Details

analyze48.0ms (3.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	62.4%	12.6%	4
37.5%	43.7%	18.8%	5
37.5%	34.3%	28.2%	6
43.7%	23.4%	32.9%	7
43.7%	18%	38.3%	8
46.8%	12.1%	41.1%	9
46.8%	9.2%	44%	10
48.4%	6.1%	45.5%	11
48.4%	4.6%	47%	12
49.2%	3.1%	47.7%	13
49.2%	2.3%	48.5%	14

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample693.0ms (50.2%)

Symmetry

(sort x y)

Results

646.0ms	8256×	body	128	valid
16.0ms	250×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify15.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
2	6	6

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x y))

series21.0ms (1.5%)

Counts

1 → 8

Calls

1 calls:

20.0ms

(sqrt.f64 (+.f64 x y))

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`sqrt-prod_binary64`
2×	`sqrt-div_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 19

Calls

1 calls:

3.0ms

(sqrt.f64 (+.f64 x y))

simplify61.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

917×	`fma-neg_binary64`
656×	`associate-l_binary64`
406×	`distribute-rgt-neg-in_binary64`
392×	`distribute-lft-neg-in_binary64`
370×	`hypot-def_binary64`

Counts

27 → 41

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	388
1	187	383
2	446	375
3	1235	372
4	2724	370
5	4709	370
6	4967	370

prune24.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	2	42

Error

0.0b

Counts

42 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x y))
▶	0.4b	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))

Compiler

Compiled 558 to 312 computations (44.1% saved)

localize7.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
✓	0.1b	(sqrt.f64 (/.f64 1 y))
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 y)) x)

series99.0ms (7.2%)

Counts

3 → 12

Calls

3 calls:

66.0ms	(sqrt.f64 (/.f64 1 y))
18.0ms	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))
14.0ms	(*.f64 (sqrt.f64 (/.f64 1 y)) x)

rewrite147.0ms (10.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
29×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`

Counts

3 → 77

Calls

3 calls:

6.0ms	(*.f64 (sqrt.f64 (/.f64 1 y)) x)
2.0ms	(sqrt.f64 (/.f64 1 y))
0.0ms	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))

simplify90.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-def_binary64`
585×	`times-frac_binary64`
466×	`distribute-rgt-in_binary64`
458×	`distribute-lft-in_binary64`
297×	`associate-l_binary64`

Counts

89 → 93

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1114
1	120	1062
2	280	1062
3	442	1062
4	1037	1062
5	3164	1062
6	4743	1062
7	4945	1062

prune85.0ms (6.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	93	2	95

Error

0.0b

Counts

95 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x y))
✓	0.4b	(fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 y)) x) (sqrt.f64 y))

Compiler

Compiled 1545 to 1007 computations (34.8% saved)

regimes37.0ms (2.7%)

Accuracy

Total 0.0b remaining (17.8%)

Threshold costs 0.0b (17.8%)

Counts

7 → 1

Compiler

Compiled 286 to 202 computations (29.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
2	6	6

end44.0ms (3.2%)

Remove: (sort x y)
Compiler: Compiled 42 to 29 computations (31% saved)

Details

analyze48.0ms (3.5%)

sample693.0ms (50.2%)

simplify15.0ms (1.1%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series21.0ms (1.5%)

rewrite3.0ms (0.2%)

simplify61.0ms (4.5%)

prune24.0ms (1.8%)

localize7.0ms (0.5%)

series99.0ms (7.2%)

rewrite147.0ms (10.6%)

simplify90.0ms (6.5%)

prune85.0ms (6.1%)

regimes37.0ms (2.7%)

simplify2.0ms (0.1%)

end44.0ms (3.2%)

Profiling