Metrics for Migdal et al, Equation (51)

analyze158.0ms (0.8%)

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 16 computations (15.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-pow: 48.0ms (48% of total)

ival-mult: 19.0ms (19% of total)

ival-div: 13.0ms (13% of total)

ival-sqrt: 7.0ms (7% of total)

ival-pi: 6.0ms (6% of total)

ival-sub: 5.0ms (5% of total)

const: 2.0ms (2% of total)

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

sample8.5s (43.8%)

Results

1.1s	8256×	0	valid
5.1s	3800×	5	exit
845.0ms	1906×	1	invalid
178.0ms	629×	0	invalid
36.0ms	214×	0	unsamplable

Precisions

Click to see histograms. Total time spent on operations: 6.2s

ival-pow: 1.7s (26.9% of total)

ival-mult: 1.2s (19.4% of total)

ival-div: 830.0ms (13.4% of total)

ival-sqrt: 730.0ms (11.8% of total)

backward-pass: 720.0ms (11.7% of total)

ival-pi: 519.0ms (8.4% of total)

ival-sub: 414.0ms (6.7% of total)

const: 101.0ms (1.6% of total)

Bogosity

preprocess132.0ms (0.7%)

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))

explain228.0ms (1.2%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
1	219	(3.537126875721426e-282 2.1727940688785115e-164)	1	(0.07259057750181679 1.1689068617645046e-55)	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	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	-	0	-	`(PI.f64)`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	0	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(sqrt.f64 k)`
0	0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	0	-	`n`
0	0	-	0	-	`k`

Results

158.0ms

512×

valid

Compiler

Compiled 132 to 93 computations (29.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-pow: 45.0ms (37.6% of total)

ival-mult: 29.0ms (24.2% of total)

ival-div: 24.0ms (20% of total)

ival-sub: 11.0ms (9.2% of total)

ival-sqrt: 4.0ms (3.3% of total)

const: 4.0ms (3.3% of total)

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

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

eval1.0ms (0%)

Compiler: Compiled 59 to 38 computations (35.6% saved)

prune4.0ms (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 28 computations (17.6% saved)

localize162.0ms (0.8%)

Localize:

Found 7 expressions with local error:

New	Accuracy	Program
✓	99.9%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64))))
✓	99.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.7%	(*.f64 (PI.f64) n)
✓	99.9%	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓	99.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
✓	99.7%	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
✓	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 k))

Results

124.0ms

256×

valid

Compiler

Compiled 105 to 65 computations (38.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 95.0ms

ival-pow: 34.0ms (35.8% of total)

ival-mult: 28.0ms (29.5% of total)

ival-div: 17.0ms (17.9% of total)

ival-sub: 9.0ms (9.5% of total)

const: 4.0ms (4.2% of total)

ival-sqrt: 2.0ms (2.1% of total)

ival-pi: 1.0ms (1.1% of total)

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

series93.0ms (0.5%)

Counts

7 → 132

Calls

Call 1

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

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

Calls

33 calls:

Time	Variable		Point	Expression
34.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
26.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
7.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	-inf	(/ 1 (sqrt k))
2.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))

rewrite288.0ms (1.5%)

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	226
1	427	222
2	4798	222

Stop Event

1×	node limit

Counts

7 → 198

Calls

Call 1

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

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

simplify207.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

644×	`times-frac`
588×	`fma-define`
331×	`associate-r`
305×	`associate-*r/`
278×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	455	17552
1	985	16254
2	3128	14844

Stop Event

1×	node limit

Counts

330 → 300

Calls

Call 1

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

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

eval108.0ms (0.6%)

Compiler: Compiled 6729 to 4479 computations (33.4% saved)

prune59.0ms (0.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	287	13	300
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	288	14	302

Accuracy

100.0%

Counts

302 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
▶	99.6%	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) #s(literal -1 binary64))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	99.7%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 k #s(literal 1/2 binary64)))))
	99.7%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
▶	73.0%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
	48.1%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64))))
	73.0%	(.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))))) (pow.f64 (.f64 (PI.f64) n) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
	38.7%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	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))))
	38.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
▶	38.7%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	96.3%	(.f64 (expm1.f64 (log1p.f64 (pow.f64 k #s(literal -1/2 binary64)))) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	90.3%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Compiler

