Metrics for Migdal et al, Equation (51)

analyze119.0ms (0.9%)

Memory

11.9MiB live, 165.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	51.5%	0%	7
52.5%	25%	22.6%	0.1%	0%	52.3%	0%	8
53.8%	25%	21.5%	0.1%	0%	53.5%	0%	9
54.5%	25%	20.9%	0.1%	0%	54%	0%	10
55.3%	25%	20.2%	0.1%	0%	54.7%	0%	11
55.7%	25%	19.9%	0.1%	0%	55.1%	0%	12

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.2s (23.3%)

Memory

27.5MiB live, 4 877.9MiB allocated

Samples

1.1s	5 517×	1	invalid
977.0ms	8 256×	0	valid
136.0ms	468×	2	invalid
31.0ms	262×	0	exit
30.0ms	393×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

ival-pow: 469.0ms (28.3% of total)

ival-mult: 384.0ms (23.2% of total)

ival-div: 324.0ms (19.6% of total)

ival-sqrt: 146.0ms (8.8% of total)

ival-sub: 108.0ms (6.5% of total)

adjust: 101.0ms (6.1% of total)

ival-pi: 90.0ms (5.4% of total)

...in/eval/compile.rkt:110:19: 17.0ms (1% of total)

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

ival-assert: 6.0ms (0.4% of total)

Bogosity

preprocess137.0ms (1%)

Memory

25.2MiB live, 143.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

explain362.0ms (2.7%)

Memory

9.2MiB live, 368.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
2	82	(1.000600173140061e-112 1.827893043522838e-133)	-	`(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	84	23

Confusion

	Predicted +	Predicted -
+	2	0
-	82	172

Precision

0.023809523809523808

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	82	23	149

Precision?

0.018691588785046728

Recall?

1.0

Freqs

test

number	freq
0	172
1	84

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

128.0ms

512×

valid

Compiler

Compiled 148 to 56 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 109.0ms

ival-div: 78.0ms (71.4% of total)

ival-pow: 12.0ms (11% of total)

ival-mult: 8.0ms (7.3% of total)

ival-sub: 4.0ms (3.7% of total)

ival-sqrt: 4.0ms (3.7% of total)

ival-pi: 2.0ms (1.8% of total)

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

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

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

eval1.0ms (0%)

Memory: 2.4MiB live, 2.4MiB allocated
Compiler: Compiled 59 to 23 computations (61% saved)

prune3.0ms (0%)

Memory

-33.7MiB live, 5.5MiB allocated

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

99.6%

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

▶

99.6%

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

Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify21.0ms (0.2%)

Memory

8.8MiB live, 48.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

localize116.0ms (0.9%)

Memory

-0.6MiB live, 157.0MiB allocated

Localize:

Found 8 expressions of interest:

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

Samples

43.0ms

256×

valid

Compiler

Compiled 104 to 22 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-pow: 9.0ms (30.5% of total)

ival-div: 7.0ms (23.7% of total)

ival-mult: 7.0ms (23.7% of total)

ival-sub: 3.0ms (10.2% of total)

ival-sqrt: 2.0ms (6.8% of total)

ival-pi: 1.0ms (3.4% of total)

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

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

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

series95.0ms (0.7%)

Memory

13.9MiB live, 210.4MiB allocated

Counts

12 → 160

Calls

Call 1

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

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

Calls

42 calls:

Time	Variable		Point	Expression
34.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
24.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
9.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
6.0ms	n	@	-inf	(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))
2.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite542.0ms (4%)

Memory

-14.9MiB live, 477.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

12 → 299

Calls

Call 1

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

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

simplify413.0ms (3%)

Memory

11.5MiB live, 368.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

459 → 408

Calls

Call 1

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

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

eval110.0ms (0.8%)

Memory: -10.7MiB live, 106.8MiB allocated
Compiler: Compiled 9 568 to 1 524 computations (84.1% saved)

prune74.0ms (0.5%)

Memory

-6.5MiB live, 151.1MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	444	15	459
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	445	16	461

Accuracy

100.0%

Counts

461 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(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))
▶	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	96.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
	78.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
	99.5%	(/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
▶	99.8%	(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
	99.7%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
▶	99.7%	(.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)))
	99.5%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (sqrt.f64 k)))
▶	45.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	35.0%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	35.0%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	88.8%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Compiler

