Details

analyze1.2s (10.1%)

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)

sample4.8s (39.9%)

Symmetry

(sort a1 a2)

Results

1.4s	1858×	body	1024	valid
1.2s	1624×	body	1024	invalid
917.0ms	4972×	body	128	valid
473.0ms	941×	body	512	valid
396.0ms	846×	body	512	invalid
153.0ms	479×	body	256	valid
142.0ms	402×	body	256	invalid
119.0ms	663×	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

0.3b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 th)
✓	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))

series80.0ms (0.7%)

Counts

3 → 64

Calls

3 calls:

58.0ms	(.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))
2.0ms	(cos.f64 th)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

9.0ms	(.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))
1.0ms	(cos.f64 th)

simplify122.0ms (1%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-l_binary64`
420×	`associate-r_binary64`
337×	`unswap-sqr_binary64`
336×	`associate-/l*_binary64`
276×	`associate-*r/_binary64`

Counts

158 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	3431
1	398	3117
2	1373	3069
3	4414	3069
4	5205	3069

prune179.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	8	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	162	8	170

Error

Counts

170 → 8

Alt Table

Status	Error	Program
	0.6b	(.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))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
▶	0.4b	(.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))))
	1.2b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2)))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (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 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 4117 to 1967 computations (52.2% saved)

localize17.0ms (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)))
✓	0.2b	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (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))))
✓	6.9b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series665.0ms (5.5%)

Counts

4 → 120

Calls

4 calls:

408.0ms	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
197.0ms	(.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))))
45.0ms	(/.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)))

rewrite62.0ms (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:

19.0ms	(.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))))
8.0ms	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
5.0ms	(/.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)))

simplify219.0ms (1.8%)

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 → 402

Iterations

Useful iterations: 2 (0.0ms)

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

prune447.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	400	2	402
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	403	7	410

Error

Counts

410 → 7

Alt Table

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

Compiler

Compiled 15588 to 9176 computations (41.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2)))
✓	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))
	6.9b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series778.0ms (6.5%)

Counts

3 → 96

Calls

3 calls:

692.0ms

(*.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))))

59.0ms

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

26.0ms

(*.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`associate-r_binary64`
54×	`times-frac_binary64`
48×	`add-sqr-sqrt_binary64`
45×	`sqrt-prod_binary64`
44×	`*-un-lft-identity_binary64`

Counts

3 → 129

Calls

3 calls:

16.0ms

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

4.0ms

(*.f64 (hypot.f64 a2 a1) (cbrt.f64 1/2))

simplify155.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

984×	`times-frac_binary64`
613×	`associate-l_binary64`
580×	`associate-r_binary64`
405×	`fma-neg_binary64`
341×	`*-commutative_binary64`

Counts

225 → 268

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	336	7535
1	1006	6351
2	4150	6351
3	6058	6351

prune393.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	321	1	322
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	323	6	329

Error

Counts

329 → 6

Alt Table

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

Compiler

Compiled 10974 to 5991 computations (45.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a2 a2 (*.f64 a1 a1))
✓	0.1b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
✓	0.2b	(/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
✓	0.3b	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))

series545.0ms (4.5%)

Counts

4 → 132

Calls

4 calls:

408.0ms	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
72.0ms	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
58.0ms	(/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
6.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`times-frac_binary64`
32×	`add-exp-log_binary64`
24×	`cbrt-prod_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`

Counts

4 → 117

Calls

4 calls:

11.0ms	(/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
6.0ms	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
3.0ms	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
0.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))

simplify198.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
731×	`cancel-sign-sub-inv_binary64`
207×	`unswap-sqr_binary64`
185×	`neg-mul-1_binary64`
181×	`neg-sub0_binary64`

Counts

249 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	6073
1	667	5381
2	2798	5372
3	4204	5372
4	4992	5372
5	5306	5372

prune255.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	235	6	241

Error

Counts

241 → 6

Alt Table

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

Compiler

Compiled 7166 to 4460 computations (37.8% saved)

regimes1.6s (13.2%)

Accuracy

Total 0.4b remaining (83%)

Threshold costs 0.4b (83%)

Counts

168 → 1

Compiler

Compiled 32841 to 22811 computations (30.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	33
1	21	33
2	21	33

end134.0ms (1.1%)

Remove: (sort a1 a2)
Compiler: Compiled 225 to 163 computations (27.6% saved)

Details

analyze1.2s (10.1%)

sample4.8s (39.9%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series80.0ms (0.7%)

rewrite19.0ms (0.2%)

simplify122.0ms (1%)

prune179.0ms (1.5%)

localize17.0ms (0.1%)

series665.0ms (5.5%)

rewrite62.0ms (0.5%)

simplify219.0ms (1.8%)

prune447.0ms (3.7%)

localize16.0ms (0.1%)

series778.0ms (6.5%)

rewrite42.0ms (0.4%)

simplify155.0ms (1.3%)

prune393.0ms (3.3%)

localize13.0ms (0.1%)

series545.0ms (4.5%)

rewrite32.0ms (0.3%)

simplify198.0ms (1.7%)

prune255.0ms (2.1%)

regimes1.6s (13.2%)

simplify2.0ms (0%)

end134.0ms (1.1%)

Profiling