Details

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)

sample865.0ms (38.1%)

Results

854.0ms

8256×

body

256

valid

Bogosity

preprocess56.0ms (2.5%)

Algorithm

2×	egg-herbie

Rules

4×	`*-commutative`
4×	`associate-r`
4×	`count-2`
2×	`fma-def`
2×	`hypot-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	14	7
2	17	7
3	20	7
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 10 to 5 computations (50% saved)

simplify12.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative`
4×	`associate-r`
4×	`count-2`
2×	`fma-def`
2×	`hypot-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	14	7
2	17	7
3	20	7

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 12 to 5 computations (58.3% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Accurracy

100.0%

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	57.4%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 13 to 6 computations (53.8% saved)

localize21.0ms (0.9%)

Local Accuracy

Found 2 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(+.f64 (.f64 x x) (.f64 x x))
✓	59.1%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 21 to 5 computations (76.2% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite56.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1208×	`pow1`
1126×	`add-exp-log`
1124×	`log1p-expm1-u`
1124×	`expm1-log1p-u`
1098×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	150	14
2	2020	14

Stop Event

1×	node limit

Counts

2 → 124

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(+.f64 (.f64 x x) (.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 (/.f64 0 0) x) (+.f64 x x))
(.f64 (.f64 (/.f64 0 0) 2) (*.f64 x x))
(.f64 (.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(/.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 0) (sqrt.f64 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 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 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 (/.f64 0 0) x) (+.f64 x x))
(.f64 (.f64 (/.f64 0 0) 2) (*.f64 x x))
(.f64 (.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(/.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 0) (sqrt.f64 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 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)))
(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))

simplify34.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	136	872
1	390	872

Stop Event

1×

unsound

Counts

148 → 77

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(+.f64 (.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 (/.f64 0 0) x) (+.f64 x x))
(.f64 (.f64 (/.f64 0 0) 2) (*.f64 x x))
(.f64 (.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(/.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 0) (sqrt.f64 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 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 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 (/.f64 0 0) x) (+.f64 x x))
(.f64 (.f64 (/.f64 0 0) 2) (*.f64 x x))
(.f64 (.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(/.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 0) (sqrt.f64 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 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)))
(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))

Outputs
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 x x)
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(*.f64 2 (pow.f64 x 2))
-2
(+.f64 (.f64 x x) (.f64 x x))
-2
(+.f64 (.f64 (/.f64 0 0) (.f64 x x)) (.f64 (/.f64 0 0) (.f64 x x)))
-2
(+.f64 (.f64 (.f64 x x) (/.f64 0 0)) (.f64 (.f64 x x) (/.f64 0 0)))
-2
(-.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))
-2
(.f64 x (.f64 (+.f64 x x) (/.f64 0 0)))
-2
(.f64 (.f64 x x) 2)
-2
(.f64 (.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
-2
(*.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 (pow.f64 (cbrt.f64 x) -2) (.f64 -2 (cbrt.f64 (*.f64 x x))))
(.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 (pow.f64 (cbrt.f64 x) -2) (.f64 -2 (cbrt.f64 (*.f64 x x))))
(*.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))
-2
(.f64 2 (.f64 (*.f64 x x) (/.f64 0 0)))
-2
(.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)
-2
(*.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 (/.f64 0 0) x) (+.f64 x x))
-2
(.f64 (.f64 (/.f64 0 0) 2) (*.f64 x x))
-2
(.f64 (.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 -2 (cbrt.f64 (*.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 (*.f64 x x)))
(/.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 0) (sqrt.f64 0))
-2
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 -2 (sqrt.f64 (*.f64 x x)))
(/.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))
-2
(fma.f64 1 (.f64 x x) (.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 (.f64 x x)) (pow.f64 (cbrt.f64 x) -2) (.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))
-2
(.f64 x (.f64 (+.f64 x x) (/.f64 0 0)))
-2
(.f64 (.f64 x x) 2)
-2
(.f64 (.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
-2
(*.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 (pow.f64 (cbrt.f64 x) -2) (.f64 -2 (cbrt.f64 (*.f64 x x))))
(.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 (pow.f64 (cbrt.f64 x) -2) (.f64 -2 (cbrt.f64 (*.f64 x x))))
(*.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))
-2
(.f64 2 (.f64 (*.f64 x x) (/.f64 0 0)))
-2
(.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)
-2
(*.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 (/.f64 0 0) x) (+.f64 x x))
-2
(.f64 (.f64 (/.f64 0 0) 2) (*.f64 x x))
-2
(.f64 (.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))
(.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 -2 (cbrt.f64 (*.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 (*.f64 x x)))
(/.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 0) (sqrt.f64 0))
-2
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) 0)))
(/.f64 -2 (sqrt.f64 (*.f64 x x)))
(/.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
(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))
-2
(fma.f64 1 (.f64 x x) (.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 (.f64 x x)) (pow.f64 (cbrt.f64 x) -2) (.f64 x x))

localize59.0ms (2.6%)

