Metrics for Migdal et al, Equation (51)

analyze181.0ms (1.2%)

Algorithm

1×

Search

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

Compiler

Compiled 19 to 14 computations (26.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-pow: 83.0ms (63.8% of total)

ival-mult: 18.0ms (13.8% of total)

ival-div: 12.0ms (9.2% of total)

ival-sqrt: 7.0ms (5.4% of total)

ival-sub: 5.0ms (3.8% of total)

ival-pi: 4.0ms (3.1% of total)

const: 1.0ms (0.8% of total)

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

sample5.9s (40.3%)

Results

2.3s	4074×	5	exit
1.6s	8256×	0	valid
617.0ms	2002×	1	invalid
179.0ms	257×	0	unsamplable
101.0ms	456×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 3.5s

ival-pow: 1.2s (33.8% of total)

ival-pi: 580.0ms (16.8% of total)

ival-mult: 537.0ms (15.6% of total)

ival-div: 397.0ms (11.5% of total)

backward-pass: 276.0ms (8% of total)

ival-sqrt: 270.0ms (7.8% of total)

ival-sub: 188.0ms (5.4% of total)

const: 39.0ms (1.1% of total)

Bogosity

preprocess135.0ms (0.9%)

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))

explain146.0ms (1%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
2	217	(1.3331092477175143e+215 1.3623719888004418e-236)	-	`(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64)))`
0	0	-	-	`(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))`
0	0	-	-	`(PI.f64)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) (PI.f64))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 k))`
0	0	-	-	`(-.f64 #s(literal 1 binary64) k)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(sqrt.f64 k)`
0	0	-	-	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))`
0	0	-	-	`n`
0	0	-	-	`k`

Results

86.0ms

512×

valid

Compiler

Compiled 132 to 41 computations (68.9% saved)

Precisions

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

ival-pow: 20.0ms (36.3% of total)

ival-mult: 11.0ms (20% of total)

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

ival-pi: 6.0ms (10.9% of total)

ival-sqrt: 6.0ms (10.9% of total)

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

const: 1.0ms (1.8% of total)

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

eval1.0ms (0%)

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

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.5%	(.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))

▶

99.5%

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

Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

localize94.0ms (0.6%)

Localize:

Found 8 expressions of interest:

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

Results

68.0ms

256×

valid

Compiler

Compiled 105 to 21 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-pow: 18.0ms (42% of total)

ival-mult: 9.0ms (21% of total)

ival-div: 7.0ms (16.3% of total)

ival-sub: 3.0ms (7% of total)

ival-sqrt: 3.0ms (7% of total)

ival-pi: 2.0ms (4.7% of total)

const: 1.0ms (2.3% of total)

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

series97.0ms (0.7%)

Counts

12 → 160

Calls

Call 1

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

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

Calls

42 calls:

Time	Variable		Point	Expression
33.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
23.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
9.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
4.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
1.0ms	n	@	0	(/ (pow (* 2 (* (PI) n)) (- 1/2 (/ k 2))) (sqrt k))

rewrite306.0ms (2.1%)

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	274
1	427	270
2	4798	270

Stop Event

1×	node limit

Counts

12 → 299

Calls

Call 1

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

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

simplify233.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

459 → 408

Calls

Call 1

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

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

eval58.0ms (0.4%)

Compiler: Compiled 9568 to 1524 computations (84.1% saved)

prune73.0ms (0.5%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	444	15	459
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	444	17	461

Accuracy

100.0%

Counts

461 → 17

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))
	99.4%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (pow.f64 (pow.f64 k #s(literal 1/4 binary64)) #s(literal 2 binary64)))
	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	95.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
▶	71.3%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
	98.9%	(/.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)))))
	94.9%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
▶	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
▶	99.6%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	75.9%	(.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)))
✓	99.5%	(.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))))
	98.8%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 k #s(literal -1/2 binary64)))))
	94.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
	43.8%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
▶	43.8%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	88.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Compiler

