Metrics for Migdal et al, Equation (51)

analyze162.0ms (1.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
50%	25%	25%	0.1%	0%	50%	0%	3
50%	25%	25%	0.1%	0%	50%	0%	4
50%	25%	25%	0.1%	0%	50%	0%	5
50%	25%	25%	0.1%	0%	50%	0%	6
51.6%	25%	23.4%	0.1%	0%	50%	1.6%	7
52.5%	25%	22.6%	0.1%	0%	50%	2.3%	8
53.8%	25%	21.5%	0.1%	0%	50%	3.5%	9
54.5%	25%	20.9%	0.1%	0%	50%	4.1%	10
55.3%	25%	20.2%	0.1%	0%	50%	4.8%	11
55.7%	25%	19.9%	0.1%	0%	50%	5.1%	12

Compiler

Compiled 19 to 14 computations (26.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-pow: 50.0ms (49.1% of total)

ival-mult: 18.0ms (17.7% of total)

ival-div: 12.0ms (11.8% of total)

ival-sqrt: 11.0ms (10.8% of total)

ival-sub: 5.0ms (4.9% of total)

ival-pi: 3.0ms (2.9% of total)

const: 1.0ms (1% of total)

backward-pass: 0.0ms (0% of total)

sample5.7s (41.1%)

Results

1.6s	8256×	0	valid
2.4s	3776×	5	exit
621.0ms	1870×	1	invalid
50.0ms	599×	0	invalid
45.0ms	240×	0	unsamplable

Precisions

Click to see histograms. Total time spent on operations: 3.3s

ival-pow: 845.0ms (25.8% of total)

backward-pass: 676.0ms (20.7% of total)

ival-div: 567.0ms (17.3% of total)

ival-mult: 486.0ms (14.9% of total)

ival-sqrt: 295.0ms (9% of total)

ival-sub: 155.0ms (4.7% of total)

const: 145.0ms (4.4% of total)

ival-pi: 102.0ms (3.1% of total)

Bogosity

preprocess135.0ms (1%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-define`
240×	`fma-neg`
124×	`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	1698	352
8	2017	352
9	2060	352
10	2088	352
11	2099	352
12	2101	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))

explain240.0ms (1.7%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
3	212	(2.0471640338582713e+126 7.37406440284624e-295)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
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)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`n`
0	0	-	-	`k`

Results

104.0ms

512×

valid

Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-mult: 33.0ms (46.7% of total)

ival-pow: 19.0ms (26.9% of total)

ival-div: 8.0ms (11.3% of total)

ival-sqrt: 4.0ms (5.7% of total)

ival-sub: 3.0ms (4.2% of total)

ival-pi: 2.0ms (2.8% of total)

const: 1.0ms (1.4% of total)

backward-pass: 0.0ms (0% of total)

eval1.0ms (0%)

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

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.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)

localize122.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 k #s(literal 2 binary64))
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) k)
✓	cost-diff	0	(PI.f64)
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (PI.f64))
✓	cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (PI.f64))
✓	accuracy	100.0%	(sqrt.f64 k)
✓	accuracy	100.0%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	accuracy	99.7%	(/.f64 (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	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))
✓	accuracy	99.6%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	accuracy	99.6%	(*.f64 (PI.f64) n)

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)

Results

69.0ms

256×

valid

Compiler

Compiled 105 to 21 computations (80% saved)

Precisions

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

ival-pow: 17.0ms (39.1% of total)

ival-div: 9.0ms (20.7% of total)

ival-mult: 9.0ms (20.7% of total)

ival-sub: 4.0ms (9.2% of total)

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

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

const: 1.0ms (2.3% of total)

backward-pass: 0.0ms (0% of total)

series101.0ms (0.7%)

Counts

13 → 172

Calls

Call 1

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

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

Calls

45 calls:

Time	Variable		Point	Expression
31.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
28.0ms	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)))
3.0ms	k	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	0	(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))

rewrite744.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1096×	`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	284
1	427	280
2	4798	280

Stop Event

1×	node limit

Counts

13 → 329

Calls

Call 1

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

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

simplify303.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-define`
472×	`associate-r`
392×	`associate-l`
385×	`exp-prod`
285×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	670	20065
1	1375	18361
2	4676	17353

Stop Event

1×	node limit

Counts

501 → 440

Calls

Call 1

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

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

eval73.0ms (0.5%)

Compiler: Compiled 10098 to 1707 computations (83.1% saved)

prune90.0ms (0.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	475	16	491
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	476	17	493