Compiled 452 to 371 computations (17.9% saved)

localize1.5s (7.6%)

Localize:

Found 20 expressions with local error:

New	Accuracy	Program
✓	99.7%	(/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k))
✓	99.6%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
✓	99.2%	(pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64))))
✓	50.4%	(PI.f64)
✓	99.9%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
✓	99.8%	(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))) #s(literal -1 binary64))
✓	99.8%	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
✓	50.4%	(PI.f64)
✓	99.9%	(/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
✓	99.9%	(.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))
✓	90.4%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
✓	50.4%	(PI.f64)
✓	99.8%	(*.f64 n (/.f64 (PI.f64) k))
✓	99.7%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	90.3%	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓	50.4%	(PI.f64)
	99.9%	(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))
✓	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) k))
✓	99.8%	(.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))))
✓	50.4%	(PI.f64)

Results

154.0ms	125×	0	valid
157.0ms	67×	0	unsamplable
989.0ms	64×	5	exit

Compiler

Compiled 264 to 161 computations (39% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-pow: 651.0ms (58.8% of total)

ival-mult: 172.0ms (15.5% of total)

backward-pass: 97.0ms (8.8% of total)

ival-sub: 67.0ms (6.1% of total)

ival-div: 64.0ms (5.8% of total)

ival-sqrt: 35.0ms (3.2% of total)

const: 19.0ms (1.7% of total)

ival-pi: 2.0ms (0.2% of total)

series145.0ms (0.7%)

Counts

19 → 292

Calls

Call 1

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

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

Calls

75 calls:

Time	Variable		Point	Expression
45.0ms	n	@	0	(* (pow (* 2 (PI)) (- 1/2 (* k 1/2))) (/ (pow n (- 1/2 (* k 1/2))) (sqrt k)))
15.0ms	n	@	inf	(* (pow (* 2 (PI)) (- 1/2 (* k 1/2))) (/ (pow n (- 1/2 (* k 1/2))) (sqrt k)))
14.0ms	n	@	-inf	(* (pow (* 2 (PI)) (- 1/2 (* k 1/2))) (/ (pow n (- 1/2 (* k 1/2))) (sqrt k)))
3.0ms	n	@	-inf	(/ (pow n (- 1/2 (* k 1/2))) (sqrt k))
2.0ms	k	@	0	(* (pow (* 2 (PI)) (- 1/2 (* k 1/2))) (/ (pow n (- 1/2 (* k 1/2))) (sqrt k)))

rewrite163.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

323×	`log1p-expm1-u`
323×	`expm1-log1p-u`
313×	`pow1`
311×	`add-exp-log`
305×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	557
1	775	497

Stop Event

1×	node limit

Counts

19 → 507

Calls

Call 1

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

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

simplify435.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

517×	`times-frac`
412×	`fma-define`
338×	`*-commutative`
255×	`associate-*r/`
223×	`associate-*l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1098	41088
1	2616	37316
2	5947	36350

Stop Event

1×	node limit

Counts

799 → 657

Calls

Call 1

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

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

eval315.0ms (1.6%)

Compiler: Compiled 18611 to 12695 computations (31.8% saved)

prune215.0ms (1.1%)

Pruning

14 alts after pruning (9 fresh and 5 done)

	Pruned	Kept	Total
New	785	7	792
Fresh	6	2	8
Picked	1	4	5
Done	0	1	1
Total	792	14	806

Accuracy

100.0%

Counts

806 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	91.1%	(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.7%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
✓	73.0%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
▶	48.2%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	38.7%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	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))))
▶	38.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓	38.7%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	90.3%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	38.4%	(sqrt.f64 (/.f64 (+.f64 (.f64 #s(literal -2 binary64) (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))) (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) k))
	38.9%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
▶	38.9%	(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
	87.8%	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1/2 binary64)))

Compiler

Compiled 337 to 268 computations (20.5% saved)

localize936.0ms (4.8%)

Localize:

Found 20 expressions with local error:

New	Accuracy	Program
✓	99.8%	(/.f64 (PI.f64) k)
✓	99.7%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n))
✓	99.7%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	50.4%	(PI.f64)
✓	99.9%	(.f64 (.f64 n #s(literal 2 binary64)) (PI.f64))
✓	99.8%	(/.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)))
✓	91.1%	(pow.f64 (/.f64 k (pow.f64 (.f64 (.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k))) #s(literal -1/2 binary64))
	50.4%	(PI.f64)
✓	99.8%	(*.f64 (PI.f64) (/.f64 n k))
✓	99.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓	90.3%	(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
	50.4%	(PI.f64)
✓	99.8%	(/.f64 (*.f64 (PI.f64) #s(literal 2 binary64)) k)
✓	99.8%	(.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k))
✓	90.4%	(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
	50.4%	(PI.f64)
	99.9%	(*.f64 (PI.f64) n)
	99.9%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
✓	99.8%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	50.4%	(PI.f64)

Results

114.0ms	125×	0	valid
597.0ms	68×	5	exit
51.0ms	63×	0	unsamplable

Compiler

Compiled 192 to 101 computations (47.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 653.0ms

ival-mult: 213.0ms (32.6% of total)

ival-pow: 198.0ms (30.3% of total)

backward-pass: 120.0ms (18.4% of total)

ival-sqrt: 58.0ms (8.9% of total)

ival-div: 28.0ms (4.3% of total)

ival-sub: 21.0ms (3.2% of total)

const: 12.0ms (1.8% of total)

ival-pi: 3.0ms (0.5% of total)

series46.0ms (0.2%)

Counts

13 → 264

Calls

Call 1

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

Outputs
#<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)))))>
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Calls

69 calls:

Time	Variable		Point	Expression
10.0ms	k	@	0	(/ (* (PI) 2) k)
4.0ms	n	@	inf	(* (sqrt (/ (PI) k)) (sqrt n))
1.0ms	k	@	0	(/ k (pow (* (* n 2) (PI)) (- 1 k)))
1.0ms	k	@	-inf	(* (pow (* 2 (* (PI) n)) (- 1/2 (* k 1/2))) (pow k -1/2))
1.0ms	k	@	-inf	(pow (/ k (pow (* (* n 2) (PI)) (- 1 k))) -1/2)

rewrite136.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

309×	`log1p-expm1-u`
309×	`expm1-log1p-u`
306×	`pow1`
304×	`add-exp-log`
304×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	387
1	701	383

Stop Event

1×	node limit

Counts

13 → 276

Calls

Call 1

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

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

simplify328.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

448×	`associate-r`
399×	`associate-l`
330×	`exp-prod`
318×	`*-commutative`
270×	`cube-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	787	20392
1	1688	19609
2	5328	19371

Stop Event

1×	node limit

Counts

540 → 450

Calls

Call 1

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

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

eval247.0ms (1.3%)

Compiler: Compiled 16195 to 10321 computations (36.3% saved)

prune130.0ms (0.7%)

Pruning

25 alts after pruning (18 fresh and 7 done)

	Pruned	Kept	Total
New	966	14	980
Fresh	0	4	4
Picked	1	4	5
Done	2	3	5
Total	969	25	994

Accuracy

100.0%

Counts

994 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.9%	(pow.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	38.7%	(pow.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	39.6%	(pow.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 n (PI.f64))) #s(literal -1/2 binary64))
▶	91.0%	(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64))
	48.3%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
✓	99.7%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
✓	73.0%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
✓	48.2%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	38.7%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	38.7%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
✓	38.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓	38.7%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	48.3%	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
✓	90.3%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
▶	38.9%	(sqrt.f64 (/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64))))
	38.4%	(sqrt.f64 (/.f64 (+.f64 (.f64 #s(literal -2 binary64) (.f64 k (.f64 n (.f64 (PI.f64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))))) (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) k))
	38.9%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
	38.9%	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n)))
✓	38.9%	(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
	38.8%	(sqrt.f64 (.f64 n (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))))))
	38.9%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
▶	38.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
	87.8%	(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (*.f64 n #s(literal 2 binary64)) (PI.f64)) (-.f64 #s(literal 1 binary64) k)) k)) #s(literal 1/2 binary64)))
▶	36.3%	(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
	31.7%	(cbrt.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)))

Compiler

Compiled 547 to 441 computations (19.4% saved)

localize583.0ms (3%)

Localize:

Found 19 expressions with local error:

New	Accuracy	Program
✓	99.7%	(.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))
✓	94.5%	(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
✓	90.2%	(log.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
	74.3%	(PI.f64)
✓	99.7%	(/.f64 (PI.f64) (/.f64 k n))
✓	99.5%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
✓	90.3%	(sqrt.f64 (/.f64 (PI.f64) (/.f64 k n)))
	74.3%	(PI.f64)
✓	99.8%	(/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64)))
✓	99.8%	(/.f64 k (PI.f64))
✓	90.3%	(sqrt.f64 (/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64))))
	74.3%	(PI.f64)
	99.7%	(*.f64 (PI.f64) (/.f64 n k))
✓	90.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
	74.3%	(PI.f64)
	99.7%	(.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))
✓	99.7%	(pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 k #s(literal -1 binary64)))
✓	91.1%	(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64))
	74.3%	(PI.f64)

Results

135.0ms	188×	0	valid
345.0ms	68×	5	exit

Compiler

Compiled 183 to 89 computations (51.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 375.0ms

ival-mult: 106.0ms (28.3% of total)

ival-pow: 97.0ms (25.9% of total)

backward-pass: 55.0ms (14.7% of total)

ival-div: 38.0ms (10.1% of total)

ival-sqrt: 24.0ms (6.4% of total)

ival-log: 22.0ms (5.9% of total)

ival-add: 12.0ms (3.2% of total)

const: 10.0ms (2.7% of total)

ival-exp: 6.0ms (1.6% of total)

ival-pi: 4.0ms (1.1% of total)

series309.0ms (1.6%)

Counts

12 → 264

Calls

Call 1

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

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

69 calls:

Time	Variable		Point	Expression
140.0ms	k	@	-inf	(exp (* (log (* n (* 2 (/ (PI) k)))) 1/2))
66.0ms	k	@	-inf	(log (* n (* 2 (/ (PI) k))))
20.0ms	n	@	-inf	(log (* n (* 2 (/ (PI) k))))
17.0ms	k	@	0	(log (* n (* 2 (/ (PI) k))))
15.0ms	n	@	0	(log (* n (* 2 (/ (PI) k))))

rewrite308.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

273×	`associate-r`
243×	`log1p-expm1-u`
243×	`expm1-log1p-u`
242×	`add-exp-log`
241×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	348
1	640	348
2	7971	348

Stop Event

1×	node limit

Counts

12 → 548

Calls

Call 1

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

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

simplify473.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

583×	`associate-r`
568×	`associate-l`
460×	`*-commutative`
447×	`exp-prod`
291×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1020	31736
1	2257	31121
2	7227	30911

