Metrics for sqrt A (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 10 to 5 computations (50% saved)

sample677.0ms (32.1%)

Results

665.0ms	8252×	body	256	valid
0.0ms	4×	body	256	infinite

Bogosity

preprocess41.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

174×	`fma-def`
40×	`associate-r`
28×	`distribute-lft-neg-in`
22×	`distribute-lft-in`
22×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	31	21
2	75	21
3	183	21
4	284	21
5	341	21

Stop Event

1×

saturated

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 9 to 4 computations (55.6% saved)

eval0.0ms (0%)

Compiler: Compiled 4 to 2 computations (50% saved)

prune2.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	59.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
▶	100.0%	(hypot.f64 x x)
▶	59.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 26 to 12 computations (53.8% saved)

localize43.0ms (2%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	59.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 25 to 6 computations (76% saved)

series11.0ms (0.5%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(hypot.f64 x x)
3.0ms	x	@	inf	(hypot.f64 x x)
2.0ms	x	@	-inf	(hypot.f64 x x)
2.0ms	x	@	0	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	x	@	inf	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

rewrite95.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1210×	`pow1`
1128×	`add-exp-log`
1126×	`log1p-expm1-u`
1126×	`expm1-log1p-u`
1100×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	169	14
2	2039	14

Stop Event

1×	node limit

Counts

2 → 126

Calls

Call 1

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

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

simplify29.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

52×	`*-commutative`
22×	`sqr-pow`
20×	`associate-r`
18×	`distribute-lft-in`
16×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	135	1336
1	374	1336

Stop Event

1×

unsound

Counts

150 → 79

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

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

eval14.0ms (0.7%)

Compiler: Compiled 628 to 438 computations (30.3% saved)

prune13.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	76	5	81

Accuracy

100.0%

Counts

81 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	20.3%	(+.f64 x x)
▶	99.3%	(*.f64 (sqrt.f64 2) x)
✓	59.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
	1.7%	-2
✓	100.0%	(hypot.f64 x x)
▶	20.3%	(+.f64 x x)
▶	99.3%	(*.f64 (sqrt.f64 2) x)
✓	59.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
	1.7%	-2

Compiler

Compiled 48 to 28 computations (41.7% saved)

localize27.0ms (1.3%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite65.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1182×	`pow1`
1084×	`add-exp-log`
1084×	`log1p-expm1-u`
1084×	`expm1-log1p-u`
1058×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	138	11
2	1508	11

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

simplify70.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1896×	`log-prod`
954×	`fma-neg`
774×	`*-commutative`
670×	`distribute-lft-out`
640×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	253
1	79	253
2	271	253
3	1563	253
4	4450	253
5	6816	253

Stop Event

1×	node limit

Counts

23 → 12

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 (+.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)
(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))
(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 (+.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))
(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))
(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))

eval8.0ms (0.4%)

Compiler: Compiled 78 to 65 computations (16.7% saved)

prune15.0ms (0.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	11	1	12
Fresh	0	1	1
Picked	0	2	2
Done	1	1	2
Total	12	5	17

Accuracy

100.0%

Counts

17 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	20.3%	(+.f64 x x)
✓	99.3%	(*.f64 (sqrt.f64 2) x)
▶	59.5%	(sqrt.f64 (.f64 2 (.f64 x x)))
	1.7%	-2
✓	100.0%	(hypot.f64 x x)
✓	20.3%	(+.f64 x x)
✓	99.3%	(*.f64 (sqrt.f64 2) x)
▶	59.5%	(sqrt.f64 (.f64 2 (.f64 x x)))
	1.7%	-2

Compiler

Compiled 44 to 30 computations (31.8% saved)

localize64.0ms (3.1%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	59.5%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite154.0ms (7.3%)

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	17
1	160	11
2	1810	11

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(sqrt.f64 (.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))))

simplify115.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

1358×	`log-prod`
808×	`distribute-rgt-in`
806×	`associate-r`
776×	`distribute-lft-in`
720×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	504
1	135	504
2	483	504
3	2720	504
4	6921	504

Stop Event

1×	node limit

Counts

36 → 30

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 (+.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))))

