Details

analyze1.2s (10.2%)

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)

sample4.8s (40.7%)

Symmetry

(sort a1 a2)

Results

1.3s	1825×	body	1024	valid
1.2s	1582×	body	1024	invalid
933.0ms	5041×	body	128	valid
456.0ms	859×	body	512	invalid
453.0ms	973×	body	512	valid
132.0ms	401×	body	256	invalid
131.0ms	413×	body	256	valid
125.0ms	644×	body	128	invalid
4.0ms	4×	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 (.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)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.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))

series93.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

69.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
24.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite21.0ms (0.2%)

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:

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))

simplify112.0ms (1%)

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

prune169.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	146	7	153

Error

0.0b

Counts

153 → 7

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)))
	0.5b	(.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) (.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 (cos.f64 th) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2)))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2)))))
	0.6b	(.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 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 3767 to 1780 computations (52.7% 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) (.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))))
✓	7.5b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series677.0ms (5.8%)

Counts

4 → 120

Calls

4 calls:

418.0ms	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
199.0ms	(.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)))
14.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite63.0ms (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:

20.0ms	(.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)))

simplify252.0ms (2.2%)

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

prune443.0ms (3.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	403	1	404
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	403	8	411

Error

Counts

411 → 8

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)))
	0.5b	(.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) (.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))))
	29.0b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (.f64 (neg.f64 a1) (cbrt.f64 (/.f64 1 (sqrt.f64 2)))))
	1.2b	(.f64 (cos.f64 th) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2)))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2)))))
	0.6b	(.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 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 15746 to 9254 computations (41.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a2 a1)
✓	0.2b	(.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))

series215.0ms (1.8%)

Counts

4 → 108

Calls

4 calls:

113.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
67.0ms	(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
21.0ms	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))
13.0ms	(hypot.f64 a2 a1)

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 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))
0.0ms	(hypot.f64 a2 a1)

simplify148.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

760×	`times-frac_binary64`
619×	`fma-neg_binary64`
356×	`fma-def_binary64`
223×	`cancel-sign-sub-inv_binary64`
166×	`associate-r_binary64`

Counts

228 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	4908
1	682	4559
2	2328	4453
3	4630	4453
4	5037	4453

prune234.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	261	8	269

Error

Counts

269 → 8

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)))
	0.5b	(.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) (.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))))
	0.6b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (hypot.f64 a2 a1)) (*.f64 (sqrt.f64 (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))))
	1.2b	(.f64 (cos.f64 th) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2)))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2)))))
	0.6b	(.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 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 6411 to 3426 computations (46.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series140.0ms (1.2%