Metrics for sqrt E (should all be same)

analyze5.0ms (0.3%)

Algorithm

1×

Search

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

Compiler

Compiled 10 to 8 computations (20% saved)

sample880.0ms (46.5%)

Results

869.0ms	8254×	body	256	valid
0.0ms	2×	body	256	infinite

Bogosity

preprocess261.0ms (13.8%)

Algorithm

1×	egg-herbie

Rules

1068×	`fma-neg`
982×	`distribute-lft-out`
896×	`fma-def`
886×	`hypot-def`
744×	`distribute-lft-neg-in`

Problems

132×	No Errors
124×	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	26	21
2	68	21
3	235	21
4	1047	21
5	2829	21
6	5830	21
7	7894	21

Stop Event

1×	node limit

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(hypot.f64 x x)

Symmetry

(abs x)

Compiler

Compiled 31 to 23 computations (25.8% saved)

eval0.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

prune2.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	55.3%	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	100.0%	(hypot.f64 x x)
▶	55.3%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize68.0ms (3.6%)

Localize:

Found 3 expressions with local error:

New	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	100.0%	(.f64 2 (.f64 x x))
✓	55.4%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 22 to 10 computations (54.5% 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	@	0	(sqrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	inf	(hypot.f64 x x)
1.0ms	x	@	inf	(.f64 2 (.f64 x x))
0.0ms	x	@	0	(hypot.f64 x x)

rewrite62.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1392×	`pow1`
1280×	`add-exp-log`
1280×	`log1p-expm1-u`
1280×	`expm1-log1p-u`
1250×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	47
1	181	27
2	2098	27

Stop Event

1×	node limit

Counts

3 → 68

Calls

Call 1

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

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

simplify27.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

110×	`associate-r`
90×	`associate-l`
82×	`sqr-pow`
52×	`fma-def`
52×	`unswap-sqr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	1464
1	225	1464
2	799	1464

Stop Event

1×

unsound

Counts

104 → 57

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

eval10.0ms (0.6%)

Compiler: Compiled 463 to 265 computations (42.8% saved)

prune8.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	56	3	59

Accuracy

100.0%

Counts

59 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.6%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 2) x)
✓	100.0%	(hypot.f64 x x)
▶	99.6%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize115.0ms (6.1%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	99.6%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 28 to 19 computations (32.1% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite58.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1708×	`pow1`
1568×	`add-exp-log`
1568×	`log1p-expm1-u`
1568×	`expm1-log1p-u`
1530×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	219	22
2	2493	22

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

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

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

simplify76.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1276×	`fma-neg`
1162×	`log-prod`
666×	`distribute-lft-out`
644×	`distribute-rgt-in`
634×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	744
1	124	744
2	398	744
3	1886	744
4	4890	744
5	7246	744

Stop Event

1×	node limit

Counts

56 → 24

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

eval5.0ms (0.3%)

Compiler: Compiled 184 to 152 computations (17.4% saved)

prune5.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	24	3	27

Accuracy

100.0%

Counts

27 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.6%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 46 to 32 computations (30.4% saved)

regimes22.0ms (1.1%)

Accuracy

Total -28.8b remaining (-147521.8%)

Threshold costs -28.8b (-147521.8%)

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))
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

9.0ms	(pow.f64 x 2)
4.0ms	x
3.0ms	(+.f64 (pow.f64 x 2) (pow.f64 x 2))
3.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))

Results

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

Compiler

Compiled 52 to 37 computations (28.8% saved)

simplify5.0ms (0.3%)

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)

soundness250.0ms (13.2%)

Rules

1068×	`fma-neg`
982×	`distribute-lft-out`
896×	`fma-def`
886×	`hypot-def`
744×	`distribute-lft-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	26	21
2	68	21
3	235	21
4	1047	21
5	2829	21
6	5830	21
7	7894	21

Stop Event

1×	node limit

Compiler

Compiled 28 to 15 computations (46.4% saved)

end0.0ms (0%)

preprocess24.0ms (1.3%)

Remove: (abs x)
Compiler: Compiled 34 to 22 computations (35.3% saved)

analyze5.0ms (0.3%)

sample880.0ms (46.5%)

preprocess261.0ms (13.8%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize68.0ms (3.6%)

series4.0ms (0.2%)

rewrite62.0ms (3.3%)

simplify27.0ms (1.4%)

eval10.0ms (0.6%)

prune8.0ms (0.4%)

localize115.0ms (6.1%)

series2.0ms (0.1%)

rewrite58.0ms (3.1%)

simplify76.0ms (4%)

eval5.0ms (0.3%)

prune5.0ms (0.2%)

regimes22.0ms (1.1%)

simplify5.0ms (0.3%)

soundness250.0ms (13.2%)

end0.0ms (0%)

preprocess24.0ms (1.3%)

Profiling