Accuracy

100.0%

Counts

493 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	74.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
▶	99.5%	(/.f64 (/.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)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
	76.4%	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (+.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))))) (sqrt.f64 k))
	99.3%	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
	48.6%	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))))) (sqrt.f64 k))
	47.4%	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k))
	96.3%	(/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))) (sqrt.f64 k))
▶	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
	99.5%	(.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)))) (pow.f64 k #s(literal -1/2 binary64)))
	47.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))))
	37.2%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	96.3%	(.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)))))
▶	37.2%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	89.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) k))

Compiler

Compiled 586 to 438 computations (25.3% saved)

localize441.0ms (3.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 n (/.f64 (PI.f64) k))
✓	cost-diff	0	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	cost-diff	0	(-.f64 #s(literal 1 binary64) k)
	cost-diff	0	(PI.f64)
	cost-diff	0	(*.f64 #s(literal 2 binary64) (PI.f64))
	cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) k)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓	cost-diff	384	(/.f64 (/.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)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
✓	accuracy	99.8%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.8%	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
✓	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 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
✓	accuracy	99.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	accuracy	99.6%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	89.6%	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓	accuracy	83.3%	(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
	accuracy	50.8%	(PI.f64)

Rules

23×	`*-commutative`
16×	`fma-define`
16×	`sub-neg`
12×	`associate-r`
11×	`associate-l`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	944
1	77	928
2	98	916
3	116	876
4	159	876
5	212	876
6	250	876
7	281	876
8	289	876
9	290	876

Stop Event

1×

saturated

Calls

Call 1

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

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

Results

66.0ms	126×	0	valid
208.0ms	72×	5	exit
40.0ms	58×	0	unsamplable

Compiler

Compiled 280 to 42 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 161.0ms

ival-pow: 57.0ms (35.4% of total)

backward-pass: 35.0ms (21.7% of total)

ival-div: 25.0ms (15.5% of total)

ival-mult: 22.0ms (13.7% of total)

ival-sqrt: 9.0ms (5.6% of total)

ival-sub: 4.0ms (2.5% of total)

ival-cbrt: 4.0ms (2.5% of total)

ival-add: 2.0ms (1.2% of total)

const: 1.0ms (0.6% of total)

ival-pi: 1.0ms (0.6% of total)

series59.0ms (0.4%)

Counts

12 → 220

Calls

Call 1

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

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

Calls

60 calls:

Time	Variable		Point	Expression
5.0ms	k	@	0	(* (sqrt (/ 1 k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
4.0ms	k	@	0	(/ (sqrt k) (pow (* (PI) (* n 2)) (+ 1/2 (* k -1/2))))
2.0ms	k	@	-inf	(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (cbrt (pow k 3/2)))
2.0ms	k	@	-inf	(cbrt (pow k 3/2))
1.0ms	k	@	-inf	(/ (sqrt k) (pow (* (PI) (* n 2)) (+ 1/2 (* k -1/2))))

rewrite114.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

337×	`log1p-expm1-u`
337×	`expm1-log1p-u`
329×	`pow1`
325×	`add-cube-cbrt`
322×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	428
1	851	373

Stop Event

1×	node limit

Counts

12 → 258

Calls

Call 1

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

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

simplify299.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

412×	`associate-r`
379×	`associate-l`
336×	`distribute-lft-in`
332×	`distribute-rgt-in`
303×	`exp-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	665	4294989934
1	1380	4294987068
2	4595	4294986854

Stop Event

1×	node limit

Counts

478 → 349

Calls

Call 1

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

Outputs
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))
(*.f64 (neg.f64 (sqrt.f64 k)) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))
(*.f64 (sqrt.f64 k) (neg.f64 (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))
(*.f64 (neg.f64 (sqrt.f64 k)) (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))
(*.f64 (sqrt.f64 k) (neg.f64 (cbrt.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))
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(cbrt.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 3/2 binary64)))
(cbrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 3/2 binary64))))
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(log1p.f64 (expm1.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 n (/.f64 (PI.f64) k))
(exp.f64 (log.f64 (*.f64 n (/.f64 (PI.f64) k))))
(*.f64 n (/.f64 (PI.f64) k))
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eval86.0ms (0.6%)

Compiler: Compiled 11176 to 1991 computations (82.2% saved)

prune105.0ms (0.8%)

Pruning

18 alts after pruning (14 fresh and 4 done)

	Pruned	Kept	Total
New	554	6	560
Fresh	3	8	11
Picked	2	3	5
Done	0	1	1
Total	559	18	577

