Metrics for Migdal et al, Equation (51)

analyze216.0ms (1.3%)

Algorithm

1×

Search

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

Operation ival-mult, time spent: 70.0ms, 46.0% of total-time

Operation ival-pow, time spent: 48.0ms, 31.0% of total-time

Operation ival-div, time spent: 16.0ms, 10.0% of total-time

Operation ival-sqrt, time spent: 8.0ms, 5.0% of total-time

Operation ival-sub, time spent: 5.0ms, 3.0% of total-time

Operation ival-pi, time spent: 4.0ms, 3.0% of total-time

Operation const, time spent: 3.0ms, 2.0% of total-time

sample4.6s (28.2%)

Results

1.3s	6207×	256	valid
1.5s	2958×	1024	invalid
479.0ms	2048×	256	infinite
216.0ms	1645×	256	invalid
515.0ms	1571×	512	invalid
41.0ms	202×	256	unsamplable
67.0ms	106×	2048	invalid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 2.7s

Operation ival-pow, time spent: 957.0ms, 36.0% of total-time

Operation ival-mult, time spent: 610.0ms, 23.0% of total-time

Operation ival-div, time spent: 465.0ms, 17.0% of total-time

Operation ival-sqrt, time spent: 248.0ms, 9.0% of total-time

Operation ival-pi, time spent: 175.0ms, 7.0% of total-time

Operation ival-sub, time spent: 147.0ms, 5.0% of total-time

Operation const, time spent: 79.0ms, 3.0% of total-time

Bogosity

preprocess463.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

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

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
4	223	(1.3382124841530207e-187 9.113940849605003e-185)	-	`(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`

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

Compiler

Compiled 132 to 93 computations (29.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 184.0ms

Operation ival-mult, time spent: 90.0ms, 49.0% of total-time

Operation ival-pow, time spent: 47.0ms, 25.0% of total-time

Operation ival-div, time spent: 23.0ms, 12.0% of total-time

Operation ival-sub, time spent: 12.0ms, 7.0% of total-time

Operation ival-sqrt, time spent: 5.0ms, 3.0% of total-time

Operation const, time spent: 5.0ms, 3.0% of total-time

Operation ival-pi, time spent: 2.0ms, 1.0% of total-time

eval1.0ms (0%)

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

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.4%	(.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

▶

99.5%

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

▶

99.4%

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

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize192.0ms (1.2%)

Localize:

Found 7 expressions with local error:

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

Compiler

Compiled 105 to 65 computations (38.1% saved)

Precisions

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

Operation ival-pow, time spent: 41.0ms, 40.0% of total-time

Operation ival-mult, time spent: 23.0ms, 23.0% of total-time

Operation ival-div, time spent: 19.0ms, 19.0% of total-time

Operation ival-sub, time spent: 11.0ms, 11.0% of total-time

Operation const, time spent: 4.0ms, 4.0% of total-time

Operation ival-sqrt, time spent: 3.0ms, 3.0% of total-time

Operation ival-pi, time spent: 1.0ms, 1.0% of total-time

series92.0ms (0.6%)

Counts

7 → 132

Calls

Call 1

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

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

Calls

33 calls:

Time	Variable		Point	Expression
32.0ms	n	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
26.0ms	n	@	-inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
9.0ms	n	@	inf	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
5.0ms	k	@	0	(* (/ 1 (sqrt k)) (pow (* (* 2 (PI)) n) (/ (- 1 k) 2)))
3.0ms	k	@	0	(pow (* 2 (* (PI) n)) (- 1/2 (/ k 2)))

rewrite294.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1096×	`log1p-expm1-u`
523×	`expm1-log1p-u`
292×	`prod-diff`
148×	`add-exp-log`
148×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	226
1	427	222
2	4798	222

Stop Event

1×	node limit

Counts

7 → 198

Calls

Call 1

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

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

simplify302.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

330 → 300

Calls

Call 1

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

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

eval124.0ms (0.8%)

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

prune62.0ms (0.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	285	15	300
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	286	16	302