Compiled 558 to 404 computations (27.6% saved)

simplify41.0ms (0.3%)

Memory

18.0MiB live, 55.8MiB allocated

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)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	cost-diff	6528	(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	cost-diff	0	(sqrt.f64 k)
	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(*.f64 k #s(literal -1/2 binary64))
	cost-diff	0	(PI.f64)
	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(/.f64 (PI.f64) k)
✓	cost-diff	0	(*.f64 n (/.f64 (PI.f64) k))
✓	cost-diff	0	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
✓	cost-diff	0	(pow.f64 k #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓	cost-diff	0	(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))

Rules

43×	`associate-r`
32×	`associate-l`
25×	`*-commutative`
25×	`associate-*r/`
15×	`associate-/l*`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	840
1	71	808
2	115	806
3	152	806
4	188	802
5	262	802
6	312	802
7	329	802
8	340	802
9	343	802

Stop Event

1×

saturated

Calls

Call 1

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

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

localize220.0ms (1.6%)

Memory

4.6MiB live, 281.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	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)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.4%	(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
	accuracy	75.4%	(PI.f64)
✓	accuracy	99.6%	(*.f64 n (PI.f64))
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	accuracy	75.4%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
✓	accuracy	99.7%	(.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	99.6%	(*.f64 (PI.f64) n)
	accuracy	75.4%	(PI.f64)
✓	accuracy	99.7%	(*.f64 n (/.f64 (PI.f64) k))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	89.2%	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
	accuracy	75.4%	(PI.f64)
✓	accuracy	99.8%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
	accuracy	75.4%	(PI.f64)

Samples

80.0ms	65×	0	exit
66.0ms	191×	0	valid

Compiler

Compiled 244 to 39 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 123.0ms

ival-sqrt: 65.0ms (52.9% of total)

ival-pow: 25.0ms (20.4% of total)

ival-mult: 18.0ms (14.7% of total)

ival-div: 8.0ms (6.5% of total)

ival-pow2: 3.0ms (2.4% of total)

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

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

...in/eval/compile.rkt:110:19: 1.0ms (0.8% of total)

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

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

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

series48.0ms (0.4%)

Memory

8.5MiB live, 125.2MiB allocated

Counts

17 → 280

Calls

Call 1

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

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

Calls

78 calls:

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

rewrite229.0ms (1.7%)

Memory

-5.1MiB live, 195.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

309×	`associate-r`
300×	`log1p-expm1-u`
300×	`expm1-log1p-u`
290×	`pow1`
278×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	466
1	756	432

Stop Event

1×	node limit

Counts

17 → 488

Calls

Call 1

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

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

simplify870.0ms (6.4%)

Memory

-218.5MiB live, 621.0MiB allocated

Algorithm

1×	egg-herbie

Rules

720×	`associate-r`
641×	`associate-l`
441×	`*-commutative`
389×	`exp-prod`
222×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	946	33847
1	2104	32682
2	7449	32582

