of total)

ival-sub: 118.0ms (4.7% of total)

adjust: 94.0ms (3.7% of total)

exact: 23.0ms (0.9% of total)

ival-true: 13.0ms (0.5% of total)

ival-assert: 6.0ms (0.2% of total)

Bogosity

preprocess138.0ms (1.2%)

Memory

10.9MiB live, 132.2MiB 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))

explain158.0ms (1.3%)

Memory

-2.0MiB live, 474.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
2	99	(6.384607195427605e-285 1.203085156885773e+92)	-	`(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	101	23

Confusion

	Predicted +	Predicted -
+	2	0
-	99	155

Precision

0.019801980198019802

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	99	23	132

Precision?

0.016129032258064516

Recall?

1.0

Freqs

test

number	freq
0	155
1	101

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

57.0ms

512×

valid

Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-pow: 11.0ms (29.3% of total)

ival-div: 8.0ms (21.3% of total)

ival-mult: 8.0ms (21.3% of total)

ival-sqrt: 5.0ms (13.3% of total)

ival-sub: 3.0ms (8% of total)

ival-pi: 2.0ms (5.3% of total)

ival-true: 1.0ms (2.7% of total)

exact: 1.0ms (2.7% of total)

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

eval1.0ms (0%)

Memory: 2.5MiB live, 2.5MiB allocated
Compiler: Compiled 59 to 23 computations (61% saved)

prune2.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.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

▶

99.6%

(/.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)

simplify22.0ms (0.2%)

Memory

-0.6MiB live, 37.6MiB 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)

localize78.0ms (0.7%)

Memory

-36.6MiB live, 177.8MiB 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	99.7%	(.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 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.6%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Samples

50.0ms

256×

valid

Compiler

Compiled 104 to 22 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-pow: 9.0ms (32% of total)

ival-mult: 7.0ms (24.9% of total)

ival-div: 6.0ms (21.3% of total)

ival-sub: 3.0ms (10.7% of total)

ival-sqrt: 2.0ms (7.1% of total)

ival-pi: 1.0ms (3.6% of total)

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

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

exact: 0.0ms (0% of total)

series89.0ms (0.7%)

Memory

31.7MiB live, 186.3MiB 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))))>
#<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 #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)))))>
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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 (+.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)>
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#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 (+.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))))>
#<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))))>
#<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))))>
#<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))))>
#<alt (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 1/2 binary64) (.f64 #s(literal 1/2 binary64) k))))>
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#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
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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))))>
#<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
34.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
23.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
7.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	n	@	inf	(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
2.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite332.0ms (2.8%)

Memory

-22.3MiB live, 415.6MiB 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)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 k))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 k) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 k)))
(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 k) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 k)) #s(literal -1 binary64))
(pow.f64 k #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 k) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal 3 binary64))
(pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
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(.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)))

simplify221.0ms (1.9%)

Memory

15.4MiB live, 413.0MiB 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))))
(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))))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
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(.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))))
(.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))))
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(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #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))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
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(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (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))))
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(.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 (pow.f64 #s(literal 2 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 n (PI.f64)) (+.f64 #s(literal 1/2 binary64) (.f64 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 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 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 (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)))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 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))))))
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(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
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(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 k #s(literal 1/2 binary64))))
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(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (*.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))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) k)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) k)))
(.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)))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #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 (pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #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 n (PI.f64)))) (+.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 n (PI.f64)))) #s(literal 2 binary64)) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (pow.f64 (cbrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (fma.f64 k #s(literal 1/2 binary64) #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)))))
(pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))
(pow.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) k))
(/.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 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (*.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 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (*.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)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (*.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))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (-.f64 #s(literal 1 binary64) k) (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))))
(sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (+.f64 #s(literal 1 binary64) k)))
(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))))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (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 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #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)))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 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))))))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(expm1.f64 (log1p.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #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))))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #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)))))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(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)))
(pow.f64 (exp.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))))) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (fma.f64 k #s(literal 1/2 binary64) #s(literal 1/2 binary64)))

eval55.0ms (0.5%)