Accuracy

100.0%

Counts

577 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	74.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
	99.3%	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
	48.6%	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))))) (sqrt.f64 k))
	96.3%	(/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))))) (sqrt.f64 k))
	38.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
✓	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
▶	99.6%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
	99.5%	(.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)))) (pow.f64 k #s(literal -1/2 binary64)))
	47.4%	(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
	47.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))))
▶	47.4%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	37.2%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	96.3%	(.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)))))
✓	37.2%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
▶	89.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
▶	37.3%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))

Compiler

Compiled 517 to 400 computations (22.6% saved)

localize541.0ms (3.9%)

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) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	64	(neg.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	64	(pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	64	(.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
✓	cost-diff	64	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
✓	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))
✓	accuracy	99.7%	(/.f64 (PI.f64) k)
	accuracy	99.7%	(*.f64 n (/.f64 (PI.f64) k))
	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
✓	accuracy	99.6%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
✓	accuracy	99.5%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.4%	(pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	accuracy	89.5%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
✓	accuracy	89.3%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
	accuracy	78.1%	(PI.f64)

Rules

305×	`fma-define`
280×	`fma-neg`
233×	`times-frac`
207×	`distribute-lft-neg-in`
164×	`distribute-rgt-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	805
1	79	799
2	132	797
3	186	773
4	242	773
5	345	773
6	423	773
7	591	773
8	894	773
9	1478	773
10	1884	773
11	2376	773
12	2719	773
13	2786	773
14	2814	773
15	2914	773
16	3438	773
17	3446	773
18	3446	773

Stop Event

1×

saturated

Calls

Call 1

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

Results

262.0ms	198×	0	valid
32.0ms	58×	0	unsamplable

Compiler

Compiled 235 to 38 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-pow: 40.0ms (46.6% of total)

ival-mult: 17.0ms (19.8% of total)

ival-sqrt: 11.0ms (12.8% of total)

ival-div: 8.0ms (9.3% of total)

ival-fma: 3.0ms (3.5% of total)

ival-sub: 3.0ms (3.5% of total)

ival-pi: 1.0ms (1.2% of total)

const: 1.0ms (1.2% of total)

ival-neg: 1.0ms (1.2% of total)

backward-pass: 0.0ms (0% of total)

series88.0ms (0.6%)

Counts

13 → 228

Calls

Call 1

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

Calls

60 calls:

Time	Variable		Point	Expression
41.0ms	n	@	0	(pow (* n (* (PI) 2)) (neg (+ (* k -1/2) 1/2)))
3.0ms	k	@	0	(/ 1 (* (sqrt k) (pow (* n (* (PI) 2)) (neg (+ (* k -1/2) 1/2)))))
2.0ms	k	@	0	(sqrt (/ (pow (* n (* (PI) 2)) (- 1 k)) k))
2.0ms	n	@	inf	(/ 1 (* (sqrt k) (pow (* n (* (PI) 2)) (neg (+ (* k -1/2) 1/2)))))
2.0ms	n	@	-inf	(/ 1 (* (sqrt k) (pow (* n (* (PI) 2)) (neg (+ (* k -1/2) 1/2)))))

rewrite131.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

303×	`log1p-expm1-u`
303×	`expm1-log1p-u`
299×	`pow1`
295×	`add-exp-log`
295×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	391
1	751	371

Stop Event

1×	node limit

Counts

13 → 307

Calls

Call 1

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

Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #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 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) (cbrt.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #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 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 (/.f64 #s(literal 1 binary64) k)))
(.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) (pow.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)))
(.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 k))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #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 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.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 (pow.f64 (.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 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (cbrt.f64 k)) (/.f64 (pow.f64 (.f64 n (PI.f64)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (cbrt.f64 (sqrt.f64 k))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (pow.f64 k #s(literal 1/4 binary64))) (/.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (pow.f64 k #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (cbrt.f64 (sqrt.f64 k))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))) (sqrt.f64 k))
(/.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) (sqrt.f64 (neg.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64)) (.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 k #s(literal 1/2 binary64))) (sqrt.f64 k)))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k))))) (neg.f64 (neg.f64 (sqrt.f64 k))))
(pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #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 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #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 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))) #s(literal -1 binary64))
(fabs.f64 (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
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(/.f64 (+.f64 (pow.f64 (.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 (.f64 (.f64 k #s(literal -1/2 binary64)) (.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 k #s(literal -1/2 binary64)) (.f64 k #s(literal -1/2 binary64))) #s(literal 1/4 binary64)) (-.f64 (.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(log.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(cbrt.f64 (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(log1p.f64 (expm1.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)))

simplify516.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-r`
535×	`associate-l`
417×	`*-commutative`
354×	`exp-prod`
252×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	837	25140
1	1932	23936
2	6502	22976

