Details

analyze1.1s (7.2%)

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 (29.8%)

Symmetry

(sort a1 a2)

Results

1.2s	1750×	body	1024	valid
1.1s	1685×	body	1024	invalid
879.0ms	5090×	body	128	valid
429.0ms	958×	body	512	valid
340.0ms	802×	body	512	invalid
143.0ms	455×	body	256	valid
133.0ms	424×	body	256	invalid
113.0ms	665×	body	128	invalid
3.0ms	3×	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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(+.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))

series75.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

54.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
21.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

2 → 85

Calls

2 calls:

43.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
3.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify105.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-l_binary64`
410×	`associate-r_binary64`
396×	`fma-neg_binary64`
332×	`associate-/l*_binary64`
299×	`sub-neg_binary64`

Counts

145 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3315
1	365	3012
2	1289	2968
3	4359	2968
4	5076	2968

prune150.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	143	8	151
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	144	9	153

Error

0.0b

Counts

153 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	0.8b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
✓	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	37.0b	(cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))) (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))) (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

Compiler

Compiled 3808 to 1792 computations (52.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
✓	0.5b	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
✓	6.8b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series339.0ms (2.3%)

Counts

4 → 108

Calls

4 calls:

187.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
108.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
24.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
19.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite105.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

526×	`times-frac_binary64`
306×	`add-sqr-sqrt_binary64`
281×	`*-un-lft-identity_binary64`
281×	`add-cube-cbrt_binary64`
272×	`sqrt-prod_binary64`

Counts

4 → 401

Calls

4 calls:

27.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
9.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
3.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify383.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
353×	`associate-/r/_binary64`
280×	`*-commutative_binary64`
274×	`cancel-sign-sub-inv_binary64`
268×	`associate-/l*_binary64`

Counts

509 → 572

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	476	16630
1	1170	13399
2	3926	12746
3	4782	12746
4	4931	12746

prune544.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	569	3	572
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	574	7	581

Error

Counts

581 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (hypot.f64 a2 a1))) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	1.2b	(.f64 (.f64 (cos.f64 th) (/.f64 (cbrt.f64 (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (cbrt.f64 (hypot.f64 a2 a1))))) (/.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))) (/.f64 1 (hypot.f64 a2 a1))))
✓	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
▶	0.4b	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))

Compiler

Compiled 18102 to 7144 computations (60.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
	0.5b	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))

series142.0ms (1%)

Counts

2 → 72

Calls

2 calls:

108.0ms	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
34.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

2 → 86

Calls

2 calls:

7.0ms	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
3.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))

simplify127.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

777×	`associate-/r/_binary64`
384×	`fma-neg_binary64`
360×	`fma-def_binary64`
264×	`associate-/l*_binary64`
221×	`cancel-sign-sub-inv_binary64`

Counts

158 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	4223
1	699	3721
2	2586	3604
3	4473	3597
4	4970	3597

prune234.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	266	2	268
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	268	7	275

Error

Counts

275 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
✓	0.4b	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
	0.5b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (hypot.f64 a2 a1))) (/.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
▶	0.4b	(/.f64 (/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (sqrt.f64 2)) 1)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1)))
✓	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 6731 to 3370 computations (49.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.2b	(/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))
✓	0.3b	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (sqrt.f64 2)) 1))
✓	0.4b	(/.f64 (/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (sqrt.f64 2)) 1)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1)))

series204.0ms (1.4%)

Counts

3 → 96

Calls

3 calls:

111.0ms

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

62.0ms

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

31.0ms

(/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))

rewrite446.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

4083×	`times-frac_binary64`
1953×	`sqrt-prod_binary64`
1406×	`*-un-lft-identity_binary64`
1406×	`add-sqr-sqrt_binary64`
1406×	`add-cube-cbrt_binary64`

Counts

3 → 1361

Calls

3 calls:

31.0ms

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

10.0ms

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

4.0ms

(/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))

simplify1.5s (9.9%)

Algorithm

1×	egg-herbie

Rules

780×	`associate-/r/_binary64`
606×	`associate-/l*_binary64`
417×	`associate-/r*_binary64`
387×	`times-frac_binary64`
380×	`associate-/l/_binary64`

Counts

1457 → 1352

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	852	69168
1	2201	65957
2	4860	65838
3	5080	65838

prune1.7s (11.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1427	1	1428
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	1428	7	1435

Error

Counts

1435 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	0.5b	(.f64 1 (.f64 (/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 2)) (hypot.f64 a2 a1)))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
✓	0.4b	(/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
✓	0.4b	(/.f64 (/.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (sqrt.f64 2)) 1)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1)))
✓	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 53793 to 35266 computations (34.4% saved)

regimes3.0s (20.4%)

Accuracy

Total 0.4b remaining (95.7%)

Threshold costs 0.4b (95.7%)

Counts

300 → 1

Compiler

Compiled 58656 to 37917 computations (35.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	17	33
2	17	33

end126.0ms (0.9%)

Remove: (sort a1 a2)
Compiler: Compiled 231 to 163 computations (29.4% saved)

Details

analyze1.1s (7.2%)

sample4.4s (29.8%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series75.0ms (0.5%)

rewrite52.0ms (0.4%)

simplify105.0ms (0.7%)

prune150.0ms (1%)

localize11.0ms (0.1%)

series339.0ms (2.3%)

rewrite105.0ms (0.7%)

simplify383.0ms (2.6%)

prune544.0ms (3.7%)

localize8.0ms (0.1%)

series142.0ms (1%)

rewrite17.0ms (0.1%)

simplify127.0ms (0.9%)

prune234.0ms (1.6%)

localize12.0ms (0.1%)

series204.0ms (1.4%)

rewrite446.0ms (3%)

simplify1.5s (9.9%)

prune1.7s (11.7%)

regimes3.0s (20.4%)

simplify2.0ms (0%)

end126.0ms (0.9%)

Profiling