Memory: 13.8MiB live, 131.7MiB allocated
Compiler: Compiled 9 568 to 1 524 computations (84.1% saved)

prune71.0ms (0.6%)

Memory

2.6MiB live, 164.0MiB allocated

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	446	13	459
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	447	14	461

Accuracy

100.0%

Counts

461 → 14

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))
	72.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
✓	99.6%	(/.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))
	96.0%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
▶	75.2%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
	99.7%	(/.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))))
▶	99.7%	(/.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)))))
	96.1%	(/.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
▶	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)))
	99.7%	(.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)))))
	42.5%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	42.5%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	89.4%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Compiler

Compiled 476 to 352 computations (26.1% saved)

simplify48.0ms (0.4%)

Memory

-22.4MiB live, 57.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
	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 k #s(literal 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	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))
✓	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

91×	`fma-define`
42×	`distribute-lft-in`
36×	`*-commutative`
35×	`fmm-def`
29×	`associate-r`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	45	942
1	71	922
2	106	922
3	136	902
4	176	900
5	222	894
6	345	894
7	528	894
8	613	894
9	638	894
10	639	894

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 (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))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
(.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
(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
(pow.f64 k #s(literal 3/2 binary64))
#s(literal 3/2 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))

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

localize154.0ms (1.3%)

Memory

8.5MiB live, 324.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	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	99.7%	(*.f64 (PI.f64) n)
✓	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	77.7%	(PI.f64)
✓	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)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
	accuracy	99.7%	(*.f64 (PI.f64) n)
	accuracy	77.7%	(PI.f64)
✓	accuracy	73.6%	(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
✓	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	99.7%	(.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	99.7%	(*.f64 (PI.f64) n)
	accuracy	77.7%	(PI.f64)
✓	accuracy	99.6%	(/.f64 (PI.f64) k)
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	89.9%	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
	accuracy	77.7%	(PI.f64)
✓	accuracy	99.8%	(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	77.7%	(PI.f64)

Samples

70.0ms	197×	0	valid
21.0ms	59×	0	exit

Compiler

Compiled 270 to 41 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-pow: 31.0ms (45.2% of total)

ival-mult: 12.0ms (17.5% of total)

ival-div: 8.0ms (11.7% of total)

ival-sqrt: 7.0ms (10.2% of total)

ival-cbrt: 2.0ms (2.9% of total)

ival-sub: 2.0ms (2.9% of total)

ival-pow2: 2.0ms (2.9% of total)

ival-pi: 1.0ms (1.5% of total)

ival-add: 1.0ms (1.5% of total)

exact: 1.0ms (1.5% of total)

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

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

series130.0ms (1.1%)

Memory

6.0MiB live, 241.6MiB allocated

Counts

14 → 264

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 k #s(literal -1/2 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 (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))))>
#<alt (cbrt.f64 (pow.f64 k #s(literal 3/2 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)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 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)))))))))>
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#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 1/2 binary64) (*.f64 #s(literal 1/2 binary64) k)))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 1/2 binary64) (*.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 (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 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (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 (.f64 (sqrt.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)))) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))>
#<alt (.f64 (sqrt.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)))) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))>
#<alt (.f64 (sqrt.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)))) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))>
#<alt (.f64 (sqrt.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)))) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #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

69 calls:

Time	Variable		Point	Expression
42.0ms	n	@	0	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
16.0ms	k	@	-inf	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
15.0ms	k	@	inf	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
3.0ms	k	@	-inf	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
3.0ms	k	@	-inf	(pow (/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4)) 2)

rewrite123.0ms (1%)

Memory

-6.6MiB live, 152.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

350×	`log1p-expm1-u`
350×	`expm1-log1p-u`
342×	`pow1`
332×	`add-cube-cbrt`
331×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	491
1	800	459

Stop Event

1×	node limit

Counts

14 → 266

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

simplify311.0ms (2.6%)

Memory

-3.3MiB live, 556.1MiB allocated

Algorithm

1×	egg-herbie

Rules

600×	`associate-r`
512×	`associate-l`
488×	`times-frac`
368×	`exp-prod`
350×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	803	25394
1	1741	24840
2	5545	23472