Stop Event

1×	node limit

Counts

812 → 607

Calls

Call 1

Inputs
(.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 (+.f64 (.f64 #s(literal -2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 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 #s(literal 1 binary64) (.f64 k (.f64 n (PI.f64))))) (/.f64 (+.f64 (.f64 #s(literal -2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (/.f64 (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))))) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))))) (+.f64 (.f64 #s(literal 1/3 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)))))))))) k)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 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 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 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 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 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 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 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 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 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 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 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 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 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 k #s(literal 1 binary64)))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 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 k #s(literal 1 binary64)))))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 k #s(literal 1 binary64))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 k #s(literal 1 binary64))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 k #s(literal 1 binary64))))
(exp.f64 (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 k #s(literal 1 binary64))))
(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 k #s(literal 1 binary64))))
(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 k #s(literal 1 binary64))))
(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 k #s(literal 1 binary64))))
(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 k #s(literal 1 binary64))))
(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 k #s(literal 1 binary64))))
(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 k #s(literal 1 binary64))))
(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 k #s(literal 1 binary64))))
(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 k #s(literal 1 binary64))))
(/.f64 #s(literal 1/2 binary64) (*.f64 n (PI.f64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 k (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))))) (.f64 n (PI.f64)))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(+.f64 (.f64 k (+.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 k (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))) (.f64 n (PI.f64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 n (PI.f64)))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 n (PI.f64)))))
(+.f64 (.f64 k (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (.f64 n (PI.f64)))) (.f64 k (+.f64 (.f64 #s(literal 1/12 binary64) (/.f64 (.f64 k (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))) (.f64 n (PI.f64)))) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)) (.f64 n (PI.f64)))))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 n (PI.f64)))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 k #s(literal 1 binary64))))
(exp.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(exp.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(exp.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(exp.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k))
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(log1p.f64 (-.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))))
(exp.f64 (.f64 (log.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64)))))) #s(literal 1 binary64)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64))))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64))))))
(.f64 (cbrt.f64 #s(literal 2 binary64)) (.f64 (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))) (cbrt.f64 (.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64))))))
(.f64 (cbrt.f64 (.f64 n (/.f64 (PI.f64) k))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))) (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64)))))))
(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) 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 n (/.f64 (PI.f64) k)))))
(.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (sqrt.f64 n))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64))))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64))))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 n (.f64 k #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))) #s(literal 2 binary64))) (sqrt.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n (*.f64 k #s(literal 1/2 binary64)))))))
(.f64 (sqrt.f64 (/.f64 n (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (cbrt.f64 #s(literal 2 binary64))) (cbrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) 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 n (/.f64 (PI.f64) k)))) (cbrt.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (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 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (PI.f64))) (sqrt.f64 (*.f64 n #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 k n)))
(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n #s(literal -2 binary64))) (sqrt.f64 (/.f64 k (neg.f64 (PI.f64)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 k (PI.f64)))))
(pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))) #s(literal 2 binary64)))) (cbrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))))) (sqrt.f64 (log.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))))
(sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))
(fabs.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 3/2 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 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))) #s(literal 1 binary64))
(/.f64 n (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))))
(/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64))))
(/.f64 (PI.f64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) k))
(/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n))
(/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k)
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
(/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (PI.f64)))
(/.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/2 binary64))
(/.f64 (/.f64 (PI.f64) k) (/.f64 #s(literal 1/2 binary64) n))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) n) (/.f64 k (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))) n))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (PI.f64)) (*.f64 (/.f64 #s(literal 1/2 binary64) n) (neg.f64 k)))
(/.f64 (neg.f64 n) (neg.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64)))))
(/.f64 (neg.f64 n) (*.f64 (/.f64 k (PI.f64)) #s(literal -1/2 binary64)))
(/.f64 (*.f64 n #s(literal -2 binary64)) (/.f64 k (neg.f64 (PI.f64))))
(/.f64 (.f64 n (PI.f64)) (.f64 #s(literal 1/2 binary64) k))
(/.f64 (/.f64 n (*.f64 k #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (.f64 (neg.f64 n) #s(literal 1 binary64)) (.f64 #s(literal -1/2 binary64) (/.f64 k (PI.f64))))
(/.f64 (.f64 n (neg.f64 (PI.f64))) (.f64 #s(literal 1/2 binary64) (neg.f64 k)))
(/.f64 (.f64 (neg.f64 n) (PI.f64)) (.f64 #s(literal -1/2 binary64) k))
(/.f64 (.f64 (neg.f64 n) (neg.f64 (PI.f64))) (.f64 #s(literal -1/2 binary64) (neg.f64 k)))
(/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 #s(literal 2 binary64) (neg.f64 (PI.f64))) (/.f64 k (neg.f64 n)))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (neg.f64 n)) (neg.f64 k))
(/.f64 (.f64 (.f64 n #s(literal 2 binary64)) (neg.f64 (PI.f64))) (neg.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))) (sqrt.f64 (.f64 n #s(literal 2 binary64)))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (*.f64 (neg.f64 (PI.f64)) #s(literal 2 binary64)) (/.f64 k (neg.f64 n)))
(/.f64 (*.f64 (neg.f64 n) (/.f64 (PI.f64) k)) #s(literal -1/2 binary64))
(/.f64 (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))) (sqrt.f64 (/.f64 k (PI.f64))))
(/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 k (PI.f64)))
(/.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (pow.f64 (cbrt.f64 (/.f64 k (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (/.f64 k (PI.f64))))
(pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))) #s(literal 2 binary64)))) (cbrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))) (sqrt.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))))
(neg.f64 (/.f64 (*.f64 n #s(literal 2 binary64)) (/.f64 k (neg.f64 (PI.f64)))))
(neg.f64 (/.f64 (*.f64 n #s(literal -2 binary64)) (/.f64 k (PI.f64))))
(sqrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (PI.f64)) (/.f64 n k)))
(log.f64 (+.f64 #s(literal 1 binary64) (expm1.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))))))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 3 binary64)))
(cbrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 (/.f64 n k) #s(literal 3 binary64))))
(cbrt.f64 (.f64 (pow.f64 n #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal 3 binary64))))
(cbrt.f64 (.f64 (pow.f64 (.f64 n #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (PI.f64) k) #s(literal 3 binary64))))
(cbrt.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)) #s(literal 3 binary64)) (pow.f64 n #s(literal 3 binary64))))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 n #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 k (PI.f64)) #s(literal 3 binary64))))
(expm1.f64 (log1p.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))
(log1p.f64 (expm1.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))
(exp.f64 (log.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64))))))

