Metrics for Migdal et al, Equation (51)

analyze128.0ms (0.9%)

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%	50%	1.6%	7
52.5%	25%	22.6%	0.1%	0%	50%	2.3%	8
53.8%	25%	21.5%	0.1%	0%	50%	3.5%	9
54.5%	25%	20.9%	0.1%	0%	50%	4.1%	10
55.3%	25%	20.2%	0.1%	0%	50%	4.8%	11
55.7%	25%	19.9%	0.1%	0%	50%	5.1%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.3s (24.2%)

Samples

1.4s	5 357×	1	invalid
1.0s	8 256×	0	valid
158.0ms	477×	2	invalid
75.0ms	661×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-pow: 543.0ms (29.2% of total)

ival-mult: 426.0ms (22.9% of total)

ival-div: 401.0ms (21.6% of total)

ival-sqrt: 137.0ms (7.4% of total)

ival-sub: 124.0ms (6.7% of total)

adjust: 103.0ms (5.5% of total)

ival-pi: 85.0ms (4.6% of total)

...in/eval/compile.rkt:70:19: 17.0ms (0.9% of total)

ival-true: 13.0ms (0.7% of total)

ival-assert: 9.0ms (0.5% of total)

Bogosity

preprocess234.0ms (1.7%)

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))

explain171.0ms (1.3%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
5	84	(6.496109365397061e-65 1.4036253557647745e-218)	-	`(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	88	26
`pow.f64`	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	oflow-rescue	1	0
↳	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`	overflow	1
↳	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`	overflow	63

Confusion

	Predicted +	Predicted -
+	5	0
-	84	167

Precision

0.056179775280898875

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	0	0
-	84	26	141

Precision?

0.043478260869565216

Recall?

1.0

Freqs

test

number	freq
0	167
1	89

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

74.0ms

512×

valid

Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-pow: 16.0ms (36.5% of total)

ival-mult: 9.0ms (20.6% of total)

ival-div: 8.0ms (18.3% of total)

ival-sqrt: 4.0ms (9.1% of total)

ival-sub: 3.0ms (6.9% of total)

ival-pi: 2.0ms (4.6% of total)

ival-true: 1.0ms (2.3% of total)

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

...in/eval/compile.rkt:70:19: 0.0ms (0% of total)

eval1.0ms (0%)

Compiler: Compiled 59 to 23 computations (61% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.1%	(.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))))

Status

Accuracy

Program

▶

99.2%

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

▶

99.1%

(*.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))))

Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify24.0ms (0.2%)

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)

localize116.0ms (0.8%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(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)))) (sqrt.f64 k))
✓	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.4%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	accuracy	99.7%	(.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 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.4%	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))

Samples

64.0ms

256×

valid

Compiler

Compiled 104 to 22 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-div: 13.0ms (32.6% of total)

ival-pow: 13.0ms (32.6% of total)

ival-mult: 7.0ms (17.6% of total)

ival-sub: 3.0ms (7.5% of total)

ival-sqrt: 2.0ms (5% of total)

ival-pi: 1.0ms (2.5% of total)

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

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

...in/eval/compile.rkt:70:19: 0.0ms (0% of total)

series242.0ms (1.8%)

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 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) 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 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 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))>

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 (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))))>
#<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))))>
#<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)))))>
#<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)))))>
#<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)))))>
#<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)))))>
#<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)))))>
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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))))>
#<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 (.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)))))>
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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)))))>

Calls

42 calls:

Time	Variable		Point	Expression
32.0ms	n	@	0	(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
24.0ms	n	@	-inf	(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
7.0ms	n	@	inf	(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))
4.0ms	n	@	inf	(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
1.0ms	k	@	0	(pow (* (* 2 (PI)) n) (/ (- 1 k) 2))

rewrite577.0ms (4.2%)

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))
(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))))
(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))

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

simplify351.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-define`
421×	`associate-r`
353×	`associate-l`
344×	`exp-prod`
258×	`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 → 413

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

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

eval160.0ms (1.2%)