Stop Event

1×	node limit

Counts

530 → 476

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

eval106.0ms (0.9%)

Memory: 31.8MiB live, 263.0MiB allocated
Compiler: Compiled 16 419 to 2 607 computations (84.1% saved)

prune110.0ms (0.9%)

Memory

-3.8MiB live, 321.1MiB allocated

Pruning

17 alts after pruning (13 fresh and 4 done)

	Pruned	Kept	Total
New	779	10	789
Fresh	5	3	8
Picked	2	3	5
Done	0	1	1
Total	786	17	803

Accuracy

100.0%

Counts

803 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	42.0%	(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	42.0%	(pow.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	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))
✓	99.6%	(/.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))
▶	99.7%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
▶	96.1%	(/.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
✓	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)))
	99.7%	(.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))) (pow.f64 k #s(literal -1/2 binary64)))
	52.3%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	42.5%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
	99.7%	(.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (/.f64 #s(literal 1 binary64) (pow.f64 (.f64 k (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) k)) #s(literal 1/2 binary64))))
✓	42.5%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
▶	42.5%	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
▶	89.4%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	42.2%	(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k)))
▶	42.2%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))

Compiler

Compiled 453 to 336 computations (25.8% saved)

simplify140.0ms (1.2%)

Memory

-0.1MiB live, 80.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
✓	cost-diff	0	(log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
✓	cost-diff	192	(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))))
✓	cost-diff	192	(/.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))
✓	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))
✓	cost-diff	128	(*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))
✓	cost-diff	128	(.f64 n (.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))
✓	cost-diff	128	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))))
✓	cost-diff	128	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (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	(.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
	cost-diff	0	(PI.f64)
✓	cost-diff	0	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))

Rules

1 011×	`fma-define`
513×	`neg-mul-1`
461×	`distribute-lft-neg-in`
456×	`distribute-rgt-neg-in`
310×	`neg-sub0`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	875
1	80	863
2	125	847
3	260	847
4	450	847
5	634	847
6	846	847
7	1279	847
8	2489	847
9	3276	847
10	4157	847
11	4675	847
12	5961	847

Stop Event

1×	node limit

Calls

Call 1

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

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

localize132.0ms (1.1%)

Memory

-18.0MiB live, 337.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.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))
✓	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	96.2%	(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))))
	accuracy	77.7%	(PI.f64)
✓	accuracy	99.9%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
✓	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	89.6%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	accuracy	77.7%	(PI.f64)
✓	accuracy	99.5%	(*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	89.9%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))))
	accuracy	77.7%	(PI.f64)
	accuracy	99.8%	(*.f64 n (/.f64 (PI.f64) k))
	accuracy	99.6%	(/.f64 (PI.f64) k)
✓	accuracy	89.6%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
	accuracy	77.7%	(PI.f64)
✓	accuracy	99.8%	(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	accuracy	99.8%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) k))))
✓	accuracy	99.7%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
	accuracy	77.7%	(PI.f64)

Samples

57.0ms	197×	0	valid
20.0ms	59×	0	exit

Compiler

Compiled 249 to 38 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 17.0ms (30.7% of total)

ival-sqrt: 12.0ms (21.7% of total)

ival-div: 8.0ms (14.5% of total)

ival-pow: 8.0ms (14.5% of total)

ival-exp: 3.0ms (5.4% of total)

ival-log: 3.0ms (5.4% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series53.0ms (0.4%)

Memory

7.0MiB live, 128.1MiB allocated

Counts

17 → 308

Calls

Call 1

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

Outputs
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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 (.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 (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 -1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (.f64 #s(literal -1/2 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)))))))) 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 -1/2 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 #s(literal 1 binary64) (.f64 k (.f64 n (PI.f64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))))))) (+.f64 (.f64 #s(literal -1/2 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 #s(literal 1/6 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))))) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) k))))))))))))) k)>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.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 #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)))>
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#<alt (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))>
#<alt (+.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 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.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 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.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 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.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 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>

Calls

84 calls:

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

rewrite160.0ms (1.3%)

Memory

11.2MiB live, 288.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

310×	`associate-r`
292×	`log1p-expm1-u`
292×	`expm1-log1p-u`
291×	`add-exp-log`
289×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	508
1	762	495

Stop Event

1×	node limit

Counts

17 → 480

Calls

Call 1

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

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

simplify488.0ms (4.1%)

Memory

3.3MiB live, 836.8MiB allocated

Algorithm

1×	egg-herbie

Rules

332×	`exp-prod`
325×	`associate-/l*`
287×	`times-frac`
284×	`*-commutative`
272×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1134	37641
1	2530	36531
2	6932	34227

Stop Event

1×	node limit

Counts

788 → 725

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.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)))))
(.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 (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 -1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (.f64 #s(literal -1/2 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)))))))) 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 -1/2 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 #s(literal 1 binary64) (.f64 k (.f64 n (PI.f64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))))))) (+.f64 (.f64 #s(literal -1/2 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 #s(literal 1/6 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))))) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) k))))))))))))) k)
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.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 #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)))
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(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (PI.f64) n))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64)))

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

eval140.0ms (1.2%)

Memory: 5.8MiB live, 290.5MiB allocated
Compiler: Compiled 18 280 to 3 278 computations (82.1% saved)

prune230.0ms (1.9%)

Memory

-18.0MiB live, 300.8MiB allocated

Pruning

22 alts after pruning (17 fresh and 5 done)

	Pruned	Kept	Total
New	909	15	924
Fresh	6	2	8
Picked	3	2	5
Done	1	3	4
Total	919	22	941

Accuracy

100.0%

Counts

941 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	30.6%	(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
✓	99.6%	(/.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 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
▶	89.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) 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)))
	52.4%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	42.4%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
✓	42.5%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	52.4%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
▶	52.4%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
✓	89.4%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	89.5%	(sqrt.f64 (/.f64 (/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k)) k))
	42.2%	(sqrt.f64 (/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k))
	89.5%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 k))) k))
	89.5%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) k))
	42.2%	(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k)))
✓	42.2%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
	42.1%	(sqrt.f64 (.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
▶	42.1%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
	39.4%	(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
▶	32.5%	(cbrt.f64 (pow.f64 (/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k) #s(literal 3/2 binary64)))
	32.5%	(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)))

Compiler

Compiled 522 to 401 computations (23.2% saved)

simplify35.0ms (0.3%)

Memory

18.1MiB live, 60.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

20×	`*-commutative`
13×	`associate-r`
10×	`fma-define`
10×	`sub-neg`
9×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	798
1	70	782
2	100	776
3	123	776
4	144	776
5	154	776
6	165	776
7	184	776
8	202	776
9	206	776

Stop Event

1×

saturated

Calls

Call 1

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

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

localize135.0ms (1.1%)

Memory

-15.6MiB live, 348.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))))
✓	accuracy	99.7%	(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
✓	accuracy	90.1%	(sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))
	accuracy	54.2%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k) #s(literal 3/2 binary64))
✓	accuracy	99.7%	(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
✓	accuracy	78.9%	(cbrt.f64 (pow.f64 (/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k) #s(literal 3/2 binary64)))
	accuracy	54.2%	(PI.f64)
✓	accuracy	99.9%	(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
✓	accuracy	99.8%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
✓	accuracy	99.7%	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
	accuracy	54.2%	(PI.f64)
✓	accuracy	99.8%	(/.f64 k (PI.f64))
✓	accuracy	99.8%	(/.f64 n (/.f64 k (PI.f64)))
✓	accuracy	89.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
	accuracy	54.2%	(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 (sqrt.f64 k) (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	99.7%	(*.f64 (PI.f64) n)
	accuracy	54.2%	(PI.f64)

Samples

39.0ms	135×	0	valid
37.0ms	121×	0	exit

Compiler

Compiled 225 to 37 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-pow: 14.0ms (25.2% of total)

ival-div: 13.0ms (23.4% of total)

ival-mult: 13.0ms (23.4% of total)

ival-sqrt: 9.0ms (16.2% of total)