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

eval243.0ms (1.2%)

Compiler: Compiled 16129 to 9686 computations (39.9% saved)

prune169.0ms (0.9%)

Pruning

37 alts after pruning (28 fresh and 9 done)

	Pruned	Kept	Total
New	1055	20	1075
Fresh	5	8	13
Picked	0	5	5
Done	3	4	7
Total	1063	37	1100

Accuracy

100.0%

Counts

1100 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.9%	(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	29.9%	(pow.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	39.6%	(pow.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 n (PI.f64))) #s(literal -1/2 binary64))
✓	91.0%	(pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64))
	39.6%	(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
	39.6%	(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
	91.1%	(pow.f64 (.f64 k (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)) (pow.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))) #s(literal -1/2 binary64))
	48.3%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
	39.4%	(/.f64 (sqrt.f64 (*.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 k n)))
	48.3%	(/.f64 (sqrt.f64 (*.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 k (PI.f64))))
	48.3%	(/.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 k (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
	39.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 k (PI.f64)) (/.f64 #s(literal 1/2 binary64) n))))
	91.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal -1 binary64))))))
	39.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)))))
	39.5%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
	48.3%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (PI.f64)))) (sqrt.f64 (.f64 n #s(literal 2 binary64))))
	38.7%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
✓	38.7%	(*.f64 (sqrt.f64 (/.f64 (PI.f64) (/.f64 k n))) (sqrt.f64 #s(literal 2 binary64)))
	38.7%	(.f64 (sqrt.f64 (/.f64 n (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 (PI.f64)))
✓	38.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	48.3%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) (sqrt.f64 n))
	38.7%	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
✓	38.7%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	48.3%	(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
✓	90.3%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
✓	38.9%	(sqrt.f64 (/.f64 (/.f64 n #s(literal 1/2 binary64)) (/.f64 k (PI.f64))))
	38.9%	(sqrt.f64 (/.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))) k))
	36.5%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k)) #s(literal -1 binary64))))
	38.9%	(sqrt.f64 (.f64 (PI.f64) (.f64 (/.f64 #s(literal 2 binary64) k) n)))
✓	38.9%	(sqrt.f64 (.f64 n (/.f64 (.f64 (PI.f64) #s(literal 2 binary64)) k)))
	38.8%	(sqrt.f64 (.f64 n (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 k (PI.f64))))))
	38.9%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
	38.9%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))
✓	38.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
✓	36.3%	(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k)))) #s(literal 1/2 binary64)))
	31.7%	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n (.f64 k #s(literal 1/2 binary64)))) #s(literal 3/2 binary64)))
	31.7%	(cbrt.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) (.f64 k #s(literal 1/2 binary64)))) #s(literal 3/2 binary64)))

Compiler

Compiled 1085 to 772 computations (28.8% saved)

regimes69.0ms (0.4%)

Counts

56 → 1

Calls

Call 1

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

Outputs
(.f64 (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))))

Calls

4 calls:

19.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
17.0ms	n
17.0ms	k
11.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 31 to 25 computations (19.4% saved)

regimes32.0ms (0.2%)

Counts

43 → 1

Calls

Call 1

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

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

Calls

2 calls:

15.0ms	n
13.0ms	k

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes30.0ms (0.2%)

Counts

42 → 1

Calls

Call 1

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

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

Calls

2 calls:

13.0ms	k
12.0ms	n

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes37.0ms (0.2%)

Counts

41 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

22.0ms	k
12.0ms	n

Results

Accuracy	Segments	Branch
99.7%	2	`k`
91.1%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes39.0ms (0.2%)