Stop Event

1×	node limit

Counts

535 → 489

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k))) k))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.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 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 (-.f64 (.f64 #s(literal -1/3 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))))) (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))) (.f64 k (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))) k)
(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(.f64 (sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(.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))))
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(sqrt.f64 k)
(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 #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 (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))))
(.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)))))
(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)))
(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))))
(.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)))
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(*.f64 (sqrt.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 k #s(literal -1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 (.f64 (.f64 k #s(literal -1/2 binary64)) (.f64 k #s(literal -1/2 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 k #s(literal -1/2 binary64)) (.f64 k #s(literal -1/2 binary64))) #s(literal 1/4 binary64)) (-.f64 (.f64 k #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(log.f64 (exp.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))
(cbrt.f64 (pow.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(log1p.f64 (expm1.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(exp.f64 (log.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 1 binary64))
(pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(log.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (PI.f64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #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 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(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 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(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 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(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 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(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 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(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 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(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 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(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 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (exp.f64 (log.f64 n))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(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 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k)) 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 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k)) 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 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k)) 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 (log.f64 (*.f64 (PI.f64) #s(literal -2 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) #s(literal -2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) n) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1 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 n (.f64 #s(literal 2 binary64) (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 n (.f64 (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))))) 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 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (/.f64 (log.f64 (.f64 n (.f64 #s(literal 2 binary64) (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 n (*.f64 #s(literal 2 binary64) (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 (sqrt.f64 (.f64 n (.f64 (PI.f64) k))) (.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))) #s(literal 1/2 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 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) k))))) k)
(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 (-.f64 (.f64 #s(literal -1/3 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))))) (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))) (.f64 k (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))))) k)
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(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (PI.f64))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(expm1.f64 (log1p.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (PI.f64))
(exp.f64 (log.f64 (*.f64 (PI.f64) #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (PI.f64))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (PI.f64))

eval116.0ms (0.8%)

Compiler: Compiled 14164 to 2719 computations (80.8% saved)

prune213.0ms (1.5%)

Pruning

24 alts after pruning (19 fresh and 5 done)

	Pruned	Kept	Total
New	710	13	723
Fresh	3	6	9
Picked	2	3	5
Done	2	2	4
Total	717	24	741

Accuracy

100.0%

Counts

741 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	30.7%	(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	37.1%	(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	99.4%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	74.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
	99.3%	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
	48.6%	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))))) (sqrt.f64 k))
	37.1%	(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
	38.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
	37.9%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
	47.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
▶	99.5%	(.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)))) (pow.f64 k #s(literal -1/2 binary64)))
▶	37.2%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	47.5%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	96.3%	(.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)))))
	47.5%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
✓	89.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
	86.7%	(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
▶	37.3%	(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
	37.2%	(sqrt.f64 (.f64 (.f64 n (pow.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64))) #s(literal 2 binary64)))
✓	37.3%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
	37.3%	(sqrt.f64 (.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
▶	35.0%	(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
	32.5%	(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))

Compiler

Compiled 615 to 485 computations (21.1% saved)

localize247.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (*.f64 n (PI.f64)) k)
✓	cost-diff	0	(.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
✓	cost-diff	0	(pow.f64 k #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 k #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 n #s(literal 2 binary64))
	cost-diff	0	(PI.f64)
	cost-diff	0	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	cost-diff	64	(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
✓	cost-diff	6528	(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))
	accuracy	99.6%	(/.f64 (PI.f64) k)
	accuracy	99.6%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	accuracy	99.6%	(*.f64 n (PI.f64))
✓	accuracy	99.3%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	92.0%	(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
✓	accuracy	77.4%	(sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))
✓	accuracy	77.4%	(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
✓	accuracy	76.9%	(log.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
✓	accuracy	52.8%	(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))

Rules

16×	`*-commutative`
9×	`associate-l`
7×	`associate-/l*`
6×	`associate-r`
4×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	694
1	60	682
2	83	682
3	95	682
4	97	682

Stop Event

1×

saturated

Calls

Call 1

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

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

Results

121.0ms

256×

valid

Compiler

Compiled 200 to 31 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-pow: 38.0ms (49.4% of total)

ival-mult: 20.0ms (26% of total)

ival-sqrt: 5.0ms (6.5% of total)

ival-div: 3.0ms (3.9% of total)

ival-exp: 3.0ms (3.9% of total)

ival-log: 3.0ms (3.9% of total)

ival-add: 2.0ms (2.6% of total)

ival-pi: 1.0ms (1.3% of total)

const: 1.0ms (1.3% of total)

backward-pass: 0.0ms (0% of total)

series158.0ms (1.1%)

