Metrics for sqrt C (should all be same)

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample843.0ms (44.2%)

Results

831.0ms	8253×	body	256	valid
0.0ms	3×	body	256	infinite

Bogosity

preprocess52.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

136×	`fma-def`
32×	`associate-r`
26×	`distribute-lft-neg-in`
26×	`associate-l`
24×	`distribute-lft-in`

Problems

129×	`(sqrt.f64 (.f64 2 (.f64 x x)))`
127×	No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	96
1	30	96
2	69	96
3	141	96
4	215	96
5	290	96
6	292	96

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 x) (neg.f64 x))))
(neg.f64 (sqrt.f64 (.f64 2 (.f64 (neg.f64 x) (neg.f64 x)))))

Outputs
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (.f64 2 (.f64 (neg.f64 x) (neg.f64 x))))
(sqrt.f64 (.f64 2 (.f64 x x)))
(neg.f64 (sqrt.f64 (.f64 2 (.f64 (neg.f64 x) (neg.f64 x)))))
(neg.f64 (sqrt.f64 (.f64 2 (.f64 x x))))

Symmetry

(abs x)

Compiler

Compiled 25 to 14 computations (44% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize27.0ms (1.4%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(.f64 2 (.f64 x x))
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 18 to 9 computations (50% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	inf	(.f64 2 (.f64 x x))
0.0ms	x	@	inf	(sqrt.f64 (.f64 2 (.f64 x x)))
0.0ms	x	@	0	(.f64 2 (.f64 x x))
0.0ms	x	@	-inf	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite102.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

726×	`unpow-prod-down`
418×	`log-prod`
398×	`cbrt-prod`
368×	`prod-exp`
318×	`log1p-expm1-u`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	89	30
2	976	30

Stop Event

1×	node limit

Counts

2 → 94

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 2 (.f64 x x))

Outputs
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (sqrt.f64 2)) 1)
(.f64 1 (.f64 x (sqrt.f64 2)))
(.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) 2) 1/2))
(.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (.f64 2 (*.f64 x (sqrt.f64 2))) 1/3))
(.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (.f64 2 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) 2)))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (pow.f64 x 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (cbrt.f64 2) (pow.f64 (.f64 (pow.f64 x 2) (*.f64 x (sqrt.f64 2))) 1/3))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 (pow.f64 x 2) (*.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (pow.f64 (pow.f64 (*.f64 2 (pow.f64 x 2)) 5/6) 1/3))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x 2)) 5/6)))
(.f64 (cbrt.f64 (.f64 2 x)) (pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/3))
(.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 (.f64 x (.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) 2) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2) 1/2))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)))
(.f64 (pow.f64 1 1/3) (.f64 x (sqrt.f64 2)))
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3/2) 1/2) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
(.f64 (pow.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) 1/2) (cbrt.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 2 (pow.f64 x 2)) 5/6) 1/2) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 (*.f64 2 x) 1) 1/2) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 (*.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) 1/2) (pow.f64 x 1/6))
(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (pow.f64 x 1/4))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 2) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (*.f64 2 (pow.f64 x 2)) (sqrt.f64 2)) 1/3) (cbrt.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 5/2) 1/3) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (cbrt.f64 (.f64 (*.f64 2 (pow.f64 x 2)) (sqrt.f64 2))) (cbrt.f64 x))
(.f64 (cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 5/2)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (pow.f64 x 2)) 5/6)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (sqrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3/2)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
(.f64 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4))) (cbrt.f64 x))
(.f64 (sqrt.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2))) (sqrt.f64 x))
(.f64 (sqrt.f64 (.f64 (*.f64 2 x) 1)) (sqrt.f64 x))
(.f64 (sqrt.f64 (.f64 (*.f64 2 x) (pow.f64 (cbrt.f64 x) 2))) (pow.f64 x 1/6))
(.f64 (sqrt.f64 (.f64 (*.f64 2 x) (sqrt.f64 x))) (pow.f64 x 1/4))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 2))) 3/2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/4)
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/6)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 2 (pow.f64 x 2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 0 (*.f64 2 (pow.f64 x 2)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 4))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x 2))) 1)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 2))) 3)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 6)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 2/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 4)
(pow.f64 (E.f64) (log.f64 (*.f64 2 (pow.f64 x 2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 2 (pow.f64 x 2)))) 2)) (cbrt.f64 (log.f64 (.f64 2 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 2 (pow.f64 x 2))))) (sqrt.f64 (log.f64 (.f64 2 (pow.f64 x 2)))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 2 (pow.f64 x 2))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 4) 4)) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) 8)) 1/3))
(log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x 2))))

simplify67.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1236×	`fma-def`
690×	`log-prod`
584×	`sqr-pow`
526×	`*-commutative`
518×	`unswap-sqr`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	3082
1	507	3033
2	1513	2947
3	4761	2915