Counts

40 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

35.0ms

Results

Accuracy	Segments	Branch
99.7%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes24.0ms (0.1%)

Counts

38 → 2

Calls

Call 1

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

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

Calls

1 calls:

21.0ms

Results

Accuracy	Segments	Branch
99.7%	2	`k`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes51.0ms (0.3%)

Counts

37 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

28.0ms	n
20.0ms	k

Results

Accuracy	Segments	Branch
55.2%	3	`n`
57.3%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes21.0ms (0.1%)

Counts

31 → 1

Calls

Call 1

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

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

Calls

2 calls:

10.0ms	k
9.0ms	n

Results

Accuracy	Segments	Branch
48.3%	1	`n`
48.3%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	k
4.0ms	n

Results

Accuracy	Segments	Branch
48.3%	1	`k`
48.3%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	n
4.0ms	k

Results

Accuracy	Segments	Branch
39.6%	1	`k`
39.6%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	k
3.0ms	n

Results

Accuracy	Segments	Branch
39.6%	1	`k`
39.6%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	n
3.0ms	k

Results

Accuracy	Segments	Branch
39.6%	1	`k`
39.6%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	n
3.0ms	k

Results

Accuracy	Segments	Branch
38.9%	1	`k`
38.9%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

0.0ms	k
0.0ms	n

Results

Accuracy	Segments	Branch
38.9%	1	`k`
38.9%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch23.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	1.6834407779632826e-33	2.3129825845781428e-29

Results

16.0ms

128×

valid

Compiler

Compiled 255 to 211 computations (17.3% saved)

Precisions

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

ival-mult: 3.0ms (25.8% of total)

ival-pow: 3.0ms (25.8% of total)

ival-div: 2.0ms (17.2% of total)

ival-pi: 1.0ms (8.6% of total)

ival-sub: 1.0ms (8.6% of total)

ival-sqrt: 1.0ms (8.6% of total)

const: 0.0ms (0% of total)

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

bsearch7.0ms (0%)

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
6.0ms	1.6834407779632826e-33	2.3129825845781428e-29

Results

4.0ms

32×

valid

Compiler

Compiled 79 to 65 computations (17.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 1.0ms (29% of total)

ival-sqrt: 1.0ms (29% of total)

ival-pow: 1.0ms (29% of total)

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

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

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

const: 0.0ms (0% of total)

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

bsearch28.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
25.0ms	1.5615574613246147e-25	3.444768284196586e-11

Results

20.0ms

160×

valid

Compiler

Compiled 293 to 239 computations (18.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-pow: 4.0ms (31% of total)

ival-mult: 3.0ms (23.3% of total)

ival-div: 2.0ms (15.5% of total)

ival-pi: 1.0ms (7.8% of total)

ival-sub: 1.0ms (7.8% of total)

ival-sqrt: 1.0ms (7.8% of total)

const: 0.0ms (0% of total)

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

bsearch26.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
24.0ms	5.2350631201924275e+78	1.4966151352480947e+83

Results

19.0ms

128×

valid

Compiler

Compiled 231 to 195 computations (15.6% saved)

Precisions

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

ival-pow: 6.0ms (39.4% of total)

ival-div: 4.0ms (26.3% of total)

ival-mult: 3.0ms (19.7% of total)

ival-pi: 1.0ms (6.6% of total)

ival-sub: 1.0ms (6.6% of total)

ival-sqrt: 1.0ms (6.6% of total)

const: 0.0ms (0% of total)

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

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`*-commutative`
10×	`+-commutative`
8×	`sub-neg`
5×	`neg-sub0`
5×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	95	768
1	131	768
2	148	768
3	158	768
4	165	768
5	167	768

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))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 7136238463529799/356811923176489970264571492362373784095686656 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal -1 binary64)))))))
(if (<=.f64 k #s(literal 1461501637330903/730750818665451459101842416358141509827966271488 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 6490371073168535/162259276829213363391578010288128 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 5400000000000000087003169674954547125078127156767069950401391795434599875608576 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k)) #s(literal -1 binary64)))))
(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 n (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))