Compiler: Compiled 9 659 to 1 552 computations (83.9% saved)

prune70.0ms (0.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	449	15	464
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	450	16	466

Accuracy

100.0%

Counts

466 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.9%	(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))
✓	99.2%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (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))))
	74.3%	(/.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))))
▶	99.3%	(/.f64 (/.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 k))
	95.9%	(/.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))
	99.1%	(/.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))))))
▶	99.1%	(.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)))
	75.1%	(.f64 (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 n (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k)))
	98.3%	(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 (sqrt.f64 k)) #s(literal 3 binary64))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	49.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	75.0%	(.f64 (.f64 (pow.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))))) (pow.f64 n (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
	40.8%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	99.1%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	40.8%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
	90.5%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Compiler

Compiled 544 to 402 computations (26.1% saved)

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	256	(/.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))))
✓	cost-diff	6528	(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	cost-diff	0	(sqrt.f64 k)
	cost-diff	64	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(*.f64 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 n (/.f64 (PI.f64) k))
✓	cost-diff	0	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
✓	cost-diff	0	(/.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))))
✓	cost-diff	0	(/.f64 (/.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 k))

Rules

41×	`*-commutative`
39×	`fmm-def`
38×	`times-frac`
32×	`associate-l`
29×	`associate-r`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	44	859
1	77	829
2	120	829
3	155	829
4	184	829
5	211	829
6	246	825
7	278	825
8	299	825
9	311	825
10	340	825
11	399	825
12	470	825
13	509	825
14	534	825
15	551	825
16	575	825
17	606	825
18	615	825

Stop Event

1×

saturated

Calls

Call 1

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

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

localize293.0ms (2.1%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
	accuracy	99.7%	(*.f64 (PI.f64) n)
	accuracy	99.4%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	accuracy	94.4%	(exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64)))
	accuracy	76.5%	(PI.f64)
✓	accuracy	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.5%	(sqrt.f64 (*.f64 n (PI.f64)))
	accuracy	76.5%	(PI.f64)
	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
✓	accuracy	99.4%	(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	76.5%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (PI.f64) k)
✓	accuracy	99.5%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
✓	accuracy	90.7%	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
	accuracy	76.5%	(PI.f64)
✓	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	99.6%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (*.f64 k #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))
	accuracy	76.5%	(PI.f64)

Samples

113.0ms	62×	5	exit
113.0ms	194×	0	valid

Compiler

Compiled 249 to 40 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 148.0ms

ival-mult: 35.0ms (23.7% of total)

ival-pow: 34.0ms (23% of total)

ival-div: 32.0ms (21.7% of total)

adjust: 25.0ms (16.9% of total)

ival-sqrt: 10.0ms (6.8% of total)

ival-log: 4.0ms (2.7% of total)

ival-exp: 3.0ms (2% of total)

ival-sub: 2.0ms (1.4% of total)

ival-pi: 2.0ms (1.4% of total)

ival-add: 2.0ms (1.4% of total)

...in/eval/compile.rkt:70:19: 1.0ms (0.7% of total)

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

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

series202.0ms (1.5%)

Counts

20 → 296

Calls

Call 1

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

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

87 calls:

Time	Variable		Point	Expression
154.0ms	k	@	0	(/ (sqrt (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) (* k 1/2)))
3.0ms	k	@	0	(* (pow (* 2 (* (PI) n)) (+ 1/2 (* k -1/2))) (pow k -1/2))
2.0ms	n	@	0	(/ (/ (sqrt (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) (* k 1/2))) (sqrt k))
2.0ms	k	@	0	(/ (/ (sqrt (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) (* k 1/2))) (sqrt k))
2.0ms	n	@	inf	(/ (/ (sqrt (* 2 (* n (PI)))) (pow (* 2 (* n (PI))) (* k 1/2))) (sqrt k))

rewrite234.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

316×	`associate-r`
290×	`log1p-expm1-u`
290×	`expm1-log1p-u`
276×	`add-exp-log`
276×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	522
1	797	496