Stop Event

1×	node limit

Counts

118 → 140

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (sqrt.f64 2)) 1)
(.f64 1 (.f64 x (sqrt.f64 2)))
(.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) 2) 1/2))
(.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (.f64 2 (*.f64 x (sqrt.f64 2))) 1/3))
(.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (.f64 2 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) 2)))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (pow.f64 x 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (cbrt.f64 2) (pow.f64 (.f64 (pow.f64 x 2) (*.f64 x (sqrt.f64 2))) 1/3))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 (pow.f64 x 2) (*.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (pow.f64 (pow.f64 (*.f64 2 (pow.f64 x 2)) 5/6) 1/3))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x 2)) 5/6)))
(.f64 (cbrt.f64 (.f64 2 x)) (pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/3))
(.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 (.f64 x (.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) 2) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2) 1/2))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)))
(.f64 (pow.f64 1 1/3) (.f64 x (sqrt.f64 2)))
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3/2) 1/2) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
(.f64 (pow.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) 1/2) (cbrt.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 2 (pow.f64 x 2)) 5/6) 1/2) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 (*.f64 2 x) 1) 1/2) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 (*.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) 1/2) (pow.f64 x 1/6))
(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (pow.f64 x 1/4))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 2) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (*.f64 2 (pow.f64 x 2)) (sqrt.f64 2)) 1/3) (cbrt.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 5/2) 1/3) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (cbrt.f64 (.f64 (*.f64 2 (pow.f64 x 2)) (sqrt.f64 2))) (cbrt.f64 x))
(.f64 (cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 5/2)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (pow.f64 x 2)) 5/6)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (sqrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3/2)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
(.f64 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4))) (cbrt.f64 x))
(.f64 (sqrt.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2))) (sqrt.f64 x))
(.f64 (sqrt.f64 (.f64 (*.f64 2 x) 1)) (sqrt.f64 x))
(.f64 (sqrt.f64 (.f64 (*.f64 2 x) (pow.f64 (cbrt.f64 x) 2))) (pow.f64 x 1/6))
(.f64 (sqrt.f64 (.f64 (*.f64 2 x) (sqrt.f64 x))) (pow.f64 x 1/4))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 2))) 3/2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/4)
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/6)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 2 (pow.f64 x 2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3)) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 0 (*.f64 2 (pow.f64 x 2)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 4))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x 2))) 1)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 2))) 3)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 6)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 2/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 4)
(pow.f64 (E.f64) (log.f64 (*.f64 2 (pow.f64 x 2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 2 (pow.f64 x 2)))) 2)) (cbrt.f64 (log.f64 (.f64 2 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 2 (pow.f64 x 2))))) (sqrt.f64 (log.f64 (.f64 2 (pow.f64 x 2)))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 x 2))))
(exp.f64 (log.f64 (*.f64 2 (pow.f64 x 2))))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 4) 4)) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) 8)) 1/3))
(log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x 2))))