Compiled 572 to 427 computations (25.3% saved)

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
	cost-diff	0	(PI.f64)
	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
✓	cost-diff	256	(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
	cost-diff	0	(/.f64 k #s(literal 2 binary64))
	cost-diff	0	(PI.f64)
	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
	cost-diff	0	(PI.f64)
	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))
	cost-diff	0	(sqrt.f64 k)
✓	cost-diff	0	(/.f64 (PI.f64) k)
✓	cost-diff	0	(*.f64 n (/.f64 (PI.f64) k))
✓	cost-diff	0	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 k #s(literal -1/2 binary64))
	cost-diff	0	(PI.f64)
	cost-diff	0	(*.f64 (PI.f64) n)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))

Rules

86×	`fma-define`
56×	`associate-r`
53×	`associate-l`
42×	`distribute-lft-in`
40×	`fma-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	933
1	66	893
2	102	881
3	136	865
4	192	865
5	241	865
6	367	865
7	583	865
8	738	865
9	808	865
10	812	865

Stop Event

1×

saturated

Calls

Call 1

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

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

localize302.0ms (2.1%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64)))
✓	accuracy	99.6%	(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
	accuracy	57.2%	(PI.f64)
	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
✓	accuracy	78.7%	(cbrt.f64 (pow.f64 k #s(literal 3/2 binary64)))
	accuracy	57.2%	(PI.f64)
	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.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))))))
✓	accuracy	99.7%	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
	accuracy	57.2%	(PI.f64)
✓	accuracy	99.8%	(/.f64 (PI.f64) k)
✓	accuracy	99.6%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	88.2%	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
	accuracy	57.2%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))
	accuracy	99.8%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	accuracy	57.2%	(PI.f64)

Results

103.0ms	52×	5	exit
88.0ms	143×	0	valid
36.0ms	59×	0	unsamplable
3.0ms	2×	0	invalid

Compiler

Compiled 273 to 37 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 131.0ms

ival-pow: 65.0ms (49.8% of total)

backward-pass: 19.0ms (14.5% of total)

ival-div: 15.0ms (11.5% of total)

ival-mult: 15.0ms (11.5% of total)

ival-sqrt: 7.0ms (5.4% of total)

ival-sub: 3.0ms (2.3% of total)

ival-pi: 2.0ms (1.5% of total)

ival-add: 2.0ms (1.5% of total)

ival-cbrt: 2.0ms (1.5% of total)

const: 1.0ms (0.8% of total)

series143.0ms (1%)

Counts

14 → 276

Calls

Call 1

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

Outputs
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (*.f64 #s(literal -1/2 binary64) k)>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (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 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (sqrt.f64 (/.f64 (*.f64 n (PI.f64)) k))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<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 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (/.f64 (*.f64 n (PI.f64)) k)>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (.f64 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 1/8 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 (pow.f64 k #s(literal 3 binary64))) (+.f64 (.f64 #s(literal -1/64 binary64) (.f64 (sqrt.f64 (.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 -1/192 binary64) (.f64 (sqrt.f64 (.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 (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)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (.f64 (pow.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) k))))) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 n) (log.f64 (.f64 #s(literal 2 binary64) (PI.f64)))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))>
#<alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) k)) (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n)))))))>
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#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64))>
#<alt (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) #s(literal 1/4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))) (.f64 #s(literal 1/32 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) #s(literal 1/4 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))))) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)))>
#<alt (+.f64 (.f64 k (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))))) (.f64 k (+.f64 (.f64 #s(literal -1/384 binary64) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) #s(literal 1/4 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64)))) (.f64 #s(literal 1/32 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))))))) (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k) #s(literal 1/4 binary64)))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64)) (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) (-.f64 #s(literal 1 binary64) k)))))>
#<alt (.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>
#<alt (.f64 (exp.f64 (.f64 #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) k))))) (exp.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) k))))))>