Counts

13 → 196

Calls

Call 1

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

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

Calls

66 calls:

Time	Variable		Point	Expression
43.0ms	n	@	0	(log (* n (* (/ (PI) k) 2)))
36.0ms	k	@	-inf	(log (* n (* (/ (PI) k) 2)))
17.0ms	k	@	0	(log (* n (* (/ (PI) k) 2)))
17.0ms	n	@	-inf	(log (* n (* (/ (PI) k) 2)))
9.0ms	n	@	inf	(log (* n (* (/ (PI) k) 2)))

rewrite208.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1039×	`log1p-expm1-u`
885×	`expm1-log1p-u`
176×	`associate-r`
162×	`pow1`
160×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	297
1	445	297
2	4848	297

Stop Event

1×	node limit

Counts

13 → 387

Calls

Call 1

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

Outputs
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #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 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) (cbrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(.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 (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 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (cbrt.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 1/4 binary64)) (pow.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 1/4 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 #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 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 n #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/4 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/4 binary64)) #s(literal 1/3 binary64)))
(.f64 (cbrt.f64 (pow.f64 n #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 3/2 binary64))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(.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)) (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 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(fabs.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #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))))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(+.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(+.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(+.f64 (log.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (log.f64 n))
(+.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))) (log.f64 #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 2 binary64))) (log.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(+.f64 (.f64 (log.f64 n) #s(literal 1 binary64)) (.f64 (log.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))) #s(literal 1 binary64))
(-.f64 (log.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 k))
(.f64 (log.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (log.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) (pow.f64 (cbrt.f64 (log.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) #s(literal 2 binary64)))
(.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) #s(literal 2 binary64)) (cbrt.f64 (log.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(.f64 (sqrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) (sqrt.f64 (log.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(/.f64 (+.f64 (pow.f64 (log.f64 n) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64))) (+.f64 (.f64 (log.f64 n) (log.f64 n)) (-.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (log.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))))
(/.f64 (-.f64 (.f64 (log.f64 n) (log.f64 n)) (.f64 (log.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (log.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) (-.f64 (log.f64 n) (log.f64 (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) #s(literal 2 binary64))
(sqrt.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 2 binary64)))
(cbrt.f64 (pow.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 3 binary64)))
(expm1.f64 (log1p.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(log1p.f64 (-.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(exp.f64 (.f64 (log.f64 (log.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #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 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) (cbrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(.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 (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 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) (cbrt.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 1/4 binary64)) (pow.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 1/4 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 #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 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 n #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(.f64 (pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/4 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/4 binary64)) #s(literal 1/3 binary64)))
(.f64 (cbrt.f64 (pow.f64 n #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 3/2 binary64))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(.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)) (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 (sqrt.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k))
(pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))))
(fabs.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #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))))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))) #s(literal 1 binary64))
(.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)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 k)))
(.f64 (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 (sqrt.f64 n) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (neg.f64 n))) (sqrt.f64 (neg.f64 k)))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (neg.f64 (sqrt.f64 k)))
(pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 1/2 binary64))
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(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 k #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 k) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (cbrt.f64 k) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 k) #s(literal -1/2 binary64)))
(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 (*.f64 #s(literal -1/2 binary64) (log.f64 k)))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 k)) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) #s(literal 1 binary64))
(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 k (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))))
(/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k)
(/.f64 (neg.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))) (neg.f64 k))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (neg.f64 n))) (neg.f64 k))
(/.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) n) k)
(/.f64 (.f64 (.f64 (PI.f64) (neg.f64 n)) #s(literal 2 binary64)) (neg.f64 k))
(/.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 1 binary64)) k)
(/.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (cbrt.f64 k))
(/.f64 (/.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 k)) (sqrt.f64 k))
(pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)) #s(literal 2/3 binary64))
(pow.f64 (sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))) #s(literal 2 binary64))) (cbrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))) (sqrt.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.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 (exp.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)))
(cbrt.f64 (.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 3 binary64))))
(cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(log1p.f64 (expm1.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(exp.f64 (log.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1 binary64))
(*.f64 n (/.f64 (PI.f64) k))
(*.f64 (PI.f64) (/.f64 n k))
(.f64 (PI.f64) (.f64 n (/.f64 #s(literal 1 binary64) k)))
(*.f64 (/.f64 (PI.f64) k) n)
(.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 1 binary64) k))
(.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(.f64 #s(literal 1 binary64) (.f64 (PI.f64) (/.f64 n k)))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) (pow.f64 (cbrt.f64 (*.f64 (PI.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 (*.f64 (PI.f64) (/.f64 n k)))))
(.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64)) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(.f64 (pow.f64 (cbrt.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) k))
(.f64 (pow.f64 (cbrt.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (.f64 (cbrt.f64 (.f64 n (PI.f64))) (/.f64 #s(literal 1 binary64) k)))
(.f64 (pow.f64 (cbrt.f64 n) #s(literal 2 binary64)) (.f64 (cbrt.f64 n) (/.f64 (PI.f64) k)))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) k))
(.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (/.f64 #s(literal 1 binary64) k)))
(.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 (*.f64 (PI.f64) (/.f64 n k)))))
(.f64 (sqrt.f64 n) (.f64 (sqrt.f64 n) (/.f64 (PI.f64) k)))
(.f64 (.f64 (PI.f64) (neg.f64 n)) (/.f64 #s(literal 1 binary64) (neg.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) k) (.f64 n (PI.f64)))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (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 (PI.f64) #s(literal 1 binary64)) (/.f64 n k))
(*.f64 (/.f64 (PI.f64) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (/.f64 n (cbrt.f64 k)))
(*.f64 (/.f64 (PI.f64) (sqrt.f64 k)) (/.f64 n (sqrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (/.f64 (.f64 n (PI.f64)) (cbrt.f64 k)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (.f64 n (PI.f64)) (sqrt.f64 k)))
(*.f64 (/.f64 n #s(literal 1 binary64)) (/.f64 (PI.f64) k))
(*.f64 (/.f64 n (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (/.f64 (PI.f64) (cbrt.f64 k)))
(*.f64 (/.f64 n (sqrt.f64 k)) (/.f64 (PI.f64) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) k))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 n (PI.f64))) #s(literal 2 binary64)) (sqrt.f64 k)) (/.f64 (cbrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) k))
(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (pow.f64 (cbrt.f64 k) #s(literal 2 binary64))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (cbrt.f64 k)))
(.f64 (.f64 n (pow.f64 (cbrt.f64 (/.f64 (PI.f64) k)) #s(literal 2 binary64))) (cbrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 n (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (cbrt.f64 (.f64 (PI.f64) (/.f64 n k)))) (cbrt.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (*.f64 (PI.f64) (/.f64 n k))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1 binary64))
(neg.f64 (/.f64 (*.f64 n (PI.f64)) (neg.f64 k)))
(neg.f64 (/.f64 (*.f64 (PI.f64) (neg.f64 n)) k))
(sqrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)))
(log.f64 (exp.f64 (*.f64 (PI.f64) (/.f64 n k))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (PI.f64) (/.f64 n k)))))
(cbrt.f64 (pow.f64 (*.f64 (PI.f64) (/.f64 n k)) #s(literal 3 binary64)))
(cbrt.f64 (*.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n (PI.f64)) #s(literal 3 binary64)) (pow.f64 k #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (*.f64 (PI.f64) (/.f64 n k))))
(log1p.f64 (expm1.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (log.f64 (*.f64 (PI.f64) (/.f64 n k))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (/.f64 n k))) #s(literal 1 binary64)))

