Details

analyze1.1s (8.9%)

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)

sample4.5s (38.2%)

Symmetry

(sort a1 a2)

Results

1.3s	1861×	body	1024	valid
1.1s	1679×	body	1024	invalid
837.0ms	5032×	body	128	valid
403.0ms	885×	body	512	valid
370.0ms	847×	body	512	invalid
149.0ms	472×	body	256	valid
133.0ms	410×	body	256	invalid
110.0ms	637×	body	128	invalid
7.0ms	6×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify10.0ms (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)

localize9.0ms (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)))
✓	0.5b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series76.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

55.0ms	(.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))

rewrite17.0ms (0.1%)

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:

8.0ms	(.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))

simplify111.0ms (0.9%)

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

prune161.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	147	6	153

Error

Counts

153 → 6

Alt Table

Status	Error	Program
	0.7b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.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 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
	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))))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 3679 to 1734 computations (52.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series243.0ms (2.1%)

Counts

3 → 84

Calls

3 calls:

114.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
108.0ms	(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
21.0ms	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
23×	`associate-r_binary64`

Counts

3 → 110

Calls

3 calls:

9.0ms	(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
6.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
3.0ms	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))

simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-/l*_binary64`
669×	`times-frac_binary64`
233×	`fma-def_binary64`
218×	`associate-/l/_binary64`
166×	`associate-r_binary64`

Counts

194 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	4340
1	586	4018
2	2016	3928
3	5092	3928

prune154.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	177	6	183

Error

Counts

183 → 6

Alt Table

Status	Error	Program
	0.7b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))))
	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))))
▶	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 4390 to 2372 computations (46% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
✓	5.8b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series643.0ms (5.4%)

Counts

4 → 120

Calls

4 calls:

386.0ms	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
196.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
47.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
13.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite61.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64`
99×	`sqrt-prod_binary64`
91×	`add-sqr-sqrt_binary64`
86×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`

Counts

4 → 219

Calls

4 calls:

18.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
7.0ms	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
6.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify230.0ms (2%)

Algorithm

1×	egg-herbie

Rules

629×	`fma-def_binary64`
486×	`associate-l_binary64`
420×	`associate-r_binary64`
263×	`associate-*r/_binary64`
258×	`fma-neg_binary64`

Counts

339 → 404

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	424	12369
1	1171	9283
2	4493	9166
3	5108	9166

prune433.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	402	2	404
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	404	6	410

Error

Counts

410 → 6

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
	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))))
▶	0.4b	(.f64 (.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
✓	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 15608 to 9168 computations (41.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
✓	0.4b	(*.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))
	5.8b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series702.0ms (6%)

Counts

2 → 60

Calls

2 calls:

676.0ms	(.f64 (.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
26.0ms	(*.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`associate-r_binary64`
54×	`times-frac_binary64`
46×	`add-sqr-sqrt_binary64`
45×	`sqrt-prod_binary64`
42×	`*-un-lft-identity_binary64`

Counts

2 → 109

Calls

2 calls:

14.0ms	(.f64 (.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(*.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))

simplify124.0ms (1%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-def_binary64`
590×	`times-frac_binary64`
542×	`associate-l_binary64`
453×	`associate-r_binary64`
255×	`*-commutative_binary64`

Counts

169 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	5636
1	792	4726
2	3334	4704
3	5229	4704

prune395.0ms (3.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	390	0	390
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	390	6	396

Error

Counts

396 → 6

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
	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))))
✓	0.4b	(.f64 (.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
✓	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 13004 to 7055 computations (45.7% saved)

regimes2.4s (20.2%)

Accuracy

Total 0.3b remaining (85.8%)

Threshold costs 0.3b (85.8%)

Counts

217 → 1

Compiler

Compiled 42223 to 28725 computations (32% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	15	24
2	15	24

end269.0ms (2.3%)

Compiler: Compiled 216 to 151 computations (30.1% saved)

Details

analyze1.1s (8.9%)

sample4.5s (38.2%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series76.0ms (0.6%)

rewrite17.0ms (0.1%)

simplify111.0ms (0.9%)

prune161.0ms (1.4%)

localize10.0ms (0.1%)

series243.0ms (2.1%)

rewrite25.0ms (0.2%)

simplify106.0ms (0.9%)

prune154.0ms (1.3%)

localize20.0ms (0.2%)

series643.0ms (5.4%)

rewrite61.0ms (0.5%)

simplify230.0ms (2%)

prune433.0ms (3.7%)

localize16.0ms (0.1%)

series702.0ms (6%)

rewrite33.0ms (0.3%)

simplify124.0ms (1%)

prune395.0ms (3.3%)

regimes2.4s (20.2%)

simplify3.0ms (0%)

end269.0ms (2.3%)

Profiling