Calls

72 calls:

Time	Variable		Point	Expression
41.0ms	n	@	0	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
15.0ms	k	@	inf	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
14.0ms	k	@	-inf	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
6.0ms	k	@	0	(/ (sqrt k) (pow (* 2 (* (PI) n)) (+ 1/2 (* k -1/2))))
4.0ms	k	@	inf	(* (sqrt (* n (/ (PI) k))) (sqrt 2))

rewrite131.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

331×	`log1p-expm1-u`
331×	`expm1-log1p-u`
324×	`pow1`
315×	`add-cube-cbrt`
312×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	502
1	732	466

Stop Event

1×	node limit

Counts

14 → 323

Calls

Call 1

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

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

simplify367.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

660×	`associate-r`
540×	`associate-l`
485×	`exp-prod`
451×	`*-commutative`
218×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	933	30818
1	2149	29463
2	7354	29343

Stop Event

1×	node limit

Counts

599 → 583

Calls

Call 1

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

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

eval132.0ms (0.9%)

Compiler: Compiled 19736 to 3019 computations (84.7% saved)

prune127.0ms (0.9%)

Pruning

21 alts after pruning (16 fresh and 5 done)

	Pruned	Kept	Total
New	930	11	941
Fresh	5	5	10
Picked	2	3	5
Done	0	2	2
Total	937	21	958

Accuracy

100.0%

Counts

958 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	43.8%	(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	43.7%	(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	95.7%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (exp.f64 (*.f64 (log.f64 k) #s(literal 1/2 binary64))))
✓	71.3%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (cbrt.f64 (pow.f64 k #s(literal 3/2 binary64))))
▶	99.6%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (.f64 k #s(literal 1/2 binary64)))))
▶	98.9%	(/.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)))))
	94.9%	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) k)))) (sqrt.f64 k))
	98.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (.f64 #s(literal -1/2 binary64) k))) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))))))
	44.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
✓	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
✓	99.6%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
✓	99.5%	(.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))))
	94.9%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (exp.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))))
	98.9%	(.f64 (.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 k #s(literal -1/2 binary64))) (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n))) (pow.f64 k #s(literal -1/2 binary64)))
	43.8%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
	43.8%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
▶	43.8%	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
▶	88.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	43.9%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
▶	44.0%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))

Compiler

Compiled 587 to 443 computations (24.5% saved)

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

53×	`associate-l`
41×	`associate-r`
22×	`*-commutative`
11×	`associate-*r/`
10×	`*-rgt-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	836
1	76	806
2	114	806
3	197	806
4	263	806
5	273	806
6	284	806
7	299	806
8	307	806
9	309	806

Stop Event

1×

saturated

Calls

Call 1

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

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

localize337.0ms (2.3%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
	accuracy	99.7%	(*.f64 (PI.f64) n)
✓	accuracy	99.7%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64)))))
	accuracy	76.9%	(PI.f64)
✓	accuracy	99.8%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)
✓	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	88.2%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	accuracy	76.9%	(PI.f64)
✓	accuracy	99.5%	(*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	88.1%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k))))
	accuracy	76.9%	(PI.f64)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))
✓	accuracy	99.7%	(*.f64 (PI.f64) (/.f64 n k))
✓	accuracy	88.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
	accuracy	76.9%	(PI.f64)
✓	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
✓	accuracy	99.7%	(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 k #s(literal -1/2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (.f64 k #s(literal 1/2 binary64)))))
✓	accuracy	99.7%	(*.f64 n (PI.f64))
	accuracy	76.9%	(PI.f64)

Results

176.0ms	59×	5	exit
97.0ms	195×	0	valid
2.0ms	2×	0	invalid

Compiler

Compiled 242 to 37 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 138.0ms

ival-pow: 58.0ms (42% of total)

ival-mult: 25.0ms (18.1% of total)

backward-pass: 18.0ms (13% of total)

ival-sqrt: 14.0ms (10.1% of total)

ival-div: 10.0ms (7.2% of total)

ival-pi: 8.0ms (5.8% of total)

