Metrics for sqrt E (should all be same)

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 10 to 8 computations (20% saved)

sample993.0ms (51.1%)

Results

845.0ms

8256×

body

256

valid

Bogosity

preprocess148.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	26	14
2	68	14
3	235	14
4	1047	14
5	2829	14
6	5830	14
7	7894	14

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 10 to 8 computations (20% saved)

simplify112.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

2556×	`fma-def`
1482×	`distribute-lft-out`
1118×	`hypot-def`
988×	`count-2`
868×	`unswap-sqr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	7
2	33	7
3	56	7
4	121	7
5	380	7
6	1381	7
7	2589	7
8	3932	7
9	4860	7
10	5626	7
11	6637	7
12	7494	7

Stop Event

1×	node limit

Counts

1 → 3

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	2	3
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	2	4

Accurracy

100.0%

Counts

4 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	51.4%	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	100.0%	(hypot.f64 x x)
▶	51.4%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize62.0ms (3.2%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	100.0%	(.f64 2 (.f64 x x))
✓	51.5%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 22 to 10 computations (54.5% saved)

series4.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

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

rewrite64.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 68

Calls

Call 1

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

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

simplify27.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	1464
1	225	1464
2	798	1464

Stop Event

1×

unsound

Counts

104 → 56

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

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

eval10.0ms (0.5%)

Compiler: Compiled 452 to 268 computations (40.7% saved)

prune8.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	55	3	58

Accurracy

100.0%

Counts

58 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 2) x)
✓	100.0%	(hypot.f64 x x)
▶	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize109.0ms (5.6%)

Local Accuracy

Found 2 expressions with local accuracy:

New	Accuracy	Program
✓	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 28 to 19 computations (32.1% saved)

series2.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

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

rewrite56.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

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

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

simplify70.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	612
1	124	612
2	398	612
3	1905	612
4	4914	612
5	7274	612

Stop Event

1×	node limit

Counts

44 → 23

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

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

eval5.0ms (0.2%)

Compiler: Compiled 174 to 144 computations (17.2% saved)

prune4.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	23	3	26

Accurracy

100.0%

Counts

26 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 46 to 32 computations (30.4% saved)

regimes20.0ms (1%)

Accuracy

Total -31.3b remaining (-114476.7%)

Threshold costs -31.3b (-114476.7%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

8.0ms	(+.f64 (pow.f64 x 2) (pow.f64 x 2))
4.0ms	x
3.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
3.0ms	(pow.f64 x 2)

Results

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

Compiler

Compiled 52 to 37 computations (28.8% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

soundness217.0ms (11.2%)

Rules

2556×	`fma-def`
1482×	`distribute-lft-out`
1118×	`hypot-def`
988×	`count-2`
868×	`unswap-sqr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	7
2	33	7
3	56	7
4	121	7
5	380	7
6	1381	7
7	2589	7
8	3932	7
9	4860	7
10	5626	7
11	6637	7
12	7494	7

Stop Event

1×	node limit

Compiler

Compiled 28 to 15 computations (46.4% saved)

end0.0ms (0%)

preprocess24.0ms (1.2%)

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

analyze1.0ms (0%)

sample993.0ms (51.1%)

preprocess148.0ms (7.6%)

simplify112.0ms (5.8%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize62.0ms (3.2%)

series4.0ms (0.2%)

rewrite64.0ms (3.3%)

simplify27.0ms (1.4%)

eval10.0ms (0.5%)

prune8.0ms (0.4%)

localize109.0ms (5.6%)

series2.0ms (0.1%)

rewrite56.0ms (2.9%)

simplify70.0ms (3.6%)

eval5.0ms (0.2%)

prune4.0ms (0.2%)

regimes20.0ms (1%)

simplify5.0ms (0.2%)

soundness217.0ms (11.2%)

end0.0ms (0%)

preprocess24.0ms (1.2%)

Profiling