Details

analyze50.0ms (4%)

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)

sample743.0ms (59.6%)

Symmetry

(sort x y)

Results

689.0ms	8256×	body	128	valid
18.0ms	269×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify6.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

Counts

1 → 1

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))

series17.0ms (1.4%)

Counts

1 → 8

Calls

1 calls:

17.0ms

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

rewrite36.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`log1p-expm1-u_binary64`
553×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
160×	`fma-def_binary64`
99×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	109	6
2	1479	6

Stop Event

1×	node limit

Counts

1 → 27

Calls

1 calls:

36.0ms

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

simplify31.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
844×	`fma-def_binary64`
541×	`associate-l_binary64`
416×	`associate-r_binary64`
224×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	212
1	137	212
2	378	204
3	1199	198
4	4325	197

Stop Event

1×	node limit

Counts

35 → 41

prune18.0ms (1.4%)

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

Counts

42 → 2

Alt Table

Status	Error	Program
▶	30.8b	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 529 to 315 computations (40.5% saved)

localize8.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (+.f64 x y)))
✓	0.4b	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
✓	0.6b	(cbrt.f64 (+.f64 x y))
✓	29.5b	(cbrt.f64 (pow.f64 (+.f64 x y) 2))

series50.0ms (4%)

Counts

4 → 48

Calls

4 calls:

14.0ms	(sqrt.f64 (cbrt.f64 (+.f64 x y)))
14.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))
13.0ms	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
9.0ms	(cbrt.f64 (+.f64 x y))

rewrite51.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

839×	`log1p-expm1-u_binary64`
839×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
103×	`egg-rr`
98×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	228	28
2	2576	28

Stop Event

1×	node limit

Counts

4 → 103

Calls

4 calls:

50.0ms	(sqrt.f64 (cbrt.f64 (+.f64 x y)))
50.0ms	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
50.0ms	(cbrt.f64 (+.f64 x y))
50.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))

simplify50.0ms (4%)

Algorithm

1×	egg-herbie

Rules

431×	`cancel-sign-sub-inv_binary64`
388×	`times-frac_binary64`
242×	`associate-/l*_binary64`
220×	`associate-r_binary64`
212×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	2020
1	692	1986
2	2447	1860

Stop Event

1×	node limit

Counts

151 → 179

prune112.0ms (9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	179	2	181

Error

Counts

181 → 2

Alt Table

Status	Error	Program
✓	30.8b	(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x y))))
✓	0.0b	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 4244 to 2687 computations (36.7% saved)

regimes26.0ms (2.1%)

Accuracy

Total 0.0b remaining (14%)

Threshold costs 0.0b (14%)

Counts

4 → 1

Compiler

Compiled 202 to 138 computations (31.7% 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

Stop Event

1×

saturated

end41.0ms (3.3%)

Remove: (sort x y)
Compiler: Compiled 45 to 30 computations (33.3% saved)

Details

analyze50.0ms (4%)

sample743.0ms (59.6%)

simplify6.0ms (0.5%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series17.0ms (1.4%)

rewrite36.0ms (2.9%)

simplify31.0ms (2.5%)

prune18.0ms (1.4%)

localize8.0ms (0.7%)

series50.0ms (4%)

rewrite51.0ms (4.1%)

simplify50.0ms (4%)

prune112.0ms (9%)

regimes26.0ms (2.1%)

simplify2.0ms (0.1%)

end41.0ms (3.3%)

Profiling