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

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

const: 1.0ms (0.7% of total)

series63.0ms (0.4%)

Counts

18 → 336

Calls

Call 1

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

Calls

90 calls:

Time	Variable		Point	Expression
4.0ms	n	@	-inf	(sqrt (/ (pow (* 2 (* n (PI))) (- 1 k)) k))
3.0ms	k	@	-inf	(/ (* 1 (pow k -1/2)) (pow (* 2 (* n (PI))) (+ -1/2 (* k 1/2))))
2.0ms	k	@	0	(/ (* 1 (pow k -1/2)) (pow (* 2 (* n (PI))) (+ -1/2 (* k 1/2))))
2.0ms	k	@	0	(/ (sqrt (* 2 (* (PI) n))) (* (sqrt k) (pow (* 2 (* (PI) n)) (* k 1/2))))
2.0ms	k	@	0	(sqrt (/ (pow (* 2 (* n (PI))) (- 1 k)) k))

rewrite232.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

305×	`log1p-expm1-u`
305×	`expm1-log1p-u`
302×	`pow1`
301×	`add-cube-cbrt`
298×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	527
1	760	498

Stop Event

1×	node limit

Counts

18 → 437

Calls

Call 1

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

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

simplify455.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

309×	`distribute-rgt-neg-in`
300×	`distribute-lft-neg-in`
288×	`exp-prod`
277×	`*-commutative`
274×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1073	32715
1	2357	31926
2	5685	30954

Stop Event

1×	node limit

Counts

773 → 648

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

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

eval188.0ms (1.3%)

Compiler: Compiled 18383 to 2846 computations (84.5% saved)

prune136.0ms (0.9%)

Pruning

20 alts after pruning (15 fresh and 5 done)

	Pruned	Kept	Total
New	858	10	868
Fresh	6	5	11
Picked	3	2	5
Done	2	3	5
Total	869	20	889

Accuracy

100.0%

Counts

889 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	43.8%	(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	28.8%	(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.6%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
▶	43.7%	(/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64)))
	76.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))) (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)))
▶	44.3%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
✓	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64))))))
✓	99.6%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	43.8%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
	43.8%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
▶	43.6%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
✓	88.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	88.1%	(sqrt.f64 (/.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) k))
	43.9%	(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
▶	43.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
	43.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 n (PI.f64))))))
✓	44.0%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
	40.9%	(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
	30.6%	(cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))

Compiler

Compiled 463 to 361 computations (22% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

16×	`*-commutative`
12×	`associate-r`
11×	`associate-l`
6×	`associate-*r/`
4×	`associate-*l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	638
1	61	626
2	86	620
3	103	620
4	117	620
5	117	620

Stop Event

1×

saturated

Calls

Call 1

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

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

localize493.0ms (3.4%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.4%	(/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	88.8%	(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
	accuracy	76.9%	(PI.f64)
	accuracy	99.7%	(*.f64 (PI.f64) (/.f64 n k))
✓	accuracy	99.5%	(/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	88.1%	(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
	accuracy	76.9%	(PI.f64)
✓	accuracy	99.5%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
✓	accuracy	98.8%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))
✓	accuracy	88.2%	(sqrt.f64 (/.f64 n k))
	accuracy	76.9%	(PI.f64)
✓	accuracy	99.7%	(/.f64 (*.f64 n (PI.f64)) k)
	accuracy	99.7%	(*.f64 n (PI.f64))
✓	accuracy	88.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
	accuracy	76.9%	(PI.f64)
	accuracy	99.8%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
✓	accuracy	99.7%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
	accuracy	99.7%	(*.f64 n (PI.f64))
	accuracy	76.9%	(PI.f64)