Stop Event

1×	node limit

Counts

768 → 627

Calls

Call 1

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

Outputs
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))))) k)
(/.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 n (.f64 (PI.f64) #s(literal 2 binary64))))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) (*.f64 n (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 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #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 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 (.f64 k (.f64 n (PI.f64))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (-.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) (.f64 n k))))) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (pow.f64 k #s(literal 3 binary64))))) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/8 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n k))))) k)
(/.f64 (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))) (+.f64 (.f64 #s(literal -1/16 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/48 binary64) (.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)
(/.f64 (fma.f64 k (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))) (sqrt.f64 (.f64 k (.f64 n (PI.f64))))) (.f64 k (fma.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) #s(literal -1/8 binary64))) (neg.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (fma.f64 #s(literal -1/2 binary64) (.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 2 binary64))) #s(literal -1/8 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)) #s(literal 3 binary64))) #s(literal -1/24 binary64)))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 k (*.f64 n (PI.f64)))))) k)
(/.f64 (fma.f64 k (fma.f64 k (neg.f64 (fma.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n k))) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n (pow.f64 k #s(literal 3 binary64))))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64))) #s(literal -1/8 binary64)) (.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 3 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/24 binary64))))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (.f64 (PI.f64) (.f64 n k)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n k))))) k)
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))))
(.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) k)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (exp.f64 (.f64 k (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))))))))
(.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64)))) k)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 1/2 binary64) (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (.f64 k #s(literal 1/2 binary64)) (log.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n))))))
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(pow.f64 (*.f64 (PI.f64) n) #s(literal 1 binary64))
(*.f64 n (PI.f64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) #s(literal 2 binary64))
(*.f64 n (PI.f64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) n)) #s(literal 3 binary64))
(*.f64 n (PI.f64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (PI.f64)))
(pow.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(*.f64 n (PI.f64))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 2 binary64)))
(sqrt.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 2 binary64)))
(fabs.f64 (*.f64 n (PI.f64)))
(log.f64 (pow.f64 (exp.f64 (PI.f64)) n))
(*.f64 n (PI.f64))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (PI.f64) n))))
(*.f64 n (PI.f64))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) n) #s(literal 3 binary64)))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(*.f64 n (PI.f64))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))))
(*.f64 n (PI.f64))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) n)))
(expm1.f64 (log1p.f64 (*.f64 n (PI.f64))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(exp.f64 (log.f64 (*.f64 (PI.f64) n)))
(*.f64 n (PI.f64))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) n)) #s(literal 1 binary64)))
(*.f64 n (PI.f64))

eval140.0ms (1%)

Memory: 27.7MiB live, 312.7MiB allocated
Compiler: Compiled 19 705 to 3 024 computations (84.7% saved)

prune149.0ms (1.1%)

Memory

-15.1MiB live, 361.1MiB allocated

Pruning

15 alts after pruning (10 fresh and 5 done)

	Pruned	Kept	Total
New	958	7	965
Fresh	7	3	10
Picked	1	4	5
Done	0	1	1
Total	966	15	981

Accuracy

100.0%

Counts

981 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
▶	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	99.5%	(/.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
✓	99.8%	(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
▶	79.8%	(/.f64 (sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal 1/2 binary64))))
✓	99.7%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
▶	45.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
	45.6%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
▶	35.0%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
	35.0%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	35.0%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 (PI.f64) n)))) (sqrt.f64 #s(literal 2 binary64)))
✓	35.0%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	88.8%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
▶	35.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k))))

Compiler

Compiled 373 to 288 computations (22.8% saved)

simplify33.0ms (0.2%)

Memory

3.5MiB live, 42.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

22×	`*-commutative`
14×	`associate-r`
12×	`fma-define`
12×	`associate-l`
11×	`sub-neg`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	40	777
1	70	765
2	108	765
3	139	765
4	157	765
5	170	753
6	189	753
7	208	753
8	219	753
9	222	753

Stop Event

1×

saturated

Calls

Call 1

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

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

localize135.0ms (1%)

Memory

-40.8MiB live, 249.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n)
	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	89.2%	(sqrt.f64 (/.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k))
	accuracy	75.4%	(PI.f64)
	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
	accuracy	75.4%	(PI.f64)
	accuracy	99.6%	(*.f64 (PI.f64) n)
✓	accuracy	99.4%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	89.2%	(sqrt.f64 (/.f64 (*.f64 (PI.f64) n) k))
	accuracy	75.4%	(PI.f64)
	accuracy	99.7%	(/.f64 (PI.f64) k)
	accuracy	99.7%	(*.f64 n (/.f64 (PI.f64) k))
✓	accuracy	89.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (/.f64 (PI.f64) k))))
	accuracy	75.4%	(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)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64)))
	accuracy	99.6%	(*.f64 (PI.f64) n)
	accuracy	75.4%	(PI.f64)

Samples

59.0ms	191×	0	valid
20.0ms	65×	0	exit

Compiler

Compiled 219 to 36 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 14.0ms (26.2% of total)

ival-pow: 14.0ms (26.2% of total)

ival-div: 12.0ms (22.5% of total)

ival-sqrt: 10.0ms (18.7% of total)

ival-pi: 1.0ms (1.9% of total)

ival-sub: 1.0ms (1.9% of total)

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

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

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

series21.0ms (0.2%)