simplify541.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-define`
344×	`distribute-lft-neg-in`
329×	`distribute-rgt-neg-in`
319×	`exp-prod`
308×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	584	8589954465
1	1087	8589953773
2	3211	8589952977

Stop Event

1×	node limit

Counts

583 → 380

Calls

Call 1

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

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

eval152.0ms (1.1%)

Compiler: Compiled 9941 to 2260 computations (77.3% saved)

prune188.0ms (1.4%)

Pruning

29 alts after pruning (21 fresh and 8 done)

	Pruned	Kept	Total
New	666	11	677
Fresh	4	10	14
Picked	1	4	5
Done	1	4	5
Total	672	29	701

Accuracy

100.0%

Counts

701 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	30.7%	(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
✓	30.7%	(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	24.7%	(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)) #s(literal 1/6 binary64))
	24.7%	(pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64))) #s(literal 1/6 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))
✓	74.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
	99.3%	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
	48.6%	(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))))) (sqrt.f64 k))
	47.4%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
	37.1%	(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
	38.0%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
	37.9%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
✓	99.5%	(.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)))) (pow.f64 k #s(literal -1/2 binary64)))
	47.5%	(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	96.3%	(.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)))))
	37.2%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	47.5%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
	47.5%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
✓	89.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
	86.7%	(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
✓	37.3%	(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
	37.3%	(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
	37.3%	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))) #s(literal 2 binary64)))
✓	37.3%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
	37.3%	(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
	37.3%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
✓	35.0%	(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
	32.5%	(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
	32.5%	(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))