Results

291.0ms	59×	5	exit
149.0ms	195×	0	valid
1.0ms	2×	0	invalid

Compiler

Compiled 178 to 32 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-mult: 24.0ms (25.6% of total)

ival-pow: 22.0ms (23.5% of total)

backward-pass: 15.0ms (16% of total)

ival-sqrt: 15.0ms (16% of total)

ival-div: 14.0ms (15% of total)

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

const: 1.0ms (1.1% of total)

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

series36.0ms (0.2%)

Counts

13 → 184

Calls

Call 1

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

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

Calls

72 calls:

Time	Variable		Point	Expression
3.0ms	k	@	0	(/ (sqrt (/ k (* n (PI)))) (sqrt 2))
1.0ms	n	@	0	(/ (sqrt (/ k (* n (PI)))) (sqrt 2))
1.0ms	n	@	-inf	(/ (sqrt (* (PI) (/ n k))) (sqrt 1/2))
1.0ms	n	@	0	(/ (sqrt (* (PI) (/ n k))) (sqrt 1/2))
1.0ms	k	@	-inf	(/ (sqrt (/ k (* n (PI)))) (sqrt 2))

rewrite153.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

267×	`log1p-expm1-u`
267×	`expm1-log1p-u`
265×	`pow1`
265×	`add-cube-cbrt`
264×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	358
1	637	354

Stop Event

1×	node limit

Counts

13 → 657

Calls

Call 1

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

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

simplify722.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-define`
452×	`times-frac`
400×	`exp-prod`
379×	`associate-*r/`
348×	`cube-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1077	35445
1	2343	32767
2	6530	32639

Stop Event

1×	node limit

Counts

841 → 681

Calls

Call 1

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

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

eval300.0ms (2.1%)

Compiler: Compiled 15111 to 3067 computations (79.7% saved)

prune270.0ms (1.8%)

Pruning

36 alts after pruning (28 fresh and 8 done)

	Pruned	Kept	Total
New	919	21	940
Fresh	3	7	10
Picked	2	3	5
Done	0	5	5
Total	924	36	960

Accuracy

100.0%

Counts

960 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	43.8%	(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	28.8%	(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	43.7%	(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
	28.8%	(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	44.5%	(pow.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 n (PI.f64))) #s(literal -1/2 binary64))
	44.6%	(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
	44.3%	(/.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
	44.3%	(/.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	99.6%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
✓	99.6%	(/.f64 (pow.f64 k #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (+.f64 #s(literal -1/2 binary64) (*.f64 k #s(literal 1/2 binary64)))))
✓	43.7%	(/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64)))
	55.5%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
	43.7%	(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
	76.8%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))) (sqrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)))
	44.4%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
✓	99.5%	(/.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))))))
	43.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 n (/.f64 (PI.f64) (.f64 k #s(literal 1/2 binary64)))))))
	44.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 n (PI.f64)))))
	43.8%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
	44.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)) k)))
✓	99.6%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
	43.8%	(.f64 (sqrt.f64 (/.f64 (.f64 (PI.f64) n) k)) (sqrt.f64 #s(literal 2 binary64)))
	43.8%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓	43.6%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
✓	88.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	88.1%	(sqrt.f64 (/.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) n) (PI.f64)) k)) k))
	43.9%	(sqrt.f64 (/.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))
	43.9%	(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
	43.9%	(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
	43.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
	38.2%	(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))))
	43.9%	(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
✓	44.0%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
	44.0%	(sqrt.f64 (.f64 #s(literal 2 binary64) (fabs.f64 (.f64 n (/.f64 (PI.f64) k)))))
	40.9%	(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
	30.6%	(cbrt.f64 (pow.f64 (.f64 n (/.f64 (PI.f64) (.f64 k #s(literal 1/2 binary64)))) #s(literal 3/2 binary64)))