Memory

3.1MiB live, 41.7MiB allocated

Counts

12 → 264

Calls

Call 1

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

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

Calls

66 calls:

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

rewrite143.0ms (1.1%)

Memory

8.6MiB live, 205.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

262×	`associate-r`
255×	`log1p-expm1-u`
255×	`expm1-log1p-u`
245×	`pow1`
242×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	371
1	710	356

Stop Event

1×	node limit

Counts

12 → 533

Calls

Call 1

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

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

simplify433.0ms (3.2%)

Memory

1.1MiB live, 552.7MiB allocated

Algorithm

1×	egg-herbie

Rules

535×	`times-frac`
520×	`fma-define`
448×	`exp-prod`
431×	`cube-prod`
344×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	970	34214
1	2212	32684
2	6413	32118

Stop Event

1×	node limit

Counts

797 → 655

Calls

Call 1

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

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

eval189.0ms (1.4%)

Memory: 39.9MiB live, 266.9MiB allocated
Compiler: Compiled 20 132 to 3 507 computations (82.6% saved)

prune341.0ms (2.5%)

Memory

-15.0MiB live, 345.3MiB allocated

Pruning

29 alts after pruning (24 fresh and 5 done)

	Pruned	Kept	Total
New	1 086	21	1 107
Fresh	2	3	5
Picked	2	3	5
Done	3	2	5
Total	1 093	29	1 122

Accuracy

100.0%

Counts

1 122 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	24.6%	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
▶	35.0%	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	45.7%	(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
▶	35.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))
	45.7%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
	45.6%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (PI.f64))))) (sqrt.f64 #s(literal 2 binary64)))
	35.6%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64)))
✓	45.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
	45.6%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
✓	35.0%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
	35.0%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	35.0%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	35.0%	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
✓	35.0%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	45.8%	(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
▶	88.8%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	79.5%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)))
	35.1%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
	37.6%	(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
	35.1%	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))))
	35.2%	(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
	35.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k)))
▶	35.2%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
	35.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))))
	32.9%	(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
	26.1%	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
▶	26.2%	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)))

Compiler

Compiled 646 to 524 computations (18.9% saved)

simplify168.0ms (1.2%)

Memory

-4.7MiB live, 39.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
	cost-diff	0	(PI.f64)
✓	cost-diff	0	(.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))
✓	cost-diff	0	(pow.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/4 binary64))
✓	cost-diff	6528	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))
✓	cost-diff	0	(*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64))))
✓	cost-diff	0	(pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64))
✓	cost-diff	0	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 k (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 (/.f64 k (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))
✓	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	(.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))
✓	cost-diff	0	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
✓	cost-diff	0	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Rules

23×	`associate-/r*`
19×	`div-sub`
17×	`*-commutative`
15×	`sub-neg`
11×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	691
1	65	691
2	101	691
3	123	691
4	138	691
5	148	691
6	159	691
7	185	691
8	240	691
9	247	691

Stop Event

1×

saturated

Calls

Call 1

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

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

localize242.0ms (1.8%)

Memory

15.4MiB live, 174.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (/.f64 n k) #s(literal 2 binary64))
✓	accuracy	99.6%	(.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64)))
✓	accuracy	99.3%	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	accuracy	79.7%	(pow.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 1/4 binary64))
✓	accuracy	99.6%	(pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64))
✓	accuracy	99.6%	(/.f64 k (PI.f64))
✓	accuracy	99.6%	(/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))
✓	accuracy	56.8%	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)))
✓	accuracy	99.6%	(/.f64 k (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))
	accuracy	99.5%	(*.f64 n (PI.f64))
✓	accuracy	80.2%	(sqrt.f64 (/.f64 k (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64))))
✓	accuracy	99.7%	(/.f64 n (/.f64 k (PI.f64)))
✓	accuracy	99.6%	(/.f64 k (PI.f64))
✓	accuracy	79.9%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
✓	accuracy	99.9%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k))
✓	accuracy	99.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
	accuracy	99.5%	(*.f64 n (PI.f64))
✓	accuracy	88.9%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Samples