Outputs
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(neg.f64 (hypot.f64 x x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) 3)
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(.f64 (.f64 x (sqrt.f64 2)) 1)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(.f64 1 (.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) 2) 1/2))
(.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (.f64 2 (*.f64 x (sqrt.f64 2))) 1/3))
(.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (.f64 2 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (.f64 2 (hypot.f64 x x))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (.f64 2 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (.f64 2 (hypot.f64 x x))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) 2)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 2 (pow.f64 x 2))))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(.f64 (cbrt.f64 2) (pow.f64 (.f64 (pow.f64 x 2) (*.f64 x (sqrt.f64 2))) 1/3))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 (*.f64 x (sqrt.f64 2)) (pow.f64 x 2))))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 x 3))))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 (pow.f64 x 2) (*.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 (*.f64 x (sqrt.f64 2)) (pow.f64 x 2))))
(.f64 (cbrt.f64 2) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 x 3))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (pow.f64 (pow.f64 (*.f64 2 (pow.f64 x 2)) 5/6) 1/3))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x 2)) 5/6)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x 2)) 5/6)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x 2)) 5/6)))
(.f64 (cbrt.f64 (.f64 2 x)) (pow.f64 (.f64 x (.f64 x (sqrt.f64 2))) 1/3))
(.f64 (cbrt.f64 (.f64 x 2)) (cbrt.f64 (*.f64 (pow.f64 x 2) (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 x 2)) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 2))))
(.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 (.f64 x (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (.f64 x 2)) (cbrt.f64 (*.f64 (pow.f64 x 2) (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 x 2)) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 2))))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) 2) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) 2) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (pow.f64 x 2) (sqrt.f64 2))))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (pow.f64 x 2) (sqrt.f64 2))))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (sqrt.f64 2) (pow.f64 x 2))))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2) 1/2))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (fabs.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)))
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (fabs.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)))
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
(.f64 (pow.f64 1 1/3) (.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3/2) 1/2) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (fabs.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)))
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
(.f64 (pow.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) 1/2) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (pow.f64 x 2)) 5/6) 1/2) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (pow.f64 x 2)) 5/6)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (pow.f64 (.f64 2 (pow.f64 x 2)) 5/12) (pow.f64 (hypot.f64 x x) 1/6))
(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(.f64 (pow.f64 (.f64 (*.f64 2 x) 1) 1/2) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(.f64 (pow.f64 (.f64 (*.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) 1/2) (pow.f64 x 1/6))
(.f64 (sqrt.f64 (.f64 2 (*.f64 x (pow.f64 (cbrt.f64 x) 2)))) (pow.f64 x 1/6))
(.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2))) (pow.f64 x 1/6))
(.f64 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5))) (pow.f64 x 1/6))
(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (pow.f64 x 1/4))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x 2))) (pow.f64 x 1/4))
(.f64 (sqrt.f64 (.f64 x (*.f64 2 (sqrt.f64 x)))) (pow.f64 x 1/4))
(.f64 (sqrt.f64 (.f64 2 (pow.f64 x 3/2))) (pow.f64 x 1/4))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 2) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 2)))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4))) 2)))
(.f64 (pow.f64 (.f64 (*.f64 2 (pow.f64 x 2)) (sqrt.f64 2)) 1/3) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 (*.f64 (pow.f64 x 2) (sqrt.f64 2)))))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 (*.f64 (sqrt.f64 2) (pow.f64 x 2)))))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 (pow.f64 x 2) (*.f64 2 (sqrt.f64 2)))))
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 5/2) 1/3) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 5/2)))
(*.f64 (pow.f64 (hypot.f64 x x) 1/6) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)))
(.f64 (cbrt.f64 (.f64 (*.f64 2 (pow.f64 x 2)) (sqrt.f64 2))) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 (*.f64 (pow.f64 x 2) (sqrt.f64 2)))))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 (*.f64 (sqrt.f64 2) (pow.f64 x 2)))))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 (pow.f64 x 2) (*.f64 2 (sqrt.f64 2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 5/2)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 5/2)))
(*.f64 (pow.f64 (hypot.f64 x x) 1/6) (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)))
(.f64 (sqrt.f64 (pow.f64 (.f64 2 (pow.f64 x 2)) 5/6)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (pow.f64 (.f64 2 (pow.f64 x 2)) 5/12) (pow.f64 (hypot.f64 x x) 1/6))
(.f64 (sqrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3/2)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/4) (fabs.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)))
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
(.f64 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4))) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4))))
(.f64 (sqrt.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2))) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(.f64 (sqrt.f64 (.f64 (*.f64 2 x) 1)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(.f64 (sqrt.f64 (.f64 (*.f64 2 x) (pow.f64 (cbrt.f64 x) 2))) (pow.f64 x 1/6))
(.f64 (sqrt.f64 (.f64 2 (*.f64 x (pow.f64 (cbrt.f64 x) 2)))) (pow.f64 x 1/6))
(.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2))) (pow.f64 x 1/6))
(.f64 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5))) (pow.f64 x 1/6))
(.f64 (sqrt.f64 (.f64 (*.f64 2 x) (sqrt.f64 x))) (pow.f64 x 1/4))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x 2))) (pow.f64 x 1/4))
(.f64 (sqrt.f64 (.f64 x (*.f64 2 (sqrt.f64 x)))) (pow.f64 x 1/4))
(.f64 (sqrt.f64 (.f64 2 (pow.f64 x 3/2))) (pow.f64 x 1/4))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 2))) 3/2)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/4)
(pow.f64 (*.f64 4 (pow.f64 x 4)) 1/4)
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/6)
(pow.f64 (*.f64 8 (pow.f64 x 6)) 1/6)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(pow.f64 (E.f64) (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 2 (pow.f64 x 2))))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x x)))) (sqrt.f64 (log.f64 (hypot.f64 x x))))
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3)) 1/3))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(hypot.f64 x x)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 0 (*.f64 2 (pow.f64 x 2)))
(*.f64 2 (pow.f64 x 2))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 4))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 4))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) 2))))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x 2))) 1)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 2))) 3)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 6)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
(pow.f64 (*.f64 (pow.f64 x 6) 8) 1/3)
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(cbrt.f64 (*.f64 8 (pow.f64 x 6)))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 2/3)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 4)
(*.f64 2 (pow.f64 x 2))
(pow.f64 (E.f64) (log.f64 (*.f64 2 (pow.f64 x 2))))
(*.f64 2 (pow.f64 x 2))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 2 (pow.f64 x 2)))) 2)) (cbrt.f64 (log.f64 (.f64 2 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 2 (pow.f64 x 2))))) (sqrt.f64 (log.f64 (.f64 2 (pow.f64 x 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 2) (pow.f64 x 2)))
(*.f64 2 (pow.f64 x 2))
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(cbrt.f64 (*.f64 8 (pow.f64 x 6)))
(expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 x 2))))
(*.f64 2 (pow.f64 x 2))
(exp.f64 (log.f64 (*.f64 2 (pow.f64 x 2))))
(*.f64 2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 2))) 2))
(*.f64 2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) 3))
(*.f64 2 (pow.f64 x 2))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 4) 4)) 1/2))
(sqrt.f64 (*.f64 4 (pow.f64 x 4)))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) 8)) 1/3))
(cbrt.f64 (*.f64 (pow.f64 x 6) 8))
(cbrt.f64 (*.f64 8 (pow.f64 x 6)))
(log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 x 2))))
(*.f64 2 (pow.f64 x 2))

eval45.0ms (2.4%)

Compiler: Compiled 1486 to 1186 computations (20.2% saved)

prune18.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	137	4	141

Accuracy

100.0%

Counts

141 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	99.2%	(*.f64 (sqrt.f64 2) x)
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	100.0%	(hypot.f64 x x)
▶	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	99.2%	(*.f64 (sqrt.f64 2) x)
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize53.0ms (2.8%)

Localize:

Found 3 expressions with local error:

New	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	99.2%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 32 to 20 computations (37.5% saved)

series4.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(hypot.f64 x x)
1.0ms	x	@	-inf	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
1.0ms	x	@	-inf	(hypot.f64 x x)
0.0ms	x	@	0	(hypot.f64 x x)
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) x)

rewrite67.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1054×	`unpow-prod-down`
758×	`prod-exp`
646×	`log-prod`
582×	`pow-prod-down`
507×	`log1p-expm1-u`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	169	39
2	1969	39

Stop Event

1×	node limit

Counts

3 → 189

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(hypot.f64 x x)

