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)

sample1.1s (53.9%)

Results

1.1s

8256×

body

256

valid

Bogosity

preprocess57.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

132×	`fma-def`
32×	`associate-r`
28×	`distribute-lft-neg-in`
28×	`associate-l`
24×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	25	51
2	62	51
3	136	51
4	206	51
5	278	51

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))))

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)))

Symmetry

(abs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.7%	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	52.7%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize129.0ms (6.5%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(.f64 2 (.f64 x x))
✓	52.7%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 18 to 9 computations (50% saved)

series6.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(sqrt.f64 (.f64 2 (.f64 x x)))
2.0ms	x	@	inf	(.f64 2 (.f64 x x))
1.0ms	x	@	inf	(sqrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	0	(.f64 2 (.f64 x x))
0.0ms	x	@	-inf	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite92.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1354×	`pow1`
1244×	`add-exp-log`
1244×	`log1p-expm1-u`
1244×	`expm1-log1p-u`
1214×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	160	24
2	1810	24

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

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

simplify164.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

1200×	`log-prod`
1148×	`fma-def`
1056×	`distribute-rgt-in`
1030×	`distribute-lft-in`
700×	`fma-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	816
1	191	816
2	737	816
3	2408	688
4	7451	688

Stop Event

1×	node limit

Counts

60 → 50

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

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

eval21.0ms (1%)

Compiler: Compiled 396 to 288 computations (27.3% saved)

prune11.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Accuracy

100.0%

Counts

51 → 3

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))
▶	99.4%	(*.f64 (sqrt.f64 2) x)
▶	100.0%	(hypot.f64 x x)
▶	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	99.4%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize48.0ms (2.4%)

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))
✓	99.4%	(*.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)

rewrite95.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1744×	`pow1`
1602×	`add-exp-log`
1602×	`log1p-expm1-u`
1602×	`expm1-log1p-u`
1564×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	240	21
2	2766	21

Stop Event

1×	node limit

Counts

3 → 73

Calls

Call 1

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

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

simplify108.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1102×	`log-prod`
1018×	`fma-neg`
774×	`associate-r`
716×	`associate-l`
600×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	2003
1	217	1781
2	580	1559
3	2542	1535
4	4799	1535
5	6933	1535

Stop Event

1×	node limit

Counts

109 → 62

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

eval15.0ms (0.8%)

Compiler: Compiled 513 to 339 computations (33.9% saved)

prune8.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	62	3	65

Accuracy

100.0%

Counts

65 → 3

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))
✓	99.4%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 38 to 26 computations (31.6% saved)

regimes15.0ms (0.7%)

Accuracy

Total -30.5b remaining (-390696.4%)

Threshold costs -30.5b (-390696.4%)

Counts

4 → 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))

Outputs
(hypot.f64 x x)

Calls

4 calls:

4.0ms	x
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
3.0ms	(.f64 2 (.f64 x x))
3.0ms	(*.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 40 to 26 computations (35% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7

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)

soundness117.0ms (5.9%)

Rules

1200×	`log-prod`
1148×	`fma-def`
1056×	`distribute-rgt-in`
1030×	`distribute-lft-in`
700×	`fma-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	816
1	191	816
2	737	816
3	2408	688
4	7451	688

Stop Event

1×	node limit

Compiler

Compiled 76 to 52 computations (31.6% saved)

end0.0ms (0%)

preprocess21.0ms (1.1%)

Remove: (abs x)
Compiler: Compiled 30 to 18 computations (40% saved)

analyze0.0ms (0%)

sample1.1s (53.9%)

preprocess57.0ms (2.9%)

eval0.0ms (0%)

prune3.0ms (0.2%)

localize129.0ms (6.5%)

series6.0ms (0.3%)

rewrite92.0ms (4.6%)

simplify164.0ms (8.2%)

eval21.0ms (1%)

prune11.0ms (0.6%)

localize48.0ms (2.4%)

series4.0ms (0.2%)

rewrite95.0ms (4.8%)

simplify108.0ms (5.4%)

eval15.0ms (0.8%)

prune8.0ms (0.4%)

regimes15.0ms (0.7%)

simplify4.0ms (0.2%)

soundness117.0ms (5.9%)

end0.0ms (0%)

preprocess21.0ms (1.1%)

Profiling