136.0ms

256×

valid

Compiler

Compiled 194 to 32 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 116.0ms

ival-mult: 78.0ms (67.4% of total)

ival-pow: 14.0ms (12.1% of total)

ival-div: 12.0ms (10.4% of total)

ival-sqrt: 5.0ms (4.3% of total)

ival-cbrt: 2.0ms (1.7% of total)

ival-pow2: 2.0ms (1.7% of total)

ival-pi: 1.0ms (0.9% of total)

ival-sub: 1.0ms (0.9% of total)

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

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

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

series263.0ms (1.9%)

Memory

7.2MiB live, 278.0MiB allocated

Counts

20 → 408

Calls

Call 1

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

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

108 calls:

Time	Variable		Point	Expression
75.0ms	k	@	inf	(pow (* (PI) (* (/ n k) 2)) 1/4)
46.0ms	n	@	0	(pow (* (PI) (* (/ n k) 2)) 1/4)
18.0ms	k	@	-inf	(pow (* (PI) (* (/ n k) 2)) 1/4)
18.0ms	n	@	-inf	(pow (* (PI) (* (/ n k) 2)) 1/4)
16.0ms	k	@	-inf	(/ k (* (* n (PI)) 2))

rewrite199.0ms (1.5%)

Memory

-42.6MiB live, 233.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

262×	`log1p-expm1-u`
262×	`expm1-log1p-u`
260×	`pow1`
256×	`add-exp-log`
256×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	562
1	627	556

Stop Event

1×	node limit

Counts

20 → 626

Calls

Call 1

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

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

simplify724.0ms (5.3%)

Memory

14.6MiB live, 918.0MiB allocated

Algorithm

1×	egg-herbie

Rules

633×	`associate-r`
593×	`associate-l`
459×	`*-commutative`
294×	`times-frac`
278×	`associate-*l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1147	4295007120
1	2388	4295005894
2	7743	4295005798

Stop Event

1×	node limit

Counts

1 034 → 792

Calls

Call 1

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

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

eval175.0ms (1.3%)

Memory: 23.1MiB live, 295.5MiB allocated
Compiler: Compiled 15 284 to 3 379 computations (77.9% saved)

prune158.0ms (1.2%)

Memory

-10.5MiB live, 425.6MiB allocated

Pruning

38 alts after pruning (29 fresh and 9 done)

	Pruned	Kept	Total
New	949	16	965
Fresh	6	13	19
Picked	1	4	5
Done	0	5	5
Total	956	38	994

Accuracy

100.0%

Counts

994 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	24.6%	(pow.f64 (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (/.f64 (PI.f64) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	24.6%	(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	35.7%	(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	35.0%	(/.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
	45.7%	(/.f64 (sqrt.f64 (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64))) (sqrt.f64 k))
	45.7%	(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
	35.7%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
	35.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))))
✓	35.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (.f64 n (PI.f64)) #s(literal 2 binary64)))))
	35.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) n)) (/.f64 k (PI.f64)))))
	35.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64))))))
	45.7%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
	35.6%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n))) (sqrt.f64 #s(literal 2 binary64)))
✓	45.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓	35.0%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
	35.0%	(*.f64 (sqrt.f64 (/.f64 n (/.f64 k (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	35.0%	(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k n))) (sqrt.f64 (PI.f64)))
	35.0%	(.f64 (sqrt.f64 (.f64 (/.f64 n k) (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))
	35.0%	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
✓	35.0%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	45.8%	(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
	45.7%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
	35.0%	(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) n)))
✓	88.8%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	79.5%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 (/.f64 n k) #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)))
	35.1%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
	37.6%	(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64))))
	35.2%	(sqrt.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)))
	35.2%	(sqrt.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))))
	35.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k)))
✓	35.2%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 n (/.f64 k (PI.f64)))))
	35.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
	35.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 n (*.f64 (/.f64 #s(literal 1 binary64) k) (PI.f64)))))
	32.9%	(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 (/.f64 n k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
	26.1%	(cbrt.f64 (pow.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) k)) #s(literal 3/2 binary64)))
✓	26.2%	(cbrt.f64 (pow.f64 (*.f64 n (/.f64 #s(literal 2 binary64) (/.f64 k (PI.f64)))) #s(literal 3/2 binary64)))