Compiler

Compiled 1179 to 566 computations (52% saved)

regimes76.0ms (0.5%)

Counts

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

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

Calls

4 calls:

20.0ms	n
18.0ms	k
17.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
16.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

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

Compiler

Compiled 31 to 23 computations (25.8% saved)

regimes30.0ms (0.2%)

Counts

40 → 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 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 (.f64 n (/.f64 (PI.f64) k)) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (/.f64 #s(literal 2 binary64) k) (.f64 n (PI.f64))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (/.f64 k (*.f64 n (PI.f64)))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) (/.f64 k n)))
(sqrt.f64 (/.f64 (*.f64 n (/.f64 (PI.f64) k)) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k 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 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 k (.f64 n (PI.f64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) n) (PI.f64)) k)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 n (/.f64 (PI.f64) k)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (.f64 k #s(literal 1/2 binary64)) (.f64 n (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 n (/.f64 (PI.f64) (.f64 k #s(literal 1/2 binary64)))))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (fabs.f64 (.f64 n (/.f64 (PI.f64) k)))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (sqrt.f64 (/.f64 n k)))
(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
(.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 #s(literal 2 binary64)) (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))))
(/.f64 (sqrt.f64 (*.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 1/2 binary64)))
(cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n 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)))
(/.f64 (pow.f64 (/.f64 k (*.f64 n (PI.f64))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (.f64 n (*.f64 (PI.f64) (/.f64 #s(literal 1 binary64) k)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (.f64 n (.f64 (/.f64 (PI.f64) k) #s(literal 2 binary64))) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
(/.f64 (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	n
13.0ms	k

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes31.0ms (0.2%)

Counts

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

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

Calls

2 calls:

15.0ms	n
12.0ms	k

Results

Accuracy	Segments	Branch
99.6%	2	`k`
90.5%	2	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes161.0ms (1.1%)

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

Outputs

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

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

Calls

2 calls:

147.0ms	k
11.0ms	n

Results

Accuracy	Segments	Branch
60.5%	3	`n`
63.3%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes22.0ms (0.1%)

Counts

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

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

Calls

2 calls:

11.0ms	k
9.0ms	n

Results

Accuracy	Segments	Branch
55.5%	1	`n`
55.5%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes21.0ms (0.1%)

Counts

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

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

Calls

2 calls:

7.0ms	n
7.0ms	k

Results

Accuracy	Segments	Branch
44.6%	1	`n`
44.6%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.3%)

Threshold costs -0.1b (-0.3%)

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

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

Calls

2 calls:

4.0ms	n
3.0ms	k

Results

Accuracy	Segments	Branch
44.0%	1	`k`
44.0%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch6.0ms (0%)

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
5.0ms	1.1095169098525436e-37	2.2139018122601957e-37

Results

4.0ms

32×

valid

Compiler

Compiled 77 to 61 computations (20.8% saved)

Precisions

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

ival-div: 1.0ms (35.7% of total)

ival-mult: 1.0ms (35.7% of total)

ival-pow: 1.0ms (35.7% of total)

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

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

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

const: 0.0ms (0% of total)

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

bsearch15.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	2.4700501020781508e+61	4.5186581516978986e+61

Results

11.0ms

64×

valid

Compiler

Compiled 127 to 105 computations (17.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-pow: 2.0ms (32.1% of total)

ival-div: 1.0ms (16% of total)

ival-mult: 1.0ms (16% of total)

ival-sqrt: 1.0ms (16% of total)

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

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

const: 0.0ms (0% of total)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	384
1	80	384
2	89	384
3	95	384
4	99	384
5	100	384

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -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 3591786423904427/23945242826029513411849172299223580994042798784118784 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 44999999999999999863292627427270670600792979669846157862895616 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))