Stop Event

1×	node limit

Counts

20 → 562

Calls

Call 1

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

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

simplify673.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

947×	`fma-define`
580×	`times-frac`
488×	`*-commutative`
270×	`associate-/l*`
228×	`associate-/r*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1057	37986
1	2269	36679
2	7118	36619

Stop Event

1×	node limit

Counts

858 → 691

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

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

eval179.0ms (1.3%)

Compiler: Compiled 20 554 to 3 375 computations (83.6% saved)

prune279.0ms (2%)

Pruning

24 alts after pruning (20 fresh and 4 done)

	Pruned	Kept	Total
New	1 005	17	1 022
Fresh	7	3	10
Picked	2	3	5
Done	0	1	1
Total	1 014	24	1 038

Accuracy

100.0%

Counts

1 038 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.9%	(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))
	40.2%	(pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))) #s(literal 3 binary64))
	98.9%	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) k))) #s(literal 2 binary64)) (sqrt.f64 k))
	95.4%	(/.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 (exp.f64 #s(literal 1/2 binary64)) (log.f64 k)))
✓	99.2%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.3%	(/.f64 (/.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 k))
	99.1%	(/.f64 (/.f64 #s(literal 1 binary64) (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))))
▶	49.7%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))
▶	99.3%	(/.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))))
	95.9%	(/.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))
▶	49.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
	99.1%	(/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (-.f64 (.f64 k #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 k)))
✓	99.1%	(.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)))
	49.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) n) (PI.f64))))
▶	50.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
	40.8%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
	40.8%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 n (PI.f64))))))
✓	40.8%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
	40.8%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
	90.5%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	40.9%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))
	40.9%	(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
▶	41.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
	38.4%	(exp.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k))))

Compiler

Compiled 631 to 491 computations (22.2% saved)

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

25×	`*-commutative`
15×	`associate-r`
15×	`associate-l`
7×	`associate-/l*`
4×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	702
1	57	702
2	81	702
3	99	702
4	121	702
5	129	702
6	132	702

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

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

localize208.0ms (1.5%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
	accuracy	99.7%	(/.f64 (PI.f64) k)
✓	accuracy	99.6%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
✓	accuracy	99.5%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)))
	accuracy	76.5%	(PI.f64)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
✓	accuracy	99.6%	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))))
✓	accuracy	99.5%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
	accuracy	76.5%	(PI.f64)
✓	accuracy	99.7%	(.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))
✓	accuracy	99.6%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))
✓	accuracy	99.5%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))
	accuracy	76.5%	(PI.f64)
✓	accuracy	99.8%	(/.f64 k (PI.f64))
✓	accuracy	99.7%	(/.f64 n (/.f64 k (PI.f64)))
✓	accuracy	90.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
	accuracy	76.5%	(PI.f64)
✓	accuracy	99.7%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	99.6%	(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
✓	accuracy	99.5%	(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
	accuracy	76.5%	(PI.f64)

Samples

89.0ms	62×	5	exit
63.0ms	194×	0	valid

Compiler

Compiled 192 to 31 computations (83.9% saved)

Precisions

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

ival-sqrt: 21.0ms (26.5% of total)

adjust: 20.0ms (25.2% of total)

ival-mult: 14.0ms (17.7% of total)

ival-div: 13.0ms (16.4% of total)

ival-pow: 8.0ms (10.1% of total)

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

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

...in/eval/compile.rkt:70:19: 0.0ms (0% of total)

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

series120.0ms (0.9%)

Counts

17 → 292

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

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

Calls

81 calls:

Time	Variable		Point	Expression
75.0ms	k	@	-inf	(* 2 (/ n (/ k (PI))))
5.0ms	k	@	-inf	(* (sqrt (/ (PI) k)) (sqrt n))
4.0ms	n	@	0	(/ (sqrt (* (PI) (* n 2))) (sqrt (* k (pow (* (PI) (* n 2)) k))))
4.0ms	k	@	0	(/ (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))))

rewrite303.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

404×	`log1p-expm1-u`
253×	`associate-r`
228×	`expm1-log1p-u`
227×	`add-exp-log`
227×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	436
1	617	436
2	7539	436