Compiler

Compiled 1 174 to 577 computations (50.9% saved)

regimes121.0ms (0.9%)

Memory

16.3MiB live, 181.3MiB allocated

Counts

61 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

60.0ms	k
19.0ms	(.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))))
18.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
18.0ms	n

Results

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

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes88.0ms (0.6%)

Memory

-23.0MiB live, 171.0MiB allocated

Counts

59 → 1

Calls

Call 1

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

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

Calls

4 calls:

23.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
19.0ms	n
18.0ms	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
99.7%	1	`k`
99.7%	1	`n`
99.7%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.7%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes77.0ms (0.6%)

Memory

-8.0MiB live, 193.0MiB allocated

Counts

57 → 1

Calls

Call 1

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

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

Calls

4 calls:

20.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
17.0ms	k
17.0ms	n
16.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes88.0ms (0.6%)

Memory

1.8MiB live, 80.7MiB allocated

Counts

44 → 1

Calls

Call 1

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

2 calls:

71.0ms	k
13.0ms	n

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes50.0ms (0.4%)

Memory

-1.3MiB live, 91.2MiB allocated

Counts

43 → 2

Calls

Call 1

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

Calls

2 calls:

32.0ms	k
13.0ms	n

Results

Accuracy	Segments	Branch
99.4%	2	`k`
88.8%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes30.0ms (0.2%)

Memory

1.8MiB live, 80.5MiB allocated

Counts

42 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

13.0ms	k
13.0ms	n

Results

Accuracy	Segments	Branch
54.2%	3	`n`
58.8%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes69.0ms (0.5%)

Memory

14.9MiB live, 54.2MiB allocated

Counts

34 → 1

Calls

Call 1

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

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

Calls

2 calls:

57.0ms	n
10.0ms	k

Results

Accuracy	Segments	Branch
45.8%	1	`n`
45.8%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

-7.5MiB live, 34.0MiB allocated

Counts

17 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	n
6.0ms	k

Results

Accuracy	Segments	Branch
45.7%	1	`k`
45.7%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

-10.6MiB live, 28.7MiB allocated

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	k
5.0ms	n

Results

Accuracy	Segments	Branch
35.7%	1	`k`
35.7%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

20.2MiB live, 20.2MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	n
3.0ms	k

Results

Accuracy	Segments	Branch
35.2%	1	`k`
35.2%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Memory

-28.8MiB live, 10.7MiB allocated

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	k
2.0ms	n

Results

Accuracy	Segments	Branch
35.2%	1	`k`
35.2%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch9.0ms (0.1%)

Memory

23.7MiB live, 23.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	1.3016571558623735e-49	2.1738467566049627e-49

Samples

6.0ms

64×

valid

Compiler

Compiled 129 to 106 computations (17.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 1.0ms (22.9% of total)

ival-mult: 1.0ms (22.9% of total)

ival-sqrt: 1.0ms (22.9% of total)

ival-pow: 1.0ms (22.9% of total)

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

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

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

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

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

bsearch14.0ms (0.1%)

Memory

-6.4MiB live, 33.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	3.152136286381554e+28	2.4831120603529485e+29

Samples

9.0ms

96×

valid

Compiler

Compiled 177 to 150 computations (15.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 2.0ms (28% of total)

ival-pow: 2.0ms (28% of total)

ival-div: 1.0ms (14% of total)

ival-sub: 1.0ms (14% of total)

ival-sqrt: 1.0ms (14% of total)

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

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

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

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

simplify12.0ms (0.1%)

Memory

-16.9MiB live, 24.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	598
1	101	598
2	110	598
3	116	598
4	120	598
5	121	598

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 1382223828149813/6582018229284824168619876730229402019930943462534319453394436096 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 67999999999999999804042117120 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #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 n (/.f64 (PI.f64) k))))

Outputs
(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(.f64 (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 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))
(/.f64 (pow.f64 (.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 1382223828149813/6582018229284824168619876730229402019930943462534319453394436096 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 1382223828149813/6582018229284824168619876730229402019930943462534319453394436096 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 67999999999999999804042117120 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(if (<=.f64 k #s(literal 67999999999999999804042117120 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) 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 n (/.f64 (PI.f64) k))))

soundness2.8s (20.9%)