Compiler

Compiled 982 to 488 computations (50.3% saved)

regimes59.0ms (0.4%)

Counts

48 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))) #s(literal 2 binary64)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(sqrt.f64 (.f64 (.f64 n (pow.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64))) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(literal 1 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)))) (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)))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) k))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 (PI.f64) (.f64 n #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 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)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(.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)))))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (.f64 k #s(literal -1/2 binary64)))) (sqrt.f64 k))
(/.f64 (/.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)))) (pow.f64 k #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (+.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))))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 k (.f64 (sqrt.f64 #s(literal 2 binary64)) (log.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))))))))) (sqrt.f64 k))

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

Calls

4 calls:

14.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
14.0ms	n
13.0ms	k
13.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)

Results

Accuracy	Segments	Branch
99.6%	1	`k`
99.6%	1	`n`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes52.0ms (0.4%)

Counts

39 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))) #s(literal 2 binary64)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(sqrt.f64 (.f64 (.f64 n (pow.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64))) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(literal 1 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)))) (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)))) (pow.f64 k #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 k))
(sqrt.f64 (/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k))) k))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) k))

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

Calls

4 calls:

12.0ms	n
12.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
11.0ms	k
10.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.6%	1	`k`
99.6%	1	`n`
99.6%	1	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes31.0ms (0.2%)

Counts

29 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))) #s(literal 2 binary64)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(sqrt.f64 (.f64 (.f64 n (pow.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64))) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) #s(literal -1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.3%	2	`k`
89.1%	1	`n`
89.1%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes20.0ms (0.1%)

Counts

26 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 (.f64 n (PI.f64)) k) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) k) (*.f64 n (PI.f64))) #s(literal 2 binary64)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(sqrt.f64 (.f64 (.f64 n (pow.f64 (/.f64 k (PI.f64)) #s(literal -1 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64))) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3 binary64)) #s(literal 1/6 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))

Outputs

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

(pow.f64 (*.f64 #s(literal 8 binary64) (pow.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64))) #s(literal 1/6 binary64))

Calls

2 calls:

10.0ms	k
8.0ms	n

Results

Accuracy	Segments	Branch
47.5%	1	`n`
56.5%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts

21 → 2

Calls

Call 1

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

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
51.3%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes12.0ms (0.1%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	n
5.0ms	k

Results

Accuracy	Segments	Branch
47.5%	1	`n`
47.5%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	n
3.0ms	k

Results

Accuracy	Segments	Branch
37.3%	1	`k`
37.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

2.0ms	n
2.0ms	k

Results

Accuracy	Segments	Branch
37.3%	1	`k`
37.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	n
1.0ms	k

Results

Accuracy	Segments	Branch
37.3%	1	`k`
37.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch29.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
26.0ms	4.799921734622066e-52	1.0456228678269805e-45

Results

21.0ms

144×

valid

Compiler

Compiled 266 to 215 computations (19.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-pow: 9.0ms (54.4% of total)

ival-mult: 3.0ms (18.1% of total)

ival-div: 2.0ms (12.1% of total)

ival-pi: 1.0ms (6% of total)

ival-sub: 1.0ms (6% of total)

ival-sqrt: 1.0ms (6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch24.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	8.016552547304199e+153	1.1871654723308049e+156

Results

16.0ms

112×

valid

Compiler

Compiled 205 to 171 computations (16.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow: 4.0ms (32.6% of total)

ival-div: 3.0ms (24.4% of total)

ival-mult: 2.0ms (16.3% of total)

ival-sub: 1.0ms (8.1% of total)

ival-sqrt: 1.0ms (8.1% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch22.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	3.0893653698295217e+255	2.5165530472248164e+257

Results

16.0ms

112×

valid

Compiler

Compiled 198 to 164 computations (17.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow: 6.0ms (48.7% of total)

ival-div: 2.0ms (16.2% of total)

ival-mult: 2.0ms (16.2% of total)

ival-sub: 1.0ms (8.1% of total)

ival-sqrt: 1.0ms (8.1% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative`
6×	`sub-neg`
6×	`+-commutative`
4×	`neg-sub0`
4×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	501
1	98	501
2	109	501
3	116	501
4	120	501
5	121	501

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 819538402572085/803469022129495137770981046170581301261101496891396417650688 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 449999999999999973457990046261517499935973494258555676005057340905580228432358972138214490305813912545954144924079784244337481911369963359210018733490700288 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64))) #s(literal 1/6 binary64)))
(if (<=.f64 k #s(literal 6200000000000000386831924367266991740316570268240843713101819144877544438829140996412013743397665879766077852853099975759292309450452752913732746535953498802393453598206313939016173560489060001231362454121517176407598122566366993798908676852083205089525760 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))