Outputs
(+.f64 0 (hypot.f64 x x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x x)) 1) 1))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 3)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(+.f64 0 (hypot.f64 x x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x x)) 1) 1))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 3)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(+.f64 0 (hypot.f64 x x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(*.f64 (hypot.f64 x x) 1)
(*.f64 (hypot.f64 x x) (log.f64 (exp.f64 1)))
(*.f64 1 (hypot.f64 x x))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x 1/6) (sqrt.f64 (*.f64 2 x))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 2 (pow.f64 x 2))))
(.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (hypot.f64 x x)))
(.f64 (cbrt.f64 (.f64 2 x)) (.f64 (pow.f64 (.f64 2 x) 1/6) (sqrt.f64 x)))
(.f64 (cbrt.f64 (.f64 2 x)) (pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) x) 1/2))
(.f64 (cbrt.f64 2) (.f64 (pow.f64 2 1/6) x))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 x (hypot.f64 x x)) 1/2))
(.f64 (pow.f64 (.f64 2 x) 1/4) (.f64 (pow.f64 (.f64 2 x) 1/4) (sqrt.f64 x)))
(.f64 (pow.f64 (.f64 2 x) 1/4) (pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 x x)) 1/2))
(.f64 (pow.f64 x 1/4) (.f64 (pow.f64 x 1/4) (sqrt.f64 (*.f64 2 x))))
(.f64 (pow.f64 x 1/4) (pow.f64 (.f64 (sqrt.f64 (*.f64 2 x)) (hypot.f64 x x)) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 x (cbrt.f64 2)) (pow.f64 2 1/6))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(.f64 (.f64 (sqrt.f64 (*.f64 2 x)) (cbrt.f64 x)) (pow.f64 x 1/6))
(.f64 (.f64 (sqrt.f64 (*.f64 2 x)) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(.f64 (.f64 (sqrt.f64 x) (cbrt.f64 (.f64 2 x))) (pow.f64 (.f64 2 x) 1/6))
(.f64 (.f64 (sqrt.f64 x) (pow.f64 (.f64 2 x) 1/4)) (pow.f64 (.f64 2 x) 1/4))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (.f64 (hypot.f64 x x) (sqrt.f64 (*.f64 2 x))) 1/2) (pow.f64 x 1/4))
(.f64 (pow.f64 (.f64 (hypot.f64 x x) (sqrt.f64 x)) 1/2) (pow.f64 (*.f64 2 x) 1/4))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (.f64 (hypot.f64 x x) x) 1/2) (pow.f64 2 1/4))
(.f64 (pow.f64 (.f64 (*.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) 1/2) (pow.f64 x 1/6))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(.f64 (pow.f64 (.f64 (.f64 2 (pow.f64 x 2)) (sqrt.f64 (.f64 2 x))) 1/3) (pow.f64 x 1/6))
(.f64 (pow.f64 (.f64 (.f64 2 (pow.f64 x 2)) (sqrt.f64 x)) 1/3) (pow.f64 (.f64 2 x) 1/6))
(.f64 (pow.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (.f64 (*.f64 2 (pow.f64 x 2)) (sqrt.f64 2)) 1/3) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 (*.f64 2 (pow.f64 x 2)) x) 1/3) (pow.f64 2 1/6))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x x)) 1) 1))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 3)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))

simplify106.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

2220×	`fma-def`
1082×	`log-prod`
842×	`associate-+l+`
638×	`*-commutative`
604×	`unswap-sqr`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	4150
1	586	4039
2	1467	4017
3	4048	3996
4	7925	3996

Stop Event

1×	node limit

Counts

225 → 136

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(+.f64 0 (hypot.f64 x x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x x)) 1) 1))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 3)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(+.f64 0 (hypot.f64 x x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x x)) 1) 1))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 3)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(+.f64 0 (hypot.f64 x x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(*.f64 (hypot.f64 x x) 1)
(*.f64 (hypot.f64 x x) (log.f64 (exp.f64 1)))
(*.f64 1 (hypot.f64 x x))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x 1/6) (sqrt.f64 (*.f64 2 x))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 2 (pow.f64 x 2))))
(.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (hypot.f64 x x)))
(.f64 (cbrt.f64 (.f64 2 x)) (.f64 (pow.f64 (.f64 2 x) 1/6) (sqrt.f64 x)))
(.f64 (cbrt.f64 (.f64 2 x)) (pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) x) 1/2))
(.f64 (cbrt.f64 2) (.f64 (pow.f64 2 1/6) x))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 x (hypot.f64 x x)) 1/2))
(.f64 (pow.f64 (.f64 2 x) 1/4) (.f64 (pow.f64 (.f64 2 x) 1/4) (sqrt.f64 x)))
(.f64 (pow.f64 (.f64 2 x) 1/4) (pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 x x)) 1/2))
(.f64 (pow.f64 x 1/4) (.f64 (pow.f64 x 1/4) (sqrt.f64 (*.f64 2 x))))
(.f64 (pow.f64 x 1/4) (pow.f64 (.f64 (sqrt.f64 (*.f64 2 x)) (hypot.f64 x x)) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 x (cbrt.f64 2)) (pow.f64 2 1/6))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(.f64 (.f64 (sqrt.f64 (*.f64 2 x)) (cbrt.f64 x)) (pow.f64 x 1/6))
(.f64 (.f64 (sqrt.f64 (*.f64 2 x)) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(.f64 (.f64 (sqrt.f64 x) (cbrt.f64 (.f64 2 x))) (pow.f64 (.f64 2 x) 1/6))
(.f64 (.f64 (sqrt.f64 x) (pow.f64 (.f64 2 x) 1/4)) (pow.f64 (.f64 2 x) 1/4))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (.f64 (hypot.f64 x x) (sqrt.f64 (*.f64 2 x))) 1/2) (pow.f64 x 1/4))
(.f64 (pow.f64 (.f64 (hypot.f64 x x) (sqrt.f64 x)) 1/2) (pow.f64 (*.f64 2 x) 1/4))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (.f64 (hypot.f64 x x) x) 1/2) (pow.f64 2 1/4))
(.f64 (pow.f64 (.f64 (*.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) 1/2) (pow.f64 x 1/6))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(.f64 (pow.f64 (.f64 (.f64 2 (pow.f64 x 2)) (sqrt.f64 (.f64 2 x))) 1/3) (pow.f64 x 1/6))
(.f64 (pow.f64 (.f64 (.f64 2 (pow.f64 x 2)) (sqrt.f64 x)) 1/3) (pow.f64 (.f64 2 x) 1/6))
(.f64 (pow.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (.f64 (*.f64 2 (pow.f64 x 2)) (sqrt.f64 2)) 1/3) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 (*.f64 2 (pow.f64 x 2)) x) 1/3) (pow.f64 2 1/6))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x x)) 1) 1))
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 3)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 2 x)))))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))

Outputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 (.f64 (sqrt.f64 -2) (sqrt.f64 -1)) (neg.f64 x))
(.f64 (sqrt.f64 -2) (.f64 (sqrt.f64 -1) (neg.f64 x)))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 (.f64 (sqrt.f64 -2) (sqrt.f64 -1)) (neg.f64 x))
(.f64 (sqrt.f64 -2) (.f64 (sqrt.f64 -1) (neg.f64 x)))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 (.f64 (sqrt.f64 -2) (sqrt.f64 -1)) (neg.f64 x))
(.f64 (sqrt.f64 -2) (.f64 (sqrt.f64 -1) (neg.f64 x)))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 -1 (.f64 x (*.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -2) (sqrt.f64 -1))))
(.f64 (.f64 (sqrt.f64 -2) (sqrt.f64 -1)) (neg.f64 x))
(.f64 (sqrt.f64 -2) (.f64 (sqrt.f64 -1) (neg.f64 x)))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(+.f64 0 (hypot.f64 x x))
(hypot.f64 x x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(hypot.f64 x x)
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(hypot.f64 x x)
(pow.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(hypot.f64 x x)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 x (sqrt.f64 2))
(log.f64 (exp.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x x)) 1) 1))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 3)) 1/3))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(hypot.f64 x x)
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(+.f64 0 (hypot.f64 x x))
(hypot.f64 x x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(hypot.f64 x x)
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(hypot.f64 x x)
(pow.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(hypot.f64 x x)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 x (sqrt.f64 2))
(log.f64 (exp.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x x)) 1) 1))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 3)) 1/3))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(hypot.f64 x x)
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(+.f64 0 (hypot.f64 x x))
(hypot.f64 x x)
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))))
(*.f64 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x x)))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x x)))))
(hypot.f64 x x)
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 x x))) 1)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(*.f64 x (sqrt.f64 2))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(*.f64 x (sqrt.f64 2))
(*.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(*.f64 (hypot.f64 x x) (log.f64 (exp.f64 1)))
(hypot.f64 x x)
(*.f64 1 (hypot.f64 x x))
(hypot.f64 x x)
(.f64 (cbrt.f64 x) (.f64 (pow.f64 x 1/6) (sqrt.f64 (*.f64 2 x))))
(.f64 (cbrt.f64 x) (.f64 (sqrt.f64 (*.f64 x 2)) (pow.f64 x 1/6)))
(.f64 (pow.f64 x 1/6) (.f64 (sqrt.f64 (*.f64 x 2)) (cbrt.f64 x)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 2 (pow.f64 x 2))))
(.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2))) (cbrt.f64 (hypot.f64 x x)))
(.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (.f64 2 (pow.f64 x 2))))
(.f64 (cbrt.f64 (.f64 2 x)) (.f64 (pow.f64 (.f64 2 x) 1/6) (sqrt.f64 x)))
(.f64 (cbrt.f64 (.f64 x 2)) (.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/6)))
(.f64 (sqrt.f64 x) (.f64 (cbrt.f64 (.f64 x 2)) (pow.f64 (.f64 x 2) 1/6)))
(.f64 (cbrt.f64 (.f64 2 x)) (pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) x) 1/2))
(.f64 (cbrt.f64 (.f64 x 2)) (sqrt.f64 (.f64 x (cbrt.f64 (.f64 x 2)))))
(.f64 (cbrt.f64 2) (.f64 (pow.f64 2 1/6) x))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(.f64 x (.f64 (cbrt.f64 2) (pow.f64 2 1/6)))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(*.f64 x (sqrt.f64 2))
(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 x (hypot.f64 x x)) 1/2))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (hypot.f64 x x))))
(.f64 (pow.f64 (.f64 2 x) 1/4) (.f64 (pow.f64 (.f64 2 x) 1/4) (sqrt.f64 x)))
(*.f64 x (sqrt.f64 2))
(.f64 (pow.f64 (.f64 2 x) 1/4) (pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 x x)) 1/2))
(.f64 (pow.f64 (.f64 x 2) 1/4) (sqrt.f64 (*.f64 (hypot.f64 x x) (sqrt.f64 x))))
(.f64 (pow.f64 x 1/4) (.f64 (pow.f64 x 1/4) (sqrt.f64 (*.f64 2 x))))
(*.f64 x (sqrt.f64 2))
(.f64 (pow.f64 x 1/4) (pow.f64 (.f64 (sqrt.f64 (*.f64 2 x)) (hypot.f64 x x)) 1/2))
(.f64 (pow.f64 x 1/4) (sqrt.f64 (.f64 (hypot.f64 x x) (sqrt.f64 (*.f64 x 2)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4)))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (hypot.f64 x x) 3/2)))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (hypot.f64 x x) 3/4))
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (cbrt.f64 2)) (pow.f64 2 1/6))
(.f64 (cbrt.f64 2) (.f64 x (pow.f64 2 1/6)))
(.f64 x (.f64 (cbrt.f64 2) (pow.f64 2 1/6)))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 (sqrt.f64 (*.f64 2 x)) (cbrt.f64 x)) (pow.f64 x 1/6))
(.f64 (cbrt.f64 x) (.f64 (sqrt.f64 (*.f64 x 2)) (pow.f64 x 1/6)))
(.f64 (pow.f64 x 1/6) (.f64 (sqrt.f64 (*.f64 x 2)) (cbrt.f64 x)))
(.f64 (.f64 (sqrt.f64 (*.f64 2 x)) (pow.f64 x 1/4)) (pow.f64 x 1/4))
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 (sqrt.f64 x) (cbrt.f64 (.f64 2 x))) (pow.f64 (.f64 2 x) 1/6))
