Details

analyze36.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample1.1s (22.8%)

Results

966.0ms	8256×	body	128	valid
51.0ms	421×	body	128	invalid

Compiler

Compiled 67 to 38 computations (43.3% saved)

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

13.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.8b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 55 to 29 computations (47.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	13.3b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

series54.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

24.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
24.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
7.0ms	(-.f64 (.f64 a a) (.f64 b b))

rewrite280.0ms (5.9%)

Algorithm

3×	egg-rewrite

Rules

120×	`egg`
65×	`egg`
30×	`egg`

Counts

3 → 215

Calls

3 calls:

122.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
93.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
60.0ms	(-.f64 (.f64 a a) (.f64 b b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	169	13
2	2419	13
3	4778	13
4	4970	13
0	9	20
1	212	15
2	2703	15
3	4707	15
4	4641	14
5	5152	14
0	6	10
1	138	10
2	1710	10
3	5346	10

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

735×	`associate-/r*_binary64`
707×	`associate-/l/_binary64`
519×	`associate-/r/_binary64`
498×	`fma-def_binary64`
444×	`fma-neg_binary64`

Counts

287 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	963
1	37	891
2	84	843
3	258	843
4	1055	843
5	4523	843
6	5163	843

prune142.0ms (3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	223	3	226

Error

0.0b

Counts

226 → 3

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
	0.8b	(sqrt.f64 (fabs.f64 1))
	13.8b	(exp.f64 (.f64 (log1p.f64 (neg.f64 (/.f64 (.f64 b b) (*.f64 a a)))) 1/2))

Compiler

Compiled 5264 to 1883 computations (64.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
✓	0.0b	(/.f64 (+.f64 a b) a)
✓	0.0b	(/.f64 (-.f64 a b) a)
✓	0.0b	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))

series51.0ms (1.1%)

Counts

4 → 96

Calls

4 calls:

25.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))
16.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
5.0ms	(/.f64 (-.f64 a b) a)
5.0ms	(/.f64 (+.f64 a b) a)

rewrite300.0ms (6.3%)

Algorithm

4×	egg-rewrite

Rules

72×	`egg`
54×	`egg`
49×	`egg`
29×	`egg`

Counts

4 → 204

Calls

4 calls:

130.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))
69.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
50.0ms	(/.f64 (-.f64 a b) a)
48.0ms	(/.f64 (+.f64 a b) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	193	16
2	3016	16
3	4922	16
4	4876	16
5	4971	16
0	5	7
1	119	7
2	1783	7
3	5369	7
0	5	7
1	115	7
2	1662	7
3	5032	7
0	10	20
1	236	15
2	3311	15
3	5056	15

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

468×	`cancel-sign-sub-inv_binary64`
378×	`div-sub_binary64`
321×	`fma-neg_binary64`
291×	`fma-def_binary64`
261×	`fabs-div_binary64`

Counts

300 → 215

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	1041
1	74	1041
2	199	1041
3	639	1041
4	2781	1041
5	5183	1041

prune122.0ms (2.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	216	2	218

Error

Counts

218 → 2

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a)) a)))
▶	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) (*.f64 (/.f64 a (+.f64 a b)) a))))

Compiler

Compiled 3758 to 1187 computations (68.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 a (+.f64 a b)) a)
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) (*.f64 (/.f64 a (+.f64 a b)) a))))
✓	0.0b	(/.f64 (-.f64 a b) (*.f64 (/.f64 a (+.f64 a b)) a))
✓	0.0b	(/.f64 a (+.f64 a b))

series60.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

25.0ms	(/.f64 (-.f64 a b) (*.f64 (/.f64 a (+.f64 a b)) a))
15.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) (*.f64 (/.f64 a (+.f64 a b)) a))))
11.0ms	(*.f64 (/.f64 a (+.f64 a b)) a)
9.0ms	(/.f64 a (+.f64 a b))

rewrite468.0ms (9.8%)

Algorithm

4×	egg-rewrite

Rules

431×	`egg`
45×	`egg`
44×	`egg`
30×	`egg`

Counts

4 → 550

Calls

4 calls:

280.0ms	(/.f64 (-.f64 a b) (*.f64 (/.f64 a (+.f64 a b)) a))
64.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) (*.f64 (/.f64 a (+.f64 a b)) a))))
52.0ms	(*.f64 (/.f64 a (+.f64 a b)) a)
46.0ms	(/.f64 a (+.f64 a b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	115	7
2	1656	7
3	5010	7
0	8	16
1	192	16
2	3087	16
3	5054	16
0	10	20
1	235	17
2	3376	17
3	5339	17
0	6	10
1	136	10
2	1934	10
3	5654	10

simplify121.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-neg_binary64`
498×	`cancel-sign-sub-inv_binary64`
319×	`associate-/l/_binary64`
180×	`sub-neg_binary64`
177×	`distribute-neg-frac_binary64`

Counts

646 → 581

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	62	1620
1	166	1620
2	506	1569
3	1881	1512
4	4372	1506
5	4993	1506
6	4951	1506

prune335.0ms (7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	581	0	581
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	581	2	583

Error

Counts

583 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a)) a)))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) (*.f64 (/.f64 a (+.f64 a b)) a))))

Compiler

Compiled 29263 to 4923 computations (83.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a)) a)))
✓	0.0b	(/.f64 (*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a)) a)
✓	0.0b	(*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a))
	0.0b	(/.f64 (-.f64 a b) a)

series51.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

25.0ms	(/.f64 (*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a)) a)
16.0ms	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a)) a)))
10.0ms	(*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a))

rewrite292.0ms (6.1%)

Algorithm

3×	egg-rewrite

Rules

67×	`egg`
62×	`egg`
30×	`egg`

Counts

3 → 159

Calls

3 calls:

128.0ms	(/.f64 (*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a)) a)
95.0ms	(*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a))
67.0ms	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a)) a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	165	13
2	2499	13
3	4906	13
4	5264	13
0	8	16
1	191	16
2	3026	16
3	4944	16
4	4904	16
5	4953	16
0	10	20
1	234	18
2	3307	18
3	5118	18

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

405×	`fabs-mul_binary64`
384×	`div-sub_binary64`
362×	`fabs-div_binary64`
349×	`fma-neg_binary64`
273×	`fma-def_binary64`

Counts

231 → 171

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	963
1	71	963
2	197	963
3	644	963
4	2840	963
5	4634	963
6	5114	963

prune119.0ms (2.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	227	2	229

Error

Counts

229 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (+.f64 a b) (/.f64 (-.f64 a b) a)) a)))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a b) (*.f64 (/.f64 a (+.f64 a b)) a))))

Compiler

Compiled 4145 to 1330 computations (67.9% saved)

regimes781.0ms (16.4%)

Accuracy

Total 0.0b remaining (49.2%)

Threshold costs 0.0b (49.2%)

Counts

44 → 1

Compiler

Compiled 4860 to 3171 computations (34.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	17	20
2	28	20
3	34	20
4	38	20
5	40	20
6	41	20
7	41	20

end151.0ms (3.2%)

Compiler: Compiled 60 to 36 computations (40% saved)

Details

analyze36.0ms (0.8%)

sample1.1s (22.8%)

simplify54.0ms (1.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series54.0ms (1.1%)

rewrite280.0ms (5.9%)

simplify71.0ms (1.5%)

prune142.0ms (3%)

localize8.0ms (0.2%)

series51.0ms (1.1%)

rewrite300.0ms (6.3%)

simplify69.0ms (1.5%)

prune122.0ms (2.6%)

localize8.0ms (0.2%)

series60.0ms (1.3%)

rewrite468.0ms (9.8%)

simplify121.0ms (2.5%)

prune335.0ms (7%)

localize10.0ms (0.2%)

series51.0ms (1.1%)

rewrite292.0ms (6.1%)

simplify82.0ms (1.7%)

prune119.0ms (2.5%)

regimes781.0ms (16.4%)

simplify3.0ms (0.1%)

end151.0ms (3.2%)

Profiling