Accuracy

100.0%

Counts

302 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(pow.f64 (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (pow.f64 k #s(literal 1/4 binary64))) #s(literal 2 binary64))
✓	99.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	95.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
▶	99.2%	(/.f64 (.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 k #s(literal 1/2 binary64))))
	99.3%	(/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 k #s(literal 1/2 binary64)))))
▶	99.5%	(/.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))))))
	99.4%	(.f64 (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)))
	99.4%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (*.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 1/4 binary64))) (sqrt.f64 k)))
	73.1%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (PI.f64)) (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (/.f64 (pow.f64 n (-.f64 #s(literal 1/2 binary64) (.f64 k #s(literal 1/2 binary64)))) (sqrt.f64 k)))
	99.2%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n) (.f64 k #s(literal 1/2 binary64)))))
	53.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (+.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)))))
	40.4%	(.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))
	99.0%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
	40.4%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
▶	40.0%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
▶	86.8%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))

Compiler

Compiled 588 to 463 computations (21.3% saved)

localize2.1s (12.9%)

Localize:

Found 20 expressions with local error:

New	Accuracy	Program
✓	99.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)))
	99.8%	(*.f64 (PI.f64) n)
✓	99.7%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) n))))
✓	55.0%	(PI.f64)
	99.8%	(*.f64 (PI.f64) n)
✓	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)))
✓	99.5%	(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))
✓	55.0%	(PI.f64)
✓	99.8%	(pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k))
✓	99.8%	(.f64 n (.f64 #s(literal 2 binary64) (PI.f64)))
✓	87.1%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
✓	55.0%	(PI.f64)
✓	99.7%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	99.5%	(*.f64 n (/.f64 (PI.f64) k))
✓	87.1%	(sqrt.f64 (*.f64 n (/.f64 (PI.f64) k)))
✓	55.0%	(PI.f64)
	99.8%	(*.f64 (PI.f64) n)
✓	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
✓	99.7%	(/.f64 (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)))))
✓	55.0%	(PI.f64)

Compiler

Compiled 278 to 158 computations (43.2% saved)

Precisions

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

Operation ival-pow, time spent: 1.4s, 81.0% of total-time

Operation ival-mult, time spent: 175.0ms, 10.0% of total-time

Operation ival-sqrt, time spent: 48.0ms, 3.0% of total-time

Operation ival-sub, time spent: 40.0ms, 2.0% of total-time

Operation ival-div, time spent: 37.0ms, 2.0% of total-time

Operation const, time spent: 21.0ms, 1.0% of total-time

Operation ival-pi, time spent: 3.0ms, 0.0% of total-time

series132.0ms (0.8%)

Counts

17 → 264

Calls

Call 1

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

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

Calls

66 calls:

Time	Variable		Point	Expression
46.0ms	n	@	0	(/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4))
16.0ms	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))
5.0ms	n	@	-inf	(/ (sqrt k) (pow (* 2 (* (PI) n)) (- 1/2 (* k 1/2))))
4.0ms	n	@	-inf	(pow (/ (pow (* 2 (* (PI) n)) (* (- 1 k) 1/4)) (pow k 1/4)) 2)

rewrite191.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

297×	`pow1`
297×	`log1p-expm1-u`
297×	`expm1-log1p-u`
292×	`add-cube-cbrt`
288×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	439
1	693	425

Stop Event

1×	node limit

Counts

17 → 430

Calls

Call 1

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

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

simplify396.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-r`
673×	`associate-l`
342×	`exp-prod`
285×	`*-commutative`
280×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	996	33288
1	2284	31832
2	7404	31666

Stop Event

1×	node limit

Counts

694 → 683

Calls

Call 1

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

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

eval675.0ms (4.2%)

Compiler: Compiled 21904 to 14282 computations (34.8% saved)

prune199.0ms (1.2%)

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	981	8	989
Fresh	6	4	10
Picked	2	3	5
Done	0	1	1
Total	989	16	1005