Stop Event

1×	node limit

Counts

17 → 728

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

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

simplify409.0ms (3%)

Algorithm

1×	egg-herbie

Rules

670×	`associate-r`
634×	`times-frac`
609×	`associate-l`
359×	`associate-/l*`
291×	`associate-*r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1104	40162
1	2343	38903

Stop Event

1×	node limit

Counts

1 020 → 684

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

eval131.0ms (1%)

Compiler: Compiled 15 467 to 3 077 computations (80.1% saved)

prune315.0ms (2.3%)

Pruning

31 alts after pruning (27 fresh and 4 done)

	Pruned	Kept	Total
New	925	25	950
Fresh	13	2	15
Picked	2	3	5
Done	3	1	4
Total	943	31	974

Accuracy

100.0%

Counts

974 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.8%	(pow.f64 (pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	41.6%	(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
✓	99.2%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	49.7%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)))
✓	49.7%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))
	50.1%	(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
✓	49.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
	40.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))))
	41.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
	41.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
▶	91.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k) (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))
	49.6%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	50.1%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	40.8%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	50.0%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
▶	50.0%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
	40.8%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
	90.5%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	40.9%	(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
	76.6%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)))
	40.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	90.6%	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (/.f64 (.f64 n #s(literal 2 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))))
	40.9%	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
	40.9%	(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
	40.9%	(sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
✓	41.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
▶	40.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
▶	40.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))
	38.4%	(exp.f64 (.f64 (log.f64 (.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))) #s(literal 1/2 binary64)))
▶	31.6%	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
	31.6%	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)))

Compiler

Compiled 718 to 564 computations (21.4% saved)

simplify26.0ms (0.2%)

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) (.f64 n (/.f64 #s(literal 2 binary64) k)))
✓	cost-diff	0	(pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64))
✓	cost-diff	0	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
✓	cost-diff	0	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
✓	cost-diff	0	(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
✓	cost-diff	0	(sqrt.f64 n)
✓	cost-diff	0	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	128	(.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))
✓	cost-diff	128	(.f64 #s(literal 2 binary64) (.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k)))
✓	cost-diff	128	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))
✓	cost-diff	0	(/.f64 n k)
✓	cost-diff	0	(*.f64 (/.f64 n k) (PI.f64))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64)))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
✓	cost-diff	0	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k) (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 k (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k) (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
✓	cost-diff	0	(sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k) (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k) (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))

Rules

84×	`times-frac`
66×	`associate-/r*`
56×	`associate-r`
47×	`associate-*r/`
40×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	771
1	73	771
2	143	771
3	309	771
4	454	771
5	466	771

Stop Event

1×

saturated

Calls

Call 1

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

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

localize184.0ms (1.4%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(*.f64 n (/.f64 #s(literal 2 binary64) k))
✓	accuracy	99.6%	(.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k)))
✓	accuracy	77.6%	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
	accuracy	76.5%	(PI.f64)
✓	accuracy	99.8%	(sqrt.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))
✓	accuracy	99.6%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
✓	accuracy	99.6%	(*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))
	accuracy	76.5%	(PI.f64)
	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(.f64 (.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))
✓	accuracy	90.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))
	accuracy	76.5%	(PI.f64)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64)))
✓	accuracy	99.6%	(*.f64 (/.f64 n k) (PI.f64))
✓	accuracy	90.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
	accuracy	76.5%	(PI.f64)
	accuracy	99.6%	(pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
✓	accuracy	99.5%	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k) (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	accuracy	91.4%	(sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k) (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))
	accuracy	76.5%	(PI.f64)

Samples

65.0ms	194×	0	valid
21.0ms	62×	0	invalid

Compiler

Compiled 216 to 33 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 17.0ms (33.8% of total)

ival-pow: 13.0ms (25.8% of total)

ival-sqrt: 9.0ms (17.9% of total)

ival-div: 8.0ms (15.9% of total)

ival-cbrt: 2.0ms (4% of total)

ival-pi: 1.0ms (2% of total)