Outputs
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (fma.f64 k #s(literal -1/2 binary64) #s(literal 1/2 binary64))))))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 819538402572085/803469022129495137770981046170581301261101496891396417650688 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 819538402572085/803469022129495137770981046170581301261101496891396417650688 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 449999999999999973457990046261517499935973494258555676005057340905580228432358972138214490305813912545954144924079784244337481911369963359210018733490700288 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64))) #s(literal 1/6 binary64)))
(if (<=.f64 k #s(literal 449999999999999973457990046261517499935973494258555676005057340905580228432358972138214490305813912545954144924079784244337481911369963359210018733490700288 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (pow.f64 (.f64 #s(literal 8 binary64) (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 3 binary64))) #s(literal 1/6 binary64)))
(if (<=.f64 k #s(literal 6200000000000000386831924367266991740316570268240843713101819144877544438829140996412013743397665879766077852853099975759292309450452752913732746535953498802393453598206313939016173560489060001231362454121517176407598122566366993798908676852083205089525760 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64))))
(if (<=.f64 k #s(literal 6200000000000000386831924367266991740316570268240843713101819144877544438829140996412013743397665879766077852853099975759292309450452752913732746535953498802393453598206313939016173560489060001231362454121517176407598122566366993798908676852083205089525760 binary64)) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) (cbrt.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(sqrt.f64 (.f64 (/.f64 n k) (.f64 (PI.f64) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 n k)))
(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))

soundness1.6s (11.5%)

Rules

1096×	`log1p-expm1-u`
1039×	`log1p-expm1-u`
885×	`expm1-log1p-u`
874×	`fma-define`
523×	`expm1-log1p-u`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	665	4294989934
1	1380	4294987068
2	4595	4294986854
0	44	391
1	751	371
0	47	428
1	851	373
0	32	297
1	445	297
2	4848	297
0	39	438
1	96	380
2	211	380
3	410	364
4	686	352
5	1171	352
6	1433	352
7	1698	352
8	2017	352
9	2060	352
10	2088	352
11	2099	352
12	2101	352
0	584	8589954465
1	1087	8589953773
2	3211	8589952977
0	670	20065
1	1375	18361
2	4676	17353
0	26	284
1	427	280
2	4798	280

Stop Event

1×	fuel
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 1576 to 538 computations (65.9% saved)

preprocess61.0ms (0.4%)

Compiler: Compiled 310 to 148 computations (52.3% saved)

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

Iter	Nodes	Cost
0	47	944
1	77	928
2	98	916
3	116	876
4	159	876
5	212	876
6	250	876
7	281	876
8	289	876
9	290	876

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	47	944
1	77	928
2	98	916
3	116	876
4	159	876
5	212	876
6	250	876
7	281	876
8	289	876
9	290	876

analyze162.0ms (1.2%)

sample5.7s (41.1%)

preprocess135.0ms (1%)

explain240.0ms (1.7%)

eval1.0ms (0%)

prune2.0ms (0%)

localize122.0ms (0.9%)

series101.0ms (0.7%)

rewrite744.0ms (5.4%)

simplify303.0ms (2.2%)

eval73.0ms (0.5%)

prune90.0ms (0.7%)

localize441.0ms (3.2%)

series59.0ms (0.4%)

rewrite114.0ms (0.8%)

simplify299.0ms (2.2%)

eval86.0ms (0.6%)

prune105.0ms (0.8%)

localize541.0ms (3.9%)

series88.0ms (0.6%)

rewrite131.0ms (1%)

simplify516.0ms (3.7%)

eval116.0ms (0.8%)

prune213.0ms (1.5%)

localize247.0ms (1.8%)

series158.0ms (1.1%)

rewrite208.0ms (1.5%)

simplify541.0ms (3.9%)

eval152.0ms (1.1%)

prune188.0ms (1.4%)

regimes59.0ms (0.4%)

regimes52.0ms (0.4%)

regimes31.0ms (0.2%)

regimes20.0ms (0.1%)

regimes10.0ms (0.1%)

regimes12.0ms (0.1%)

regimes6.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

bsearch29.0ms (0.2%)

bsearch24.0ms (0.2%)

bsearch22.0ms (0.2%)

simplify21.0ms (0.2%)

soundness1.6s (11.5%)

preprocess61.0ms (0.4%)

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	47	944
1	77	928
2	98	916
3	116	876
4	159	876
5	212	876
6	250	876
7	281	876
8	289	876
9	290	876