Accuracy

100.0%

Counts

1005 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.3%	(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.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)))) (sqrt.f64 k))
	95.5%	(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (exp.f64 (log.f64 (.f64 (PI.f64) n)))) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
	41.0%	(/.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))))))
▶	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))))
	87.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) k)))))
▶	99.4%	(.f64 (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)))
	52.8%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	99.0%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))
▶	40.4%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓	40.0%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	86.8%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
	87.0%	(sqrt.f64 (/.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) k))
	40.1%	(sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
▶	40.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))

Compiler

Compiled 409 to 334 computations (18.3% saved)

localize574.0ms (3.5%)

Localize:

Found 20 expressions with local error:

New	Accuracy	Program
	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal 1/2 binary64))))
	99.7%	(*.f64 (PI.f64) n)
✓	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)))
	74.3%	(PI.f64)
✓	99.7%	(*.f64 n (PI.f64))
✓	99.4%	(pow.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	86.8%	(pow.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k) #s(literal 1/4 binary64))
	74.3%	(PI.f64)
✓	99.7%	(*.f64 (PI.f64) (/.f64 n k))
✓	99.5%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
✓	87.0%	(sqrt.f64 (*.f64 (PI.f64) (/.f64 n k)))
	74.3%	(PI.f64)
✓	99.8%	(/.f64 (*.f64 n (PI.f64)) k)
✓	99.7%	(*.f64 n (PI.f64))
✓	87.0%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
	74.3%	(PI.f64)
✓	99.7%	(pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 k #s(literal -1/2 binary64)))))
✓	99.7%	(.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64))))))
	99.7%	(*.f64 (PI.f64) n)
	74.3%	(PI.f64)

Compiler

Compiled 225 to 117 computations (48% saved)

Precisions

Click to see histograms. Total time spent on operations: 402.0ms

Operation ival-pow, time spent: 236.0ms, 59.0% of total-time

Operation ival-mult, time spent: 111.0ms, 28.0% of total-time

Operation ival-neg, time spent: 12.0ms, 3.0% of total-time

Operation ival-div, time spent: 11.0ms, 3.0% of total-time

Operation ival-sqrt, time spent: 11.0ms, 3.0% of total-time

Operation ival-add, time spent: 8.0ms, 2.0% of total-time

Operation const, time spent: 8.0ms, 2.0% of total-time

Operation ival-sub, time spent: 4.0ms, 1.0% of total-time

Operation ival-pi, time spent: 1.0ms, 0.0% of total-time

series171.0ms (1.1%)

Counts

12 → 216

Calls

Call 1

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

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

Calls

66 calls:

Time	Variable		Point	Expression
69.0ms	k	@	0	(pow (/ (* 2 (* n (PI))) k) 1/4)
19.0ms	k	@	-inf	(pow (/ (* 2 (* n (PI))) k) 1/4)
19.0ms	n	@	0	(pow (/ (* 2 (* n (PI))) k) 1/4)
16.0ms	n	@	-inf	(pow (/ (* 2 (* n (PI))) k) 1/4)
10.0ms	k	@	inf	(pow (/ (* 2 (* n (PI))) k) 1/4)

rewrite131.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

265×	`associate-r`
252×	`log1p-expm1-u`
252×	`expm1-log1p-u`
249×	`pow1`
244×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	370
1	690	350

Stop Event

1×	node limit

Counts

12 → 355

Calls

Call 1

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

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

simplify400.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

963×	`fma-define`
548×	`associate-r`
494×	`associate-l`
405×	`exp-prod`
368×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	732	23291
1	1588	22682
2	5222	22068

Stop Event

1×	node limit

Counts

571 → 475

Calls

Call 1

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

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

eval439.0ms (2.7%)

Compiler: Compiled 19397 to 12343 computations (36.4% saved)

prune156.0ms (1%)

Pruning

26 alts after pruning (19 fresh and 7 done)

	Pruned	Kept	Total
New	1105	16	1121
Fresh	4	3	7
Picked	2	3	5
Done	0	4	4
Total	1111	26	1137