Local Accuracy

Found 1 expressions with local accuracy:

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

Compiler

Compiled 6 to 3 computations (50% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite62.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

738×	`pow1`
704×	`add-sqr-sqrt`
696×	`*-un-lft-identity`
674×	`add-exp-log`
674×	`log1p-expm1-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	80	7
2	933	7

Stop Event

1×	node limit

Counts

1 → 41

Calls

Call 1

Inputs
(hypot.f64 x x)

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

simplify54.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

924×	`associate-r`
884×	`log-prod`
766×	`associate-l`
738×	`associate-+r+`
718×	`associate-+l+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	717
1	249	681
2	686	669
3	4006	669

Stop Event

1×	node limit

Counts

53 → 55

Calls

Call 1

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

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

eval32.0ms (1.4%)

Compiler: Compiled 1120 to 625 computations (44.2% saved)

prune17.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	128	6	134

Accurracy

100.0%

Counts

134 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	11.7%	(+.f64 x x)
▶	5.2%	(*.f64 (+.f64 x x) x)
▶	5.2%	(.f64 (.f64 x x) 2)
▶	53.1%	(*.f64 (sqrt.f64 2) x)
▶	5.2%	(*.f64 x x)

Compiler

Compiled 54 to 32 computations (40.7% saved)

localize20.0ms (0.9%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	99.4%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 10 to 8 computations (20% saved)

series0.0ms (0%)

Counts

1 → 0

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)

rewrite78.0ms (3.4%)

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)))

simplify60.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	253
1	79	187
2	271	121
3	1535	121
4	4437	121
5	6814	121

Stop Event

1×	node limit

Counts

11 → 14

Calls

Call 1

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

localize12.0ms (0.5%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize38.0ms (1.7%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize16.0ms (0.7%)

Local Accuracy

Found 1 expressions with local accuracy:

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

Compiler

Compiled 12 to 6 computations (50% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite63.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1040×	`pow1`
1002×	`add-sqr-sqrt`
954×	`add-exp-log`
954×	`log1p-expm1-u`
954×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	121	13
2	1360	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

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

simplify103.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1438×	`log-prod`
1064×	`distribute-lft-in`
1000×	`distribute-rgt-in`
944×	`associate-r`
852×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	299
1	89	299
2	331	299
3	2358	299

Stop Event

1×	node limit

Counts

23 → 13

Calls

Call 1

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

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

localize16.0ms (0.7%)

Compiler: Compiled 11 to 4 computations (63.6% saved)

eval4.0ms (0.2%)

Compiler: Compiled 183 to 143 computations (21.9% saved)

prune37.0ms (1.6%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	26	7	33

Accurracy

100.0%

Counts

33 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	4.4%	(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)
✓	11.7%	(+.f64 x x)
✓	5.2%	(*.f64 (+.f64 x x) x)
✓	5.2%	(.f64 (.f64 x x) 2)
✓	53.1%	(*.f64 (sqrt.f64 2) x)
✓	5.2%	(*.f64 x x)

Compiler

Compiled 39 to 25 computations (35.9% saved)

localize53.0ms (2.4%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	70.3%	(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)

Compiler

Compiled 29 to 21 computations (27.6% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)
0.0ms	x	@	inf	(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)
0.0ms	x	@	-inf	(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)

rewrite58.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1838×	`pow1`
1716×	`add-exp-log`
1714×	`log1p-expm1-u`
1714×	`expm1-log1p-u`
200×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	197	13
2	2648	13

Stop Event

1×	node limit

Counts

1 → 50

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)

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

simplify75.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1312×	`fma-def`
1016×	`log-prod`
904×	`div-sub`
608×	`unswap-sqr`
606×	`distribute-lft-neg-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1470
1	308	1396
2	991	1364
3	4785	1244

Stop Event

1×	node limit

Counts

62 → 66

Calls

Call 1

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

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

eval20.0ms (0.9%)