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

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

...in/eval/compile.rkt:70:19: 0.0ms (0% of total)

series111.0ms (0.8%)

Counts

19 → 388

Calls

Call 1

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

Outputs
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 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 1/2 binary64))))) (.f64 (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) k)>
#<alt (/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 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 (+.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)))))) (sqrt.f64 #s(literal 1/2 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 1/2 binary64)))))))) k)>
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#<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)))>
#<alt (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.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)))))>
#<alt (.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)))))>
#<alt (.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)))))>
#<alt (.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)))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (cbrt.f64 (sqrt.f64 #s(literal 8 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (cbrt.f64 (sqrt.f64 #s(literal -8 binary64))) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (cbrt.f64 (sqrt.f64 #s(literal -8 binary64))) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (cbrt.f64 (sqrt.f64 #s(literal -8 binary64))) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (cbrt.f64 (sqrt.f64 #s(literal -8 binary64))) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))) (*.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.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)))) (*.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.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)))) (*.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.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)))) (*.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))>
#<alt (.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)))) (.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.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)))) (.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.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)))) (.f64 (sqrt.f64 #s(literal -8 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.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)))) (.f64 (sqrt.f64 #s(literal -8 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 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>
#<alt (*.f64 #s(literal 2 binary64) (/.f64 n k))>

Calls

105 calls:

Time	Variable		Point	Expression
32.0ms	n	@	inf	(* k (/ (pow (* (PI) (* n 2)) k) (* (PI) (* n 2))))
5.0ms	n	@	-inf	(* k (/ (pow (* (PI) (* n 2)) k) (* (PI) (* n 2))))
4.0ms	n	@	0	(sqrt (* k (/ (pow (* (PI) (* n 2)) k) (* (PI) (* n 2)))))
3.0ms	k	@	0	(cbrt (pow (* (PI) (* n (/ 2 k))) 3/2))
3.0ms	n	@	0	(pow (* (PI) (* n (/ 2 k))) 3/2)

rewrite312.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

308×	`associate-r`
244×	`log1p-expm1-u`
244×	`expm1-log1p-u`
242×	`add-exp-log`
242×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	601
1	632	529
2	7797	529

Stop Event

1×	node limit

Counts

19 → 598

Calls

Call 1

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

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

simplify471.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

716×	`associate-r`
706×	`associate-l`
393×	`times-frac`
290×	`associate-*r/`
275×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1055	12884941270
1	2372	12884940232

Stop Event

1×	node limit

Counts

986 → 645

Calls

Call 1

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

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

eval297.0ms (2.2%)

Compiler: Compiled 14 661 to 3 189 computations (78.2% saved)

prune212.0ms (1.5%)

Pruning

39 alts after pruning (31 fresh and 8 done)

	Pruned	Kept	Total
New	808	12	820
Fresh	3	19	22
Picked	0	5	5
Done	1	3	4
Total	812	39	851

Accuracy

100.0%

Counts

851 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.8%	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	40.8%	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	29.8%	(pow.f64 (pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	41.6%	(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
	91.1%	(pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 k #s(literal 1 binary64)))) #s(literal -1/2 binary64))
	49.7%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64)))
	40.7%	(/.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	49.7%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64))) (sqrt.f64 k))
	50.1%	(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
✓	49.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)))))
	40.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))))
	41.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 n (PI.f64)))))
✓	91.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k) (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))))
	41.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))))))
	41.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64)))))
	49.6%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	50.1%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	40.8%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	49.6%	(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 (/.f64 #s(literal 2 binary64) k)))
	50.0%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
	40.7%	(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 n k))))
	50.0%	(.f64 (sqrt.f64 n) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) #s(literal 2 binary64))))))
✓	50.0%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
	40.8%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))))
	90.5%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	40.9%	(sqrt.f64 (/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) k) (/.f64 #s(literal 1 binary64) (PI.f64))))
	76.6%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)))
	40.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 (PI.f64) n))))
	90.6%	(sqrt.f64 (.f64 (/.f64 (PI.f64) k) (/.f64 (.f64 n #s(literal 2 binary64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))))
	40.9%	(sqrt.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))))
	40.9%	(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
	40.9%	(sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
	40.9%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))
✓	41.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
✓	40.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
✓	40.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (*.f64 (PI.f64) n) (/.f64 #s(literal 1 binary64) k))))
	38.4%	(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 n (/.f64 #s(literal 2 binary64) k)))) #s(literal 1/2 binary64)))
✓	31.6%	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
	31.6%	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)))