Memory

36.1MiB live, 3 020.7MiB allocated

Rules

1 096×	`log1p-expm1-u`
720×	`associate-r`
718×	`fma-define`
641×	`associate-l`
633×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	274
1	427	270
2	4798	270
0	40	371
1	710	356
0	36	562
1	627	556
0	946	33847
1	2104	32682
2	7449	32582
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	600	19256
1	1218	17586
2	4112	16578
0	970	34214
1	2212	32684
2	6413	32118
0	43	466
1	756	432
0	1147	4295007120
1	2388	4295005894
2	7743	4295005798

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
1×	node limit

Compiler

Compiled 2 017 to 658 computations (67.4% saved)

preprocess70.0ms (0.5%)

Memory: -2.0MiB live, 154.6MiB allocated
Compiler: Compiled 360 to 148 computations (58.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

Iter	Nodes	Cost
0	43	840
1	71	808
2	115	806
3	152	806
4	188	802
5	262	802
6	312	802
7	329	802
8	340	802
9	343	802

Iter	Nodes	Cost
0	40	777
1	70	765
2	108	765
3	139	765
4	157	765
5	170	753
6	189	753
7	208	753
8	219	753
9	222	753

Iter	Nodes	Cost
0	36	691
1	65	691
2	101	691
3	123	691
4	138	691
5	148	691
6	159	691
7	185	691
8	240	691
9	247	691

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	43	840
1	71	808
2	115	806
3	152	806
4	188	802
5	262	802
6	312	802
7	329	802
8	340	802
9	343	802

Iter	Nodes	Cost
0	40	777
1	70	765
2	108	765
3	139	765
4	157	765
5	170	753
6	189	753
7	208	753
8	219	753
9	222	753

Iter	Nodes	Cost
0	36	691
1	65	691
2	101	691
3	123	691
4	138	691
5	148	691
6	159	691
7	185	691
8	240	691
9	247	691

analyze119.0ms (0.9%)

sample3.2s (23.3%)

preprocess137.0ms (1%)

explain362.0ms (2.7%)

eval1.0ms (0%)

prune3.0ms (0%)

simplify21.0ms (0.2%)

localize116.0ms (0.9%)

series95.0ms (0.7%)

rewrite542.0ms (4%)

simplify413.0ms (3%)

eval110.0ms (0.8%)

prune74.0ms (0.5%)

simplify41.0ms (0.3%)

localize220.0ms (1.6%)

series48.0ms (0.4%)

rewrite229.0ms (1.7%)

simplify870.0ms (6.4%)

eval140.0ms (1%)

prune149.0ms (1.1%)

simplify33.0ms (0.2%)

localize135.0ms (1%)

series21.0ms (0.2%)

rewrite143.0ms (1.1%)

simplify433.0ms (3.2%)

eval189.0ms (1.4%)

prune341.0ms (2.5%)

simplify168.0ms (1.2%)

localize242.0ms (1.8%)

series263.0ms (1.9%)

rewrite199.0ms (1.5%)

simplify724.0ms (5.3%)

eval175.0ms (1.3%)

prune158.0ms (1.2%)

regimes121.0ms (0.9%)

regimes88.0ms (0.6%)

regimes77.0ms (0.6%)

regimes88.0ms (0.6%)

regimes50.0ms (0.4%)

regimes30.0ms (0.2%)

regimes69.0ms (0.5%)

regimes14.0ms (0.1%)

regimes12.0ms (0.1%)

regimes7.0ms (0.1%)

regimes4.0ms (0%)

bsearch9.0ms (0.1%)

bsearch14.0ms (0.1%)

simplify12.0ms (0.1%)

soundness2.8s (20.9%)

preprocess70.0ms (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	43	840
1	71	808
2	115	806
3	152	806
4	188	802
5	262	802
6	312	802
7	329	802
8	340	802
9	343	802

Iter	Nodes	Cost
0	40	777
1	70	765
2	108	765
3	139	765
4	157	765
5	170	753
6	189	753
7	208	753
8	219	753
9	222	753

Iter	Nodes	Cost
0	36	691
1	65	691
2	101	691
3	123	691
4	138	691
5	148	691
6	159	691
7	185	691
8	240	691
9	247	691