Accuracy

100.0%

Counts

1137 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	28.6%	(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))
	26.7%	(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 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)))) (sqrt.f64 k))
▶	53.2%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
	75.7%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) 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))))))
	41.0%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (/.f64 k n) (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))))
▶	41.0%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
✓	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))))
	41.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	52.8%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	52.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
✓	40.4%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	53.1%	(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))) (pow.f64 k #s(literal -1/2 binary64)))
✓	40.0%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
✓	86.8%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
▶	87.0%	(sqrt.f64 (/.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) k))
	40.0%	(sqrt.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))))
	40.1%	(sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
	14.9%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (PI.f64) #s(literal 1 binary64))) k)))
✓	40.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
	37.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
▶	40.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
▶	37.9%	(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
	29.8%	(cbrt.f64 (pow.f64 (.f64 n (.f64 (PI.f64) (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
	30.3%	(cbrt.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))) #s(literal 3/2 binary64)))

Compiler

Compiled 583 to 477 computations (18.2% saved)

localize341.0ms (2.1%)

Localize:

Found 19 expressions with local error:

New	Accuracy	Program
	99.7%	(*.f64 n (PI.f64))
✓	99.4%	(.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	87.8%	(sqrt.f64 (/.f64 k (*.f64 n (PI.f64))))
	74.3%	(PI.f64)
	99.7%	(*.f64 (PI.f64) (/.f64 n k))
✓	94.4%	(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (/.f64 n k)))) #s(literal 1/2 binary64)))
✓	86.8%	(log.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))
	74.3%	(PI.f64)
✓	99.8%	(sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))
✓	99.7%	(.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))
✓	99.5%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
	74.3%	(PI.f64)
✓	99.7%	(*.f64 (/.f64 n k) (PI.f64))
✓	87.0%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
	74.3%	(PI.f64)
✓	99.7%	(.f64 n (.f64 (PI.f64) #s(literal 2 binary64)))
	99.7%	(*.f64 n (PI.f64))
✓	87.1%	(sqrt.f64 (/.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) k))
	74.3%	(PI.f64)

Compiler

Compiled 224 to 102 computations (54.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 172.0ms

Operation ival-mult, time spent: 69.0ms, 40.0% of total-time

Operation ival-pow, time spent: 42.0ms, 24.0% of total-time

Operation ival-div, time spent: 19.0ms, 11.0% of total-time

Operation ival-sqrt, time spent: 19.0ms, 11.0% of total-time

Operation ival-log, time spent: 12.0ms, 7.0% of total-time

Operation const, time spent: 5.0ms, 3.0% of total-time

Operation ival-exp, time spent: 4.0ms, 2.0% of total-time

Operation ival-pi, time spent: 1.0ms, 1.0% of total-time

series62.0ms (0.4%)

Counts

11 → 196

Calls

Call 1

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

Outputs
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))))))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (exp.f64 (.f64 k (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (PI.f64))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))))))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (.f64 (pow.f64 k #s(literal 3 binary64)) (.f64 n (PI.f64)))) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))) k)>
#<alt (/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64)))))))) k)>
#<alt (/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (pow.f64 k #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 2 binary64))))) (.f64 k (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 k (.f64 n (PI.f64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))))))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (+.f64 (.f64 #s(literal -1 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 2 binary64)))))))) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))))) (+.f64 (.f64 #s(literal 1/6 binary64) (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) #s(literal 3 binary64))))) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 n (.f64 (PI.f64) (pow.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64)))) #s(literal 2 binary64)))) k))))))))))))) k)>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 n (PI.f64))) k)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) (.f64 k (pow.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64))) k)))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<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 (*.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 (.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)) (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 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (.f64 n (PI.f64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))>
#<alt (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))>
#<alt (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))>
#<alt (+.f64 (log.f64 n) (log.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) n))))>
#<alt (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (/.f64 (PI.f64) k))) (.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) n))))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (log.f64 k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (log.f64 k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (log.f64 k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (*.f64 #s(literal -1 binary64) (log.f64 k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal 1 binary64) k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))>
#<alt (+.f64 (log.f64 (.f64 #s(literal -2 binary64) (.f64 n (PI.f64)))) (log.f64 (/.f64 #s(literal -1 binary64) k)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 (.f64 n (PI.f64)) k)) (*.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 k (*.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))>
#<alt (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))))>
#<alt (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))>
#<alt (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))>