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

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

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

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

exact: 1.0ms (1.8% of total)

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

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

series162.0ms (1.4%)

Memory

14.0MiB live, 131.6MiB allocated

Counts

17 → 328

Calls

Call 1

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

Calls

87 calls:

Time	Variable		Point	Expression
86.0ms	k	@	0	(sqrt (/ k (pow (* (* n 2) (PI)) (- 1 k))))
20.0ms	k	@	0	(cbrt (pow (/ (* (* n 2) (PI)) k) 3/2))
4.0ms	n	@	0	(/ (sqrt k) (pow (* 2 (* (PI) n)) (+ 1/2 (* k -1/2))))
3.0ms	n	@	0	(pow (/ (* (* n 2) (PI)) k) 3/2)
3.0ms	n	@	-inf	(/ (sqrt k) (pow (* 2 (* (PI) n)) (+ 1/2 (* k -1/2))))

rewrite148.0ms (1.2%)

Memory

5.3MiB live, 240.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

302×	`log1p-expm1-u`
302×	`expm1-log1p-u`
301×	`pow1`
299×	`add-exp-log`
296×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	504
1	690	494

Stop Event

1×	node limit

Counts

17 → 467

Calls

Call 1

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

simplify662.0ms (5.5%)

Memory

6.5MiB live, 560.1MiB allocated

Algorithm

1×	egg-herbie

Rules

721×	`associate-r`
636×	`associate-l`
381×	`associate-*r/`
326×	`times-frac`
292×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1170	8589968823
1	2664	8589966515

Stop Event

1×	node limit

Counts

795 → 735

Calls

Call 1

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

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

eval200.0ms (1.7%)

Memory: 9.5MiB live, 320.5MiB allocated
Compiler: Compiled 18 258 to 3 833 computations (79% saved)

prune151.0ms (1.3%)

Memory

20.1MiB live, 453.1MiB allocated

Pruning

28 alts after pruning (21 fresh and 7 done)

	Pruned	Kept	Total
New	957	14	971
Fresh	5	7	12
Picked	2	3	5
Done	1	4	5
Total	965	28	993

Accuracy

100.0%

Counts

993 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	30.6%	(pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
✓	99.6%	(/.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))
	52.4%	(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
	52.4%	(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
	42.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
✓	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
	42.4%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
	42.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))
	42.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
	89.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal -1 binary64))))))
	52.4%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	52.4%	(.f64 (sqrt.f64 (.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
✓	42.5%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	52.4%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
✓	89.4%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	89.5%	(sqrt.f64 (/.f64 (/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k)) k))
	42.2%	(sqrt.f64 (/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k))
	89.5%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n)) (neg.f64 k))) k))
	89.5%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k)))) k))
	42.2%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 (/.f64 k (PI.f64)) n)))
	42.2%	(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k)))
✓	42.2%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
	42.1%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
	42.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n (.f64 k (/.f64 #s(literal 1 binary64) (PI.f64))))))
	42.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) k) (/.f64 n (/.f64 #s(literal 1 binary64) (PI.f64))))))
	39.4%	(exp.f64 (.f64 (log.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (/.f64 (PI.f64) k))) #s(literal 1/2 binary64)))
✓	32.5%	(cbrt.f64 (pow.f64 (/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) k) #s(literal 3/2 binary64)))
	32.5%	(cbrt.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)))

Compiler

Compiled 1 038 to 496 computations (52.2% saved)

regimes187.0ms (1.6%)

Memory

-29.1MiB live, 139.7MiB allocated

Counts

54 → 1

Calls

Call 1

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

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

Calls

4 calls:

128.0ms	n
17.0ms	k
16.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
13.0ms	(.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)

regimes58.0ms (0.5%)

Memory

15.6MiB live, 94.2MiB allocated

Counts

45 → 1

Calls

Call 1

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

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

Calls

4 calls:

17.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
14.0ms	n
13.0ms	k
12.0ms	(.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
99.6%	1	`k`
99.6%	1	`n`
99.6%	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))))`
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes45.0ms (0.4%)