Compiler

Compiled 1 322 to 624 computations (52.8% saved)

regimes169.0ms (1.2%)

Counts

71 → 1

Calls

Call 1

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

Outputs
(/.f64 (/.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 k))

Calls

4 calls:

87.0ms	k
31.0ms	(.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))))
23.0ms	n
21.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
99.3%	1	`k`
99.3%	1	`n`
99.3%	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))))`
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes97.0ms (0.7%)

Counts

66 → 1

Calls

Call 1

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

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:

34.0ms	k
20.0ms	n
19.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms	(.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
99.3%	1	`k`
99.3%	1	`n`
99.3%	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))))`
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes271.0ms (2%)

Counts

63 → 1

Calls

Call 1

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

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:

55.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
48.0ms	n
19.0ms	k
15.0ms	(.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
99.2%	1	`k`
99.2%	1	`n`
99.2%	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))))`
99.2%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes32.0ms (0.2%)

Counts

46 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

16.0ms	k
13.0ms	n

Results

Accuracy	Segments	Branch
99.6%	2	`k`
91.1%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes21.0ms (0.2%)

Counts

45 → 2

Calls

Call 1

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

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

Calls

1 calls:

17.0ms

Results

Accuracy	Segments	Branch
99.6%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes40.0ms (0.3%)

Counts

44 → 1

Calls

Call 1

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

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

Calls

2 calls:

20.0ms	n
17.0ms	k

Results

Accuracy	Segments	Branch
50.1%	1	`n`
50.1%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes20.0ms (0.1%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

2 calls:

10.0ms	k
7.0ms	n

Results

Accuracy	Segments	Branch
50.0%	1	`n`
50.0%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes15.0ms (0.1%)

Counts

20 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	k
6.0ms	n

Results

Accuracy	Segments	Branch
41.6%	1	`n`
41.6%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	k
3.0ms	n

Results

Accuracy	Segments	Branch
41.0%	1	`k`
41.0%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	k
1.0ms	n

Results

Accuracy	Segments	Branch
40.9%	1	`k`
40.9%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch20.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	2.1195879767510408e-34	1.0038514690874656e-32

Samples

12.0ms

112×

valid

Compiler

Compiled 217 to 179 computations (17.5% saved)

Precisions

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

ival-div: 2.0ms (24.7% of total)

ival-mult: 2.0ms (24.7% of total)

ival-pow: 2.0ms (24.7% of total)

ival-sub: 1.0ms (12.4% of total)

ival-sqrt: 1.0ms (12.4% of total)

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

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

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

...in/eval/compile.rkt:70:19: 0.0ms (0% of total)

bsearch18.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	2.1195879767510408e-34	1.0038514690874656e-32

Samples

11.0ms

112×

valid

Compiler

Compiled 210 to 172 computations (18.1% saved)

Precisions

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

ival-div: 2.0ms (25.2% of total)

ival-mult: 2.0ms (25.2% of total)

ival-pow: 2.0ms (25.2% of total)

ival-sub: 1.0ms (12.6% of total)

ival-sqrt: 1.0ms (12.6% of total)

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

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

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

...in/eval/compile.rkt:70:19: 0.0ms (0% of total)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative`
11×	`unsub-neg`
10×	`neg-mul-1`
8×	`+-commutative`
7×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	545
1	94	545
2	107	545
3	118	545
4	135	545
5	160	545
6	161	545

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (/.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 k))
(/.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 7599808514120695/5846006549323611672814739330865132078623730171904 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 k #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 5378326025377723/11692013098647223345629478661730264157247460343808 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #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 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 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))))