Calls

57 calls:

Time	Variable		Point	Expression
9.0ms	n	@	inf	(log (* 2 (* (PI) (/ n k))))
7.0ms	n	@	0	(log (* 2 (* (PI) (/ n k))))
7.0ms	n	@	-inf	(log (* 2 (* (PI) (/ n k))))
7.0ms	k	@	0	(log (* 2 (* (PI) (/ n k))))
3.0ms	n	@	-inf	(sqrt (* 2 (* (/ n k) (PI))))

rewrite278.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	322
1	643	305
2	7766	305

Stop Event

1×	node limit

Counts

11 → 378

Calls

Call 1

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

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

simplify390.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-define`
382×	`distribute-lft-in`
374×	`distribute-rgt-in`
313×	`associate-r`
276×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	656	23515
1	1273	22718
2	3920	22628

Stop Event

1×	node limit

Counts

574 → 425

Calls

Call 1

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

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

eval627.0ms (3.9%)

Compiler: Compiled 16363 to 9894 computations (39.5% saved)

prune135.0ms (0.8%)

Pruning

32 alts after pruning (21 fresh and 11 done)

	Pruned	Kept	Total
New	1036	13	1049
Fresh	6	8	14
Picked	1	4	5
Done	0	7	7
Total	1043	32	1075

Accuracy

100.0%

Counts

1075 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	28.6%	(pow.f64 (pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)) #s(literal 3/2 binary64)) #s(literal 1/3 binary64))
	26.7%	(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (/.f64 n k)) #s(literal 2 binary64)) #s(literal 4 binary64)) #s(literal 1/4 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)))) (sqrt.f64 k))
✓	53.2%	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
	75.7%	(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k)))) (pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) 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))))))
	41.0%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) n)) (sqrt.f64 #s(literal 1/2 binary64))))
✓	41.0%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 k (.f64 n (PI.f64)))) (sqrt.f64 #s(literal 1/2 binary64))))
✓	99.5%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 k) (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 k #s(literal -1/2 binary64)))))))
	41.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
	41.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 k (.f64 (PI.f64) (.f64 n #s(literal 2 binary64))))))
	41.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal 1/2 binary64))))
	53.1%	(.f64 (pow.f64 k #s(literal -1/2 binary64)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
	52.8%	(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) (sqrt.f64 n)) (sqrt.f64 #s(literal 2 binary64)))
	52.7%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n #s(literal 2 binary64)))))
✓	40.4%	(.f64 (sqrt.f64 (.f64 (PI.f64) (/.f64 n k))) (sqrt.f64 #s(literal 2 binary64)))
	40.2%	(.f64 (sqrt.f64 (.f64 (PI.f64) #s(literal 2 binary64))) (sqrt.f64 (/.f64 n k)))
✓	40.0%	(.f64 (sqrt.f64 (.f64 n (/.f64 (PI.f64) k))) (sqrt.f64 #s(literal 2 binary64)))
	39.8%	(.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (.f64 n (/.f64 #s(literal 2 binary64) k))))
✓	86.8%	(sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k))
✓	87.0%	(sqrt.f64 (/.f64 (.f64 (.f64 n (PI.f64)) (/.f64 #s(literal 2 binary64) (pow.f64 (.f64 n (.f64 (PI.f64) #s(literal 2 binary64))) k))) k))
	40.5%	(sqrt.f64 (.f64 (PI.f64) (/.f64 (.f64 n #s(literal 2 binary64)) k)))
	40.0%	(sqrt.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))))
	40.1%	(sqrt.f64 (.f64 n (.f64 #s(literal 2 binary64) (/.f64 (PI.f64) k))))
	14.9%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (fma.f64 n (PI.f64) #s(literal 1 binary64))) k)))
✓	40.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
	40.5%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))
	37.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64)))))
✓	40.5%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
	37.5%	(exp.f64 (.f64 (log.f64 (.f64 n (*.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64)))) #s(literal 1/2 binary64)))
	29.9%	(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 n (/.f64 #s(literal 2 binary64) k))) #s(literal 3/2 binary64)))
	29.8%	(cbrt.f64 (pow.f64 (.f64 n (.f64 (/.f64 #s(literal 2 binary64) k) (PI.f64))) #s(literal 3/2 binary64)))