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 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 7136238463529799/356811923176489970264571492362373784095686656 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64))) (+.f64 k #s(literal -1 binary64)))))))
(if (<=.f64 k #s(literal 7136238463529799/356811923176489970264571492362373784095686656 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 k (pow.f64 (.f64 (PI.f64) (*.f64 #s(literal 2 binary64) n)) (+.f64 k #s(literal -1 binary64)))))))
(if (<=.f64 k #s(literal 1461501637330903/730750818665451459101842416358141509827966271488 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (pow.f64 (.f64 k (pow.f64 (.f64 n (*.f64 #s(literal 2 binary64) (PI.f64))) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 1461501637330903/730750818665451459101842416358141509827966271488 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (pow.f64 (.f64 k (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (+.f64 k #s(literal -1 binary64)))) #s(literal -1/2 binary64)))
(if (<=.f64 k #s(literal 6490371073168535/162259276829213363391578010288128 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 6490371073168535/162259276829213363391578010288128 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 5400000000000000087003169674954547125078127156767069950401391795434599875608576 binary64)) (.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k)) #s(literal -1 binary64)))))
(if (<=.f64 k #s(literal 5400000000000000087003169674954547125078127156767069950401391795434599875608576 binary64)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 (PI.f64) (*.f64 #s(literal 2 binary64) (/.f64 n k)) #s(literal -1 binary64)))))
(.f64 (sqrt.f64 (.f64 n #s(literal 2 binary64))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
(pow.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 n (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 (PI.f64) n)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 k (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64))) #s(literal -1/2 binary64))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 n (PI.f64)))) #s(literal -1/2 binary64))
(pow.f64 (.f64 k (/.f64 #s(literal 1/2 binary64) (.f64 (PI.f64) n))) #s(literal -1/2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))

soundness2.3s (11.8%)

Rules

1096×	`log1p-expm1-u`
644×	`times-frac`
588×	`fma-define`
583×	`associate-r`
568×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	348
1	640	348
2	7971	348
0	787	20392
1	1688	19609
2	5328	19371
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	42	557
1	775	497
0	1020	31736
1	2257	31121
2	7227	30911
0	455	17552
1	985	16254
2	3128	14844
0	1098	41088
1	2616	37316
2	5947	36350
0	40	387
1	701	383
0	26	226
1	427	222
2	4798	222

Stop Event

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

Compiler

Compiled 1863 to 1271 computations (31.8% saved)

preprocess101.0ms (0.5%)

Compiler: Compiled 456 to 300 computations (34.2% saved)

analyze158.0ms (0.8%)

sample8.5s (43.8%)

preprocess132.0ms (0.7%)

explain228.0ms (1.2%)

eval1.0ms (0%)

prune4.0ms (0%)

localize162.0ms (0.8%)

series93.0ms (0.5%)

rewrite288.0ms (1.5%)

simplify207.0ms (1.1%)

eval108.0ms (0.6%)

prune59.0ms (0.3%)

localize1.5s (7.6%)

series145.0ms (0.7%)

rewrite163.0ms (0.8%)

simplify435.0ms (2.2%)

eval315.0ms (1.6%)

prune215.0ms (1.1%)

localize936.0ms (4.8%)

series46.0ms (0.2%)

rewrite136.0ms (0.7%)

simplify328.0ms (1.7%)

eval247.0ms (1.3%)

prune130.0ms (0.7%)

localize583.0ms (3%)

series309.0ms (1.6%)

rewrite308.0ms (1.6%)

simplify473.0ms (2.4%)

eval243.0ms (1.2%)

prune169.0ms (0.9%)

regimes69.0ms (0.4%)

regimes32.0ms (0.2%)

regimes30.0ms (0.2%)

regimes37.0ms (0.2%)

regimes39.0ms (0.2%)

regimes24.0ms (0.1%)

regimes51.0ms (0.3%)

regimes21.0ms (0.1%)

regimes11.0ms (0.1%)

regimes11.0ms (0.1%)

regimes8.0ms (0%)

regimes6.0ms (0%)

regimes6.0ms (0%)

regimes1.0ms (0%)

bsearch23.0ms (0.1%)

bsearch7.0ms (0%)

bsearch28.0ms (0.1%)

bsearch26.0ms (0.1%)

simplify15.0ms (0.1%)

soundness2.3s (11.8%)

preprocess101.0ms (0.5%)

end0.0ms (0%)

Profiling