(.f64 (cbrt.f64 (.f64 x 2)) (.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/6)))
(.f64 (sqrt.f64 x) (.f64 (cbrt.f64 (.f64 x 2)) (pow.f64 (.f64 x 2) 1/6)))
(.f64 (.f64 (sqrt.f64 x) (pow.f64 (.f64 2 x) 1/4)) (pow.f64 (.f64 2 x) 1/4))
(*.f64 x (sqrt.f64 2))
(*.f64 (pow.f64 1 1/3) (hypot.f64 x x))
(hypot.f64 x x)
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 1/2) (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4)))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (pow.f64 x 2)))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 3/2) 1/2) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (hypot.f64 x x) 3/2)))
(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (hypot.f64 x x) 3/4))
(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
(.f64 (pow.f64 (.f64 (hypot.f64 x x) (sqrt.f64 (*.f64 2 x))) 1/2) (pow.f64 x 1/4))
(.f64 (pow.f64 x 1/4) (sqrt.f64 (.f64 (hypot.f64 x x) (sqrt.f64 (*.f64 x 2)))))
(.f64 (pow.f64 (.f64 (hypot.f64 x x) (sqrt.f64 x)) 1/2) (pow.f64 (*.f64 2 x) 1/4))
(.f64 (pow.f64 (.f64 x 2) 1/4) (sqrt.f64 (*.f64 (hypot.f64 x x) (sqrt.f64 x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5) 1/2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(hypot.f64 x x)
(.f64 (pow.f64 (.f64 (hypot.f64 x x) x) 1/2) (pow.f64 2 1/4))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (hypot.f64 x x))))
(.f64 (pow.f64 (.f64 (*.f64 2 x) (pow.f64 (cbrt.f64 x) 2)) 1/2) (pow.f64 x 1/6))
(.f64 (pow.f64 x 1/6) (sqrt.f64 (.f64 2 (*.f64 x (pow.f64 (cbrt.f64 x) 2)))))
(.f64 (pow.f64 x 1/6) (sqrt.f64 (.f64 x (*.f64 2 (pow.f64 (cbrt.f64 x) 2)))))
(.f64 (pow.f64 x 1/6) (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(.f64 (pow.f64 (.f64 (.f64 2 (pow.f64 x 2)) (sqrt.f64 (.f64 2 x))) 1/3) (pow.f64 x 1/6))
(.f64 (pow.f64 x 1/6) (cbrt.f64 (.f64 2 (.f64 (pow.f64 x 2) (sqrt.f64 (.f64 x 2))))))
(.f64 (pow.f64 x 1/6) (cbrt.f64 (.f64 (pow.f64 x 2) (.f64 2 (sqrt.f64 (.f64 x 2))))))
(.f64 (pow.f64 (.f64 (.f64 2 (pow.f64 x 2)) (sqrt.f64 x)) 1/3) (pow.f64 (.f64 2 x) 1/6))
(.f64 (pow.f64 (.f64 x 2) 1/6) (cbrt.f64 (.f64 (.f64 2 (pow.f64 x 2)) (sqrt.f64 x))))
(.f64 (pow.f64 (.f64 x 2) 1/6) (cbrt.f64 (.f64 (pow.f64 x 2) (.f64 2 (sqrt.f64 x)))))
(.f64 (pow.f64 (.f64 x 2) 1/6) (cbrt.f64 (.f64 2 (.f64 x (pow.f64 x 3/2)))))
(.f64 (pow.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 8)))
(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 5/2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (.f64 (*.f64 2 (pow.f64 x 2)) (sqrt.f64 2)) 1/3) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 (*.f64 (pow.f64 x 2) (sqrt.f64 2)))))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 (*.f64 (sqrt.f64 2) (pow.f64 x 2)))))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 (pow.f64 x 2) (pow.f64 2 3/2))))
(.f64 (pow.f64 (.f64 (*.f64 2 (pow.f64 x 2)) x) 1/3) (pow.f64 2 1/6))
(.f64 (pow.f64 2 1/6) (cbrt.f64 (.f64 x (*.f64 2 (pow.f64 x 2)))))
(.f64 (pow.f64 2 1/6) (cbrt.f64 (.f64 2 (pow.f64 x 3))))
(pow.f64 (hypot.f64 x x) 1)
(hypot.f64 x x)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(hypot.f64 x x)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 x (sqrt.f64 2))
(log.f64 (exp.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (hypot.f64 x x)) 1))
(hypot.f64 x x)
(exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x x)) 1) 1))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (.f64 2 (pow.f64 x 2))) 1/2))
(*.f64 x (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (hypot.f64 x x))) 3))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 x x) 3)) 1/3))
(hypot.f64 x x)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 x x))) 2))
(hypot.f64 x x)
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (*.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 2)) 1) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 2) 1/2) (log.f64 x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 2) 1/2) (.f64 (log.f64 x) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (*.f64 (log.f64 x) 1) (log.f64 (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (sqrt.f64 2)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 2) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 (.f64 2 x))) (.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (.f64 2 x)) 1/2) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (log.f64 (sqrt.f64 x))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 x) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1) (*.f64 (log.f64 (sqrt.f64 x)) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (log.f64 (sqrt.f64 x)) (.f64 (log.f64 (sqrt.f64 (.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (log.f64 (sqrt.f64 (.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 x) 1/2) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (log.f64 (sqrt.f64 (.f64 2 x)))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (*.f64 2 x)) 1/2)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) 1) (.f64 (log.f64 (sqrt.f64 (*.f64 2 x))) 1)))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(hypot.f64 x x)

eval126.0ms (6.6%)

Compiler: Compiled 1446 to 926 computations (36% saved)

prune18.0ms (0.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	135	5	140

Accuracy

100.0%

Counts

140 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.4%	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	99.2%	(*.f64 (sqrt.f64 2) x)
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	100.0%	(hypot.f64 x x)
▶	99.4%	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	99.2%	(*.f64 (sqrt.f64 2) x)
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 68 to 52 computations (23.5% saved)

localize40.0ms (2.1%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	99.7%	(*.f64 (pow.f64 2 1/4) x)
✓	99.6%	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Compiler

Compiled 22 to 19 computations (13.6% saved)

series38.0ms (2%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
36.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	0	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
0.0ms	x	@	-inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
0.0ms	x	@	inf	(*.f64 (pow.f64 2 1/4) x)

rewrite52.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

622×	`unpow-prod-down`
476×	`log-prod`
460×	`cbrt-prod`
424×	`prod-exp`
376×	`pow-prod-down`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	44
1	94	32
2	1059	30

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

Inputs
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(*.f64 (pow.f64 2 1/4) x)

Outputs
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 x (sqrt.f64 2))) 2))) (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (sqrt.f64 2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(+.f64 0 (*.f64 (pow.f64 2 1/4) x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)) 2))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))))
(-.f64 (+.f64 1 (*.f64 (pow.f64 2 1/4) x)) 1)
(pow.f64 (*.f64 (pow.f64 2 1/4) x) 1)
(pow.f64 (*.f64 (cbrt.f64 x) (pow.f64 2 1/12)) 3)
(pow.f64 (*.f64 (pow.f64 x 2) (sqrt.f64 2)) 1/2)
(pow.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3) 1/3)
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 (pow.f64 2 1/4) x)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 (pow.f64 2 1/4) x)) 2))) (cbrt.f64 (log.f64 (.f64 (pow.f64 2 1/4) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (pow.f64 2 1/4) x)))) (sqrt.f64 (log.f64 (.f64 (pow.f64 2 1/4) x))))
(sqrt.f64 (*.f64 (pow.f64 x 2) (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 2 1/4) x)))
(exp.f64 (log.f64 (*.f64 (pow.f64 2 1/4) x)))
(exp.f64 (.f64 (log.f64 (.f64 (cbrt.f64 x) (pow.f64 2 1/12))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 (pow.f64 2 1/4) x))) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 x) (pow.f64 2 1/8))) 2))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 2 1/4) x)))

simplify57.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1656×	`log-prod`
1308×	`associate-r`
1140×	`associate-l`
606×	`fma-neg`
526×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1018
1	292	987
2	855	987
3	5332	977

Stop Event

1×	node limit

Counts

54 → 53

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 x (sqrt.f64 2))) 2))) (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (sqrt.f64 2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(+.f64 0 (*.f64 (pow.f64 2 1/4) x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)) 2))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))))
(-.f64 (+.f64 1 (*.f64 (pow.f64 2 1/4) x)) 1)
(pow.f64 (*.f64 (pow.f64 2 1/4) x) 1)
(pow.f64 (*.f64 (cbrt.f64 x) (pow.f64 2 1/12)) 3)
(pow.f64 (*.f64 (pow.f64 x 2) (sqrt.f64 2)) 1/2)
(pow.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3) 1/3)
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 (pow.f64 2 1/4) x)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 (pow.f64 2 1/4) x)) 2))) (cbrt.f64 (log.f64 (.f64 (pow.f64 2 1/4) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (pow.f64 2 1/4) x)))) (sqrt.f64 (log.f64 (.f64 (pow.f64 2 1/4) x))))
(sqrt.f64 (*.f64 (pow.f64 x 2) (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 2 1/4) x)))
(exp.f64 (log.f64 (*.f64 (pow.f64 2 1/4) x)))
(exp.f64 (.f64 (log.f64 (.f64 (cbrt.f64 x) (pow.f64 2 1/12))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 (pow.f64 2 1/4) x))) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 x) (pow.f64 2 1/8))) 2))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 2 1/4) x)))

Outputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) 3)
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 x (sqrt.f64 2))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (E.f64) (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 x (sqrt.f64 2))) 2))) (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(*.f64 x (sqrt.f64 2))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 x (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) 3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 x (sqrt.f64 2)))) 1/3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x (sqrt.f64 2)))) 2))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 (pow.f64 2 1/4) x))
(*.f64 x (pow.f64 2 1/4))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)) 2))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (*.f64 2 (pow.f64 2 1/4))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 5/4)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))))
(*.f64 x (pow.f64 2 1/4))
(-.f64 (+.f64 1 (*.f64 (pow.f64 2 1/4) x)) 1)
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (*.f64 (pow.f64 2 1/4) x) 1)
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (*.f64 (cbrt.f64 x) (pow.f64 2 1/12)) 3)
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (*.f64 (pow.f64 x 2) (sqrt.f64 2)) 1/2)
(sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 2)))
(pow.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3) 1/3)
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2)
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (E.f64) (log.f64 (*.f64 (pow.f64 2 1/4) x)))
(*.f64 x (pow.f64 2 1/4))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 (pow.f64 2 1/4) x)) 2))) (cbrt.f64 (log.f64 (.f64 (pow.f64 2 1/4) x))))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (.f64 x (pow.f64 2 1/4))) 2))) (cbrt.f64 (log.f64 (.f64 x (pow.f64 2 1/4)))))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (fma.f64 1/4 (log.f64 2) (log.f64 x)) 2))) (cbrt.f64 (fma.f64 1/4 (log.f64 2) (log.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (pow.f64 2 1/4) x)))) (sqrt.f64 (log.f64 (.f64 (pow.f64 2 1/4) x))))
(*.f64 x (pow.f64 2 1/4))
(sqrt.f64 (*.f64 (pow.f64 x 2) (sqrt.f64 2)))
(sqrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 2)))
(log.f64 (pow.f64 (exp.f64 x) (pow.f64 2 1/4)))
(*.f64 x (pow.f64 2 1/4))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 2 1/4) x) 3))
(*.f64 x (pow.f64 2 1/4))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 2 1/4) x)))
(*.f64 x (pow.f64 2 1/4))
(exp.f64 (log.f64 (*.f64 (pow.f64 2 1/4) x)))
(*.f64 x (pow.f64 2 1/4))
(exp.f64 (.f64 (log.f64 (.f64 (cbrt.f64 x) (pow.f64 2 1/12))) 3))
(*.f64 x (pow.f64 2 1/4))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 (pow.f64 2 1/4) x))) 1/3))
(*.f64 x (pow.f64 2 1/4))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 x) (pow.f64 2 1/8))) 2))
(*.f64 x (pow.f64 2 1/4))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 2 1/4) x)))
(*.f64 x (pow.f64 2 1/4))

eval17.0ms (0.9%)

Compiler: Compiled 628 to 550 computations (12.4% saved)

prune8.0ms (0.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	53	5	58

Accuracy

100.0%

Counts

58 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	99.2%	(*.f64 (sqrt.f64 2) x)
✓	54.0%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 64 to 48 computations (25% saved)

regimes16.0ms (0.8%)

Accuracy

Total -29.8b remaining (-190516.5%)

Threshold costs -29.8b (-190516.5%)

Counts

5 → 1

Calls

Call 1

Inputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (.f64 2 (.f64 x x)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Outputs
(hypot.f64 x x)

Calls

4 calls:

4.0ms	x
4.0ms	(*.f64 x x)
3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
3.0ms	(.f64 2 (.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (.f64 2 (.f64 x x)))`
100.0%	1	`(.f64 2 (.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 49 to 34 computations (30.6% saved)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

soundness123.0ms (6.5%)

Rules

1236×	`fma-def`
690×	`log-prod`
584×	`sqr-pow`
526×	`*-commutative`
518×	`unswap-sqr`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	3082
1	507	3033
2	1513	2947
3	4761	2915

Stop Event

1×	node limit

Compiler

Compiled 102 to 75 computations (26.5% saved)

end0.0ms (0%)

preprocess23.0ms (1.2%)

Remove: (abs x)
Compiler: Compiled 38 to 22 computations (42.1% saved)

analyze0.0ms (0%)

sample843.0ms (44.2%)

preprocess52.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize27.0ms (1.4%)

series2.0ms (0.1%)

rewrite102.0ms (5.4%)

simplify67.0ms (3.5%)

eval45.0ms (2.4%)

prune18.0ms (1%)

localize53.0ms (2.8%)

series4.0ms (0.2%)

rewrite67.0ms (3.5%)

simplify106.0ms (5.5%)

eval126.0ms (6.6%)

prune18.0ms (0.9%)

localize40.0ms (2.1%)

series38.0ms (2%)

rewrite52.0ms (2.7%)

simplify57.0ms (3%)

eval17.0ms (0.9%)

prune8.0ms (0.4%)

regimes16.0ms (0.8%)

simplify1.0ms (0.1%)

soundness123.0ms (6.5%)

end0.0ms (0%)

preprocess23.0ms (1.2%)

Profiling