Compiler

Compiled 1085 to 764 computations (29.6% saved)

regimes63.0ms (0.4%)

Counts

54 → 1

Calls

Call 1

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

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

Calls

4 calls:

16.0ms	n
16.0ms	(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)
15.0ms	k
11.0ms	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 #s(literal 2 binary64) (PI.f64)) n) (/.f64 (-.f64 #s(literal 1 binary64) k) #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.5%	1	`k`
99.5%	1	`n`
99.5%	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))))`
99.5%	1	`(.f64 (.f64 #s(literal 2 binary64) (PI.f64)) n)`

Compiler

Compiled 31 to 25 computations (19.4% saved)

regimes49.0ms (0.3%)

Counts

37 → 2

Calls

Call 1

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

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

Calls

2 calls:

26.0ms	n
19.0ms	k

Results

Accuracy	Segments	Branch
99.5%	2	`k`
89.5%	2	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes52.0ms (0.3%)

Counts

35 → 2

Calls

Call 1

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

Calls

2 calls:

31.0ms	n
18.0ms	k

Results

Accuracy	Segments	Branch
57.8%	3	`n`
62.4%	2	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts

24 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	k
8.0ms	n

Results

Accuracy	Segments	Branch
53.2%	1	`n`
53.2%	1	`k`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes14.0ms (0.1%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	n
5.0ms	k

Results

Accuracy	Segments	Branch
41.2%	1	`k`
41.2%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	n
3.0ms	k

Results

Accuracy	Segments	Branch
41.2%	1	`k`
41.2%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	k
3.0ms	n

Results

Accuracy	Segments	Branch
40.5%	1	`k`
40.5%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	n
1.0ms	k

Results

Accuracy	Segments	Branch
40.5%	1	`k`
40.5%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	n
1.0ms	k

Results

Accuracy	Segments	Branch
40.5%	1	`k`
40.5%	1	`n`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch8.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
8.0ms	8.700318740490806e-23	2.5742002881020026e-21

Results

7.0ms	31×	256	valid
0.0ms	1×	256	valid

Compiler

Compiled 77 to 63 computations (18.2% saved)

Precisions

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

Operation ival-mult, time spent: 1.0ms, 33.0% of total-time

Operation ival-pow, time spent: 1.0ms, 33.0% of total-time

Operation ival-pi, time spent: 0.0ms, 0.0% of total-time

Operation ival-sub, time spent: 0.0ms, 0.0% of total-time

Operation ival-div, time spent: 0.0ms, 0.0% of total-time

Operation ival-sqrt, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

bsearch24.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
24.0ms	4.607103296593607e+38	1.2910747271348971e+39

Results

8.0ms	41×	256	infinite
13.0ms	38×	256	valid
0.0ms	1×	256	valid

Compiler

Compiled 153 to 129 computations (15.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

Operation ival-pow, time spent: 9.0ms, 63.0% of total-time

Operation ival-mult, time spent: 2.0ms, 14.0% of total-time

Operation ival-div, time spent: 1.0ms, 7.0% of total-time

Operation ival-sqrt, time spent: 1.0ms, 7.0% of total-time

Operation ival-pi, time spent: 0.0ms, 0.0% of total-time

Operation ival-sub, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative`
6×	`+-commutative`
5×	`sub-neg`
3×	`1-exp`
3×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	433
1	87	433
2	96	433
3	102	433
4	106	433
5	107	433