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)))
(/.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 3591786423904427/23945242826029513411849172299223580994042798784118784 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 3591786423904427/23945242826029513411849172299223580994042798784118784 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 44999999999999999863292627427270670600792979669846157862895616 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) (*.f64 k #s(literal 1/2 binary64))) #s(literal 1 binary64)))))
(if (<=.f64 k #s(literal 44999999999999999863292627427270670600792979669846157862895616 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) (*.f64 #s(literal 1/2 binary64) k)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) (sqrt.f64 k))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))

soundness2.2s (15.1%)

Rules

1096×	`log1p-expm1-u`
718×	`fma-define`
660×	`associate-r`
540×	`associate-l`
535×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1077	35445
1	2343	32767
2	6530	32639
0	37	358
1	637	354
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	933	30818
1	2149	29463
2	7354	29343
0	42	502
1	732	466
0	600	19256
1	1218	17586
2	4112	16578
0	26	274
1	427	270
2	4798	270

Stop Event

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

Compiler

Compiled 1147 to 421 computations (63.3% saved)

preprocess93.0ms (0.6%)

Compiler: Compiled 248 to 120 computations (51.6% saved)

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

Iter	Nodes	Cost
0	42	933
1	66	893
2	102	881
3	136	865
4	192	865
5	241	865
6	367	865
7	583	865
8	738	865
9	808	865
10	812	865

Iter	Nodes	Cost
0	42	836
1	76	806
2	114	806
3	197	806
4	263	806
5	273	806
6	284	806
7	299	806
8	307	806
9	309	806

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

Iter	Nodes	Cost
0	42	933
1	66	893
2	102	881
3	136	865
4	192	865
5	241	865
6	367	865
7	583	865
8	738	865
9	808	865
10	812	865

Iter	Nodes	Cost
0	42	836
1	76	806
2	114	806
3	197	806
4	263	806
5	273	806
6	284	806
7	299	806
8	307	806
9	309	806

analyze181.0ms (1.2%)

sample5.9s (40.3%)

preprocess135.0ms (0.9%)

explain146.0ms (1%)

eval1.0ms (0%)

prune2.0ms (0%)

simplify22.0ms (0.1%)

localize94.0ms (0.6%)

series97.0ms (0.7%)

rewrite306.0ms (2.1%)

simplify233.0ms (1.6%)

eval58.0ms (0.4%)

prune73.0ms (0.5%)

simplify55.0ms (0.4%)

localize302.0ms (2.1%)

series143.0ms (1%)

rewrite131.0ms (0.9%)

simplify367.0ms (2.5%)

eval132.0ms (0.9%)

prune127.0ms (0.9%)

simplify40.0ms (0.3%)

localize337.0ms (2.3%)

series63.0ms (0.4%)

rewrite232.0ms (1.6%)

simplify455.0ms (3.1%)

eval188.0ms (1.3%)

prune136.0ms (0.9%)

simplify18.0ms (0.1%)

localize493.0ms (3.4%)

series36.0ms (0.2%)

rewrite153.0ms (1%)

simplify722.0ms (4.9%)

eval300.0ms (2.1%)

prune270.0ms (1.8%)

regimes76.0ms (0.5%)

regimes30.0ms (0.2%)

regimes31.0ms (0.2%)

regimes161.0ms (1.1%)

regimes22.0ms (0.1%)

regimes21.0ms (0.1%)

regimes8.0ms (0.1%)

bsearch6.0ms (0%)

bsearch15.0ms (0.1%)

simplify8.0ms (0.1%)

soundness2.2s (15.1%)

preprocess93.0ms (0.6%)

end0.0ms (0%)

Profiling

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

Iter	Nodes	Cost
0	42	933
1	66	893
2	102	881
3	136	865
4	192	865
5	241	865
6	367	865
7	583	865
8	738	865
9	808	865
10	812	865

Iter	Nodes	Cost
0	42	836
1	76	806
2	114	806
3	197	806
4	263	806
5	273	806
6	284	806
7	299	806
8	307	806
9	309	806