Memory

6.9MiB live, 84.5MiB allocated

Counts

35 → 2

Calls

Call 1

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

Outputs

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

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

Calls

4 calls:

12.0ms	n
11.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
10.0ms	k
9.0ms	(.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%	2	`k`
89.9%	1	`n`
99.7%	3	`(.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))))`
89.9%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes15.0ms (0.1%)

Memory

-19.1MiB live, 22.4MiB allocated

Counts

34 → 2

Calls

Call 1

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

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

1 calls:

13.0ms

Results

Accuracy	Segments	Branch
99.7%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes67.0ms (0.6%)

Memory

-11.0MiB live, 67.0MiB allocated

Counts

32 → 1

Calls

Call 1

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

Calls

4 calls:

35.0ms	(.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))))
10.0ms	n
10.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
9.0ms	k

Results

Accuracy	Segments	Branch
52.4%	1	`n`
52.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
52.4%	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))))`
52.4%	1	`k`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes26.0ms (0.2%)

Memory

10.2MiB live, 49.2MiB allocated

Counts

18 → 1

Calls

Call 1

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

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

Calls

4 calls:

7.0ms	k
6.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
6.0ms	n
5.0ms	(.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
52.4%	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))))`
52.4%	1	`k`
52.4%	1	`n`
52.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes21.0ms (0.2%)

Memory

-6.0MiB live, 35.4MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	k
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
4.0ms	(.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
52.4%	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))))`
52.4%	1	`k`
52.4%	1	`n`
52.4%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes19.0ms (0.2%)

Memory

2.1MiB live, 40.7MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	k
4.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
4.0ms	n
4.0ms	(.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
42.6%	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))))`
42.6%	1	`k`
42.6%	1	`n`
42.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes14.0ms (0.1%)

Memory

27.8MiB live, 27.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	n
3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
3.0ms	k
3.0ms	(.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
42.2%	1	`k`
42.2%	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))))`
42.2%	1	`n`
42.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes10.0ms (0.1%)

Memory

-20.8MiB live, 18.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

4 calls:

3.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	n
2.0ms	(.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))))
2.0ms	k

Results

Accuracy	Segments	Branch
42.2%	1	`k`
42.2%	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))))`
42.2%	1	`n`
42.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes7.0ms (0.1%)

Memory

15.3MiB live, 15.3MiB allocated

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
2.0ms	(.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))))
2.0ms	n
1.0ms	k

Results

Accuracy	Segments	Branch
42.1%	1	`k`
42.1%	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))))`
42.1%	1	`n`
42.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

bsearch12.0ms (0.1%)

Memory

-21.2MiB live, 18.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	4.151490039790687e-75	8.812476852365914e-75

Samples

7.0ms

80×

valid

Compiler

Compiled 166 to 133 computations (19.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 1.0ms (18.6% of total)

ival-mult: 1.0ms (18.6% of total)

ival-sqrt: 1.0ms (18.6% of total)

ival-pow: 1.0ms (18.6% of total)

ival-pi: 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)

exact: 0.0ms (0% of total)

bsearch18.0ms (0.1%)

Memory

24.4MiB live, 24.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	1.2527655510165586e-17	7.303153925885367e-15

Samples

12.0ms

128×

valid

Compiler

Compiled 237 to 194 computations (18.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 2.0ms (23.7% of total)

ival-mult: 2.0ms (23.7% of total)

ival-pow: 2.0ms (23.7% of total)

ival-sub: 1.0ms (11.9% of total)

ival-sqrt: 1.0ms (11.9% of total)

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

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

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

exact: 0.0ms (0% of total)

simplify67.0ms (0.6%)

Memory

-29.1MiB live, 15.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	546
1	97	546
2	107	546
3	113	546
4	117	546
5	118	546

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 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))
(if (<=.f64 k #s(literal 8962958295871739/1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))))
(if (<=.f64 k #s(literal 2271629875608987/40564819207303340847894502572032 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k)) (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 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k)))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))