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) n)) (-.f64 #s(literal 1/2 binary64) (/.f64 k #s(literal 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 4253529586511731/42535295865117307932921825928971026432 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 659999999999999981364251648514108424192 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 k n) (PI.f64)) #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 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (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 2 binary64)))) (sqrt.f64 k))
(if (<=.f64 k #s(literal 4253529586511731/42535295865117307932921825928971026432 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 4253529586511731/42535295865117307932921825928971026432 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)) (sqrt.f64 (/.f64 (pow.f64 (.f64 n (.f64 #s(literal 2 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) k)) k)))
(if (<=.f64 k #s(literal 659999999999999981364251648514108424192 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n #s(literal 2 binary64)))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) k) #s(literal 1 binary64))))))
(if (<=.f64 k #s(literal 659999999999999981364251648514108424192 binary64)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 #s(literal 2 binary64) n))) (sqrt.f64 k)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 n (/.f64 (PI.f64) 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))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 n #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 k (PI.f64)) (*.f64 #s(literal 2 binary64) n))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 (/.f64 k n) (PI.f64)) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 k n) (PI.f64)))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 n (PI.f64)) k)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (/.f64 (.f64 (PI.f64) n) k)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (/.f64 (PI.f64) (/.f64 k n))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 n k) (PI.f64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 (PI.f64) (/.f64 n k))))

Compiler

Compiled 134 to 106 computations (20.9% saved)

soundness2.1s (12.9%)

Rules

1096×	`log1p-expm1-u`
963×	`fma-define`
768×	`fma-define`
760×	`associate-r`
673×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	439
1	693	425
0	455	17552
1	985	16254
2	3128	14844
0	656	23515
1	1273	22718
2	3920	22628
0	39	370
1	690	350
0	39	438
1	96	380
2	211	380
3	410	364
4	686	352
5	1171	352
6	1433	352
7	1696	352
8	2015	352
9	2058	352
10	2086	352
11	2097	352
12	2099	352
0	996	33288
1	2284	31832
2	7404	31666
0	26	226
1	427	222
2	4798	222
0	37	322
1	643	305
2	7766	305
0	732	23291
1	1588	22682
2	5222	22068

Stop Event

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

Compiler

Compiled 1295 to 849 computations (34.4% saved)

end0.0ms (0%)

preprocess154.0ms (0.9%)

Compiler: Compiled 272 to 184 computations (32.4% saved)

analyze216.0ms (1.3%)

sample4.6s (28.2%)

preprocess463.0ms (2.9%)

eval1.0ms (0%)

prune2.0ms (0%)

localize192.0ms (1.2%)

series92.0ms (0.6%)

rewrite294.0ms (1.8%)

simplify302.0ms (1.9%)

eval124.0ms (0.8%)

prune62.0ms (0.4%)

localize2.1s (12.9%)

series132.0ms (0.8%)

rewrite191.0ms (1.2%)

simplify396.0ms (2.4%)

eval675.0ms (4.2%)

prune199.0ms (1.2%)

localize574.0ms (3.5%)

series171.0ms (1.1%)

rewrite131.0ms (0.8%)

simplify400.0ms (2.5%)

eval439.0ms (2.7%)

prune156.0ms (1%)

localize341.0ms (2.1%)

series62.0ms (0.4%)

rewrite278.0ms (1.7%)

simplify390.0ms (2.4%)

eval627.0ms (3.9%)

prune135.0ms (0.8%)

regimes63.0ms (0.4%)

regimes49.0ms (0.3%)

regimes52.0ms (0.3%)

regimes18.0ms (0.1%)

regimes14.0ms (0.1%)

regimes8.0ms (0%)

regimes7.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

bsearch8.0ms (0.1%)

bsearch24.0ms (0.1%)

simplify12.0ms (0.1%)

soundness2.1s (12.9%)

end0.0ms (0%)

preprocess154.0ms (0.9%)

Profiling