Compiler: Compiled 999 to 734 computations (26.5% saved)

prune11.0ms (0.5%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	66	7	73

Accurracy

100.0%

Counts

73 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	4.4%	(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)
✓	11.7%	(+.f64 x x)
✓	5.2%	(*.f64 (+.f64 x x) x)
✓	5.2%	(.f64 (.f64 x x) 2)
✓	53.1%	(*.f64 (sqrt.f64 2) x)
✓	5.2%	(*.f64 x x)

Compiler

Compiled 39 to 25 computations (35.9% saved)

regimes24.0ms (1.1%)

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 x x)
(+.f64 x x)
(.f64 (.f64 x x) 2)
(*.f64 (+.f64 x x) x)
(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
5.0ms	x
4.0ms	(*.f64 x x)
4.0ms	(+.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 64 to 29 computations (54.7% saved)

regimes13.0ms (0.6%)

Counts

5 → 2

Calls

Call 1

Inputs
(*.f64 x x)
(+.f64 x x)
(.f64 (.f64 x x) 2)
(*.f64 (+.f64 x x) x)
(-.f64 (+.f64 1 (.f64 x (.f64 x 2))) 1)

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

Calls

2 calls:

9.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
13.3%	2	`x`
11.7%	1	`(*.f64 x x)`

Compiler

Compiled 32 to 16 computations (50% saved)

bsearch18.0ms (0.8%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	-1.9971420300025414e-293	2.232727307502551e-296

Results

14.0ms

176×

body

256

valid

Compiler

Compiled 145 to 95 computations (34.5% saved)

regimes9.0ms (0.4%)

Accuracy

Total -6.2b remaining (-11.2%)

Threshold costs -6.2b (-11.2%)

Counts

2 → 2

Calls

Call 1

Inputs
(*.f64 x x)
(+.f64 x x)

Outputs
(*.f64 x x)
(+.f64 x x)

Calls

2 calls:

5.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
13.3%	2	`x`
11.7%	1	`(*.f64 x x)`

Compiler

Compiled 13 to 6 computations (53.8% saved)

bsearch17.0ms (0.8%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	-1.9971420300025414e-293	2.232727307502551e-296

Results

16.0ms

176×

body

256

valid

Compiler

Compiled 123 to 73 computations (40.7% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	66
1	16	66

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (.f64 x x) 2) (+.f64 x x))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (*.f64 x x) (+.f64 x x))
(*.f64 x x)

Outputs
(hypot.f64 x x)
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (.f64 (.f64 x x) 2) (+.f64 x x))
(if (<=.f64 x -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) (*.f64 x x) (+.f64 x x))
(*.f64 x x)

Compiler

Compiled 32 to 18 computations (43.8% saved)

soundness212.0ms (9.4%)

Rules

1208×	`pow1`
1208×	`pow1`
1126×	`add-exp-log`
1126×	`add-exp-log`
1124×	`log1p-expm1-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	14	7
2	17	7
3	20	7
0	7	14
1	150	14
2	2020	14
0	136	872
1	390	872
0	136	872
1	390	872
0	7	14
1	150	14
2	2020	14

Stop Event

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

Compiler

Compiled 381 to 62 computations (83.7% saved)

end33.0ms (1.5%)

Compiler: Compiled 76 to 32 computations (57.9% saved)

Details

analyze0.0ms (0%)

sample865.0ms (38.1%)

preprocess56.0ms (2.5%)

simplify12.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize21.0ms (0.9%)

series2.0ms (0.1%)

rewrite56.0ms (2.5%)

simplify34.0ms (1.5%)

localize59.0ms (2.6%)

series2.0ms (0.1%)

rewrite62.0ms (2.7%)

simplify54.0ms (2.4%)

eval32.0ms (1.4%)

prune17.0ms (0.8%)

localize20.0ms (0.9%)

series0.0ms (0%)

rewrite78.0ms (3.4%)

simplify60.0ms (2.7%)

localize12.0ms (0.5%)

localize38.0ms (1.7%)

localize16.0ms (0.7%)

series1.0ms (0%)

rewrite63.0ms (2.8%)

simplify103.0ms (4.5%)

localize16.0ms (0.7%)

eval4.0ms (0.2%)

prune37.0ms (1.6%)

localize53.0ms (2.4%)

series0.0ms (0%)

rewrite58.0ms (2.6%)

simplify75.0ms (3.3%)

eval20.0ms (0.9%)

prune11.0ms (0.5%)

regimes24.0ms (1.1%)

regimes13.0ms (0.6%)

bsearch18.0ms (0.8%)

regimes9.0ms (0.4%)

bsearch17.0ms (0.8%)

simplify5.0ms (0.2%)

soundness212.0ms (9.4%)

end33.0ms (1.5%)

Profiling