Outputs
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 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))
(if (<=.f64 k #s(literal 8962958295871739/1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k))))))
(if (<=.f64 k #s(literal 8962958295871739/1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))))
(if (<=.f64 k #s(literal 2271629875608987/40564819207303340847894502572032 binary64)) (/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (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 2271629875608987/40564819207303340847894502572032 binary64)) (/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (sqrt.f64 k))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k)))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))

soundness2.4s (19.9%)

Memory

13.0MiB live, 2 248.5MiB allocated

Rules

1 096×	`log1p-expm1-u`
721×	`associate-r`
718×	`fma-define`
636×	`associate-l`
600×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	600	19256
1	1218	17586
2	4112	16578
0	42	508
1	762	495
0	1134	37641
1	2530	36531
2	6932	34227
0	1170	8589968823
1	2664	8589966515
0	26	274
1	427	270
2	4798	270
0	45	491
1	800	459
0	803	25394
1	1741	24840
2	5545	23472
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	40	504
1	690	494

Stop Event

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

Compiler

Compiled 1 482 to 547 computations (63.1% saved)

preprocess61.0ms (0.5%)

Memory: 16.4MiB live, 131.2MiB allocated
Compiler: Compiled 328 to 146 computations (55.5% 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	45	942
1	71	922
2	106	922
3	136	902
4	176	900
5	222	894
6	345	894
7	528	894
8	613	894
9	638	894
10	639	894

Iter	Nodes	Cost
0	41	798
1	70	782
2	100	776
3	123	776
4	144	776
5	154	776
6	165	776
7	184	776
8	202	776
9	206	776

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	45	942
1	71	922
2	106	922
3	136	902
4	176	900
5	222	894
6	345	894
7	528	894
8	613	894
9	638	894
10	639	894

Iter	Nodes	Cost
0	41	798
1	70	782
2	100	776
3	123	776
4	144	776
5	154	776
6	165	776
7	184	776
8	202	776
9	206	776

analyze193.0ms (1.6%)

sample3.8s (31.5%)

preprocess138.0ms (1.2%)

explain158.0ms (1.3%)

eval1.0ms (0%)

prune2.0ms (0%)

simplify22.0ms (0.2%)

localize78.0ms (0.7%)

series89.0ms (0.7%)

rewrite332.0ms (2.8%)

simplify221.0ms (1.9%)

eval55.0ms (0.5%)

prune71.0ms (0.6%)

simplify48.0ms (0.4%)

localize154.0ms (1.3%)

series130.0ms (1.1%)

rewrite123.0ms (1%)

simplify311.0ms (2.6%)

eval106.0ms (0.9%)

prune110.0ms (0.9%)

simplify140.0ms (1.2%)

localize132.0ms (1.1%)

series53.0ms (0.4%)

rewrite160.0ms (1.3%)

simplify488.0ms (4.1%)

eval140.0ms (1.2%)

prune230.0ms (1.9%)

simplify35.0ms (0.3%)

localize135.0ms (1.1%)

series162.0ms (1.4%)

rewrite148.0ms (1.2%)

simplify662.0ms (5.5%)

eval200.0ms (1.7%)

prune151.0ms (1.3%)

regimes187.0ms (1.6%)

regimes58.0ms (0.5%)

regimes45.0ms (0.4%)

regimes15.0ms (0.1%)

regimes67.0ms (0.6%)

regimes26.0ms (0.2%)

regimes21.0ms (0.2%)

regimes19.0ms (0.2%)

regimes14.0ms (0.1%)

regimes10.0ms (0.1%)

regimes7.0ms (0.1%)

bsearch12.0ms (0.1%)

bsearch18.0ms (0.1%)

simplify67.0ms (0.6%)

soundness2.4s (19.9%)

preprocess61.0ms (0.5%)

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

Iter	Nodes	Cost
0	45	942
1	71	922
2	106	922
3	136	902
4	176	900
5	222	894
6	345	894
7	528	894
8	613	894
9	638	894
10	639	894

Iter	Nodes	Cost
0	41	798
1	70	782
2	100	776
3	123	776
4	144	776
5	154	776
6	165	776
7	184	776
8	202	776
9	206	776