Details

analyze1.1s (13%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.4s (53.4%)

Symmetry

(sort a1 a2)

Results

1.2s	1896×	body	1024	valid
1.1s	1594×	body	1024	invalid
842.0ms	4942×	body	128	valid
481.0ms	935×	body	512	valid
338.0ms	761×	body	512	invalid
147.0ms	476×	body	256	valid
122.0ms	386×	body	256	invalid
114.0ms	671×	body	128	invalid
8.0ms	7×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	53	18
3	76	18
4	103	18
5	117	18
6	132	18
7	134	18
8	136	18
9	136	18

prune4.0ms (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

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series67.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

48.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
18.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite57.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
198×	`pow1/3_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
181×	`pow3_binary64`

Counts

2 → 68

Calls

2 calls:

55.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
55.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	223	29
2	2595	29
3	5006	29

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

492×	`associate-/r/_binary64`
338×	`unswap-sqr_binary64`
331×	`fma-neg_binary64`
276×	`sub-neg_binary64`
206×	`associate-/l/_binary64`

Counts

128 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1313
1	165	1259
2	547	1215
3	2202	1173
4	4857	1173
5	5023	1173

prune84.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Error

Counts

92 → 6

Alt Table

Status	Error	Program
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4))))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))

Compiler

Compiled 1819 to 1205 computations (33.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a1 a2)
✓	0.1b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
✓	0.2b	(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
✓	0.4b	(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

series160.0ms (2%)

Counts

4 → 108

Calls

4 calls:

87.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
47.0ms	(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
15.0ms	(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))
11.0ms	(hypot.f64 a1 a2)

rewrite66.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`log-prod_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
188×	`log-pow_binary64`
139×	`egg-rr`

Counts

4 → 139

Calls

4 calls:

64.0ms	(hypot.f64 a1 a2)
64.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
64.0ms	(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
64.0ms	(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	250	42
2	2876	42
3	5123	42

simplify88.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-neg_binary64`
569×	`times-frac_binary64`
464×	`associate-/l*_binary64`
347×	`fma-def_binary64`
341×	`associate-/r*_binary64`

Counts

247 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	2595
1	427	2499
2	1443	2423
3	4741	2423
4	5209	2423

prune209.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	281	1	282
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	282	6	288

Error

Counts

288 → 6

Alt Table

Status	Error	Program
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4))))
	0.4b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2))))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))

Compiler

Compiled 6411 to 3855 computations (39.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a1 a2)
✓	0.1b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.2b	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
✓	0.4b	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

series140.0ms (1.7%)

Counts

3 → 84

Calls

3 calls:

75.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
50.0ms	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
14.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

rewrite109.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`log-prod_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
192×	`pow3_binary64`
191×	`log-pow_binary64`

Counts

3 → 54

Calls

3 calls:

108.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
108.0ms	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
108.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	247	38
2	2718	38
3	4945	38
4	4977	38
5	4943	38

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
676×	`fma-def_binary64`
608×	`associate-l_binary64`
419×	`cancel-sign-sub-inv_binary64`
302×	`times-frac_binary64`

Counts

138 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1983
1	355	1812
2	1301	1780
3	4968	1780
4	5577	1780

prune167.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	231	6	237

Error

Counts

237 → 6

Alt Table

Status	Error	Program
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
▶	0.4b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2))))
	0.4b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))

Compiler

Compiled 5228 to 3087 computations (41% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a1 a2)
✓	0.1b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2))))
✓	0.3b	(/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2)))
	0.4b	(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

series133.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

84.0ms	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2))))
48.0ms	(/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2)))

rewrite98.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

583×	`prod-diff_binary64`
229×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
212×	`log-pow_binary64`
174×	`log-div_binary64`

Counts

2 → 67

Calls

2 calls:

97.0ms	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2))))
97.0ms	(/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	273	29
2	3272	29
3	4936	29
4	5908	29

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

492×	`associate-/r/_binary64`
338×	`unswap-sqr_binary64`
331×	`fma-neg_binary64`
276×	`sub-neg_binary64`
206×	`associate-/l/_binary64`

Counts

127 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1313
1	163	1259
2	546	1215
3	2201	1173
4	4856	1173
5	5022	1173

prune200.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	280	0	280
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	280	6	286

Error

Counts

286 → 6

Alt Table

Status	Error	Program
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.4b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2))))
	0.4b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))

Compiler

Compiled 6361 to 3748 computations (41.1% saved)

regimes795.0ms (9.7%)

Accuracy

Total 0.4b remaining (88%)

Threshold costs 0.4b (88%)

Counts

104 → 1

Compiler

Compiled 13678 to 10479 computations (23.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	13	20
2	13	20

end99.0ms (1.2%)

Remove: (sort a1 a2)
Compiler: Compiled 162 to 109 computations (32.7% saved)

Details

analyze1.1s (13%)

sample4.4s (53.4%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series67.0ms (0.8%)

rewrite57.0ms (0.7%)

simplify74.0ms (0.9%)

prune84.0ms (1%)

localize11.0ms (0.1%)

series160.0ms (2%)

rewrite66.0ms (0.8%)

simplify88.0ms (1.1%)

prune209.0ms (2.5%)

localize10.0ms (0.1%)

series140.0ms (1.7%)

rewrite109.0ms (1.3%)

simplify75.0ms (0.9%)

prune167.0ms (2%)

localize9.0ms (0.1%)

series133.0ms (1.6%)

rewrite98.0ms (1.2%)

simplify78.0ms (0.9%)

prune200.0ms (2.4%)

regimes795.0ms (9.7%)

simplify2.0ms (0%)

end99.0ms (1.2%)

Profiling