Outputs
(/.f64 (/.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 k))
(/.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 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) 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 n (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 7599808514120695/5846006549323611672814739330865132078623730171904 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (-.f64 k #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 7599808514120695/5846006549323611672814739330865132078623730171904 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (-.f64 k #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 7599808514120695/5846006549323611672814739330865132078623730171904 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (pow.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 5378326025377723/11692013098647223345629478661730264157247460343808 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #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)))
(if (<=.f64 k #s(literal 5378326025377723/11692013098647223345629478661730264157247460343808 binary64)) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n))) (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 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 #s(literal 2 binary64) n)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n)) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 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))))

soundness2.4s (17.3%)

Rules

1 096×	`log1p-expm1-u`
947×	`fma-define`
718×	`fma-define`
670×	`associate-r`
634×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1057	37986
1	2269	36679
2	7118	36619
0	44	522
1	797	496
0	37	601
1	632	529
2	7797	529
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	1104	40162
1	2343	38903
0	35	436
1	617	436
2	7539	436
0	600	19256
1	1218	17586
2	4112	16578
0	26	274
1	427	270
2	4798	270

Stop Event

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

Compiler

Compiled 1 682 to 538 computations (68% saved)

preprocess72.0ms (0.5%)

Compiler: Compiled 328 to 146 computations (55.5% saved)

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	44	859
1	77	829
2	120	829
3	155	829
4	184	829
5	211	829
6	246	825
7	278	825
8	299	825
9	311	825
10	340	825
11	399	825
12	470	825
13	509	825
14	534	825
15	551	825
16	575	825
17	606	825
18	615	825

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	44	859
1	77	829
2	120	829
3	155	829
4	184	829
5	211	829
6	246	825
7	278	825
8	299	825
9	311	825
10	340	825
11	399	825
12	470	825
13	509	825
14	534	825
15	551	825
16	575	825
17	606	825
18	615	825

analyze128.0ms (0.9%)

sample3.3s (24.2%)

preprocess234.0ms (1.7%)

explain171.0ms (1.3%)

eval1.0ms (0%)

prune2.0ms (0%)

simplify24.0ms (0.2%)

localize116.0ms (0.8%)

series242.0ms (1.8%)

rewrite577.0ms (4.2%)

simplify351.0ms (2.6%)

eval160.0ms (1.2%)

prune70.0ms (0.5%)

simplify82.0ms (0.6%)

localize293.0ms (2.1%)

series202.0ms (1.5%)

rewrite234.0ms (1.7%)

simplify673.0ms (4.9%)

eval179.0ms (1.3%)

prune279.0ms (2%)

simplify76.0ms (0.6%)

localize208.0ms (1.5%)

series120.0ms (0.9%)

rewrite303.0ms (2.2%)

simplify409.0ms (3%)

eval131.0ms (1%)

prune315.0ms (2.3%)

simplify26.0ms (0.2%)

localize184.0ms (1.4%)

series111.0ms (0.8%)

rewrite312.0ms (2.3%)

simplify471.0ms (3.4%)

eval297.0ms (2.2%)

prune212.0ms (1.5%)

regimes169.0ms (1.2%)

regimes97.0ms (0.7%)

regimes271.0ms (2%)

regimes32.0ms (0.2%)

regimes21.0ms (0.2%)

regimes40.0ms (0.3%)

regimes20.0ms (0.1%)

regimes15.0ms (0.1%)

regimes8.0ms (0.1%)

regimes3.0ms (0%)

bsearch20.0ms (0.1%)

bsearch18.0ms (0.1%)

simplify11.0ms (0.1%)

soundness2.4s (17.3%)

preprocess72.0ms (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	44	859
1	77	829
2	120	829
3	155	829
4	184	829
5	211	829
6	246	825
7	278	825
8	299	825
9	311	825
10	340	825
11	399	825
12	470	825
13	509	825
14	534	825
15	551	825
16	575	825
17	606	825
18	615	825