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 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 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (sqrt.f64 2)) 1)
(*.f64 x (sqrt.f64 2))
(.f64 1 (.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(*.f64 x (sqrt.f64 2))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 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 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 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(.f64 (pow.f64 1 1/2) (.f64 x (sqrt.f64 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 (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 (pow.f64 (.f64 2 x) 1/2) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(*.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 (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))
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(*.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))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 x (sqrt.f64 2))

eval6.0ms (0.3%)

Compiler: Compiled 243 to 189 computations (22.2% saved)

prune18.0ms (0.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	30	5	35

Accuracy

100.0%

Counts

35 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	20.3%	(+.f64 x x)
✓	99.3%	(*.f64 (sqrt.f64 2) x)
✓	59.5%	(sqrt.f64 (.f64 2 (.f64 x x)))
	1.7%	-2
✓	100.0%	(hypot.f64 x x)
✓	20.3%	(+.f64 x x)
✓	99.3%	(*.f64 (sqrt.f64 2) x)
✓	59.5%	(sqrt.f64 (.f64 2 (.f64 x x)))
	1.7%	-2

Compiler

Compiled 44 to 30 computations (31.8% saved)

localize0.0ms (0%)

eval1.0ms (0%)

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

prune13.0ms (0.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	20.3%	(+.f64 x x)
✓	99.3%	(*.f64 (sqrt.f64 2) x)
✓	59.5%	(sqrt.f64 (.f64 2 (.f64 x x)))
	1.7%	-2

Compiler

Compiled 48 to 28 computations (41.7% saved)

regimes77.0ms (3.6%)

Counts

6 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

25.0ms	x
16.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
15.0ms	(*.f64 x x)
15.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

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

Compiler

Compiled 49 to 23 computations (53.1% saved)

regimes17.0ms (0.8%)

Counts

2 → 1

Calls

Call 1

Inputs
-2
(+.f64 x x)

Outputs
(+.f64 x x)

Calls

1 calls:

14.0ms

Results

Accuracy	Segments	Branch
20.3%	1	`x`

Compiler

Compiled 7 to 4 computations (42.9% saved)

regimes16.0ms (0.7%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
-2

Outputs
-2

Calls

1 calls:

13.0ms

Results

Accuracy	Segments	Branch
1.7%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify15.0ms (0.7%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(+.f64 x x)
-2

Outputs
(hypot.f64 x x)
(+.f64 x x)
-2

Compiler

Compiled 10 to 6 computations (40% saved)

soundness433.0ms (20.6%)

Rules

1210×	`pow1`
1128×	`add-exp-log`
1126×	`log1p-expm1-u`
1126×	`expm1-log1p-u`
1100×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	31	21
2	75	21
3	183	21
4	284	21
5	341	21
0	8	14
1	169	14
2	2039	14
0	135	1336
1	374	1336
0	135	1336
1	374	1336

Stop Event

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

Compiler

Compiled 203 to 34 computations (83.3% saved)

end0.0ms (0%)

preprocess66.0ms (3.1%)

Remove: (abs x)
Compiler: Compiled 42 to 20 computations (52.4% saved)

analyze0.0ms (0%)

sample677.0ms (32.1%)

preprocess41.0ms (1.9%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize43.0ms (2%)

series11.0ms (0.5%)

rewrite95.0ms (4.5%)

simplify29.0ms (1.4%)

eval14.0ms (0.7%)

prune13.0ms (0.6%)

localize27.0ms (1.3%)

series0.0ms (0%)

rewrite65.0ms (3.1%)

simplify70.0ms (3.3%)

eval8.0ms (0.4%)

prune15.0ms (0.7%)

localize64.0ms (3.1%)

series1.0ms (0%)

rewrite154.0ms (7.3%)

simplify115.0ms (5.5%)

eval6.0ms (0.3%)

prune18.0ms (0.9%)

localize0.0ms (0%)

eval1.0ms (0%)

prune13.0ms (0.6%)

regimes77.0ms (3.6%)

regimes17.0ms (0.8%)

regimes16.0ms (0.7%)

simplify15.0ms (0.7%)

soundness433.0ms (20.6%)

end0.0ms (0%)

preprocess66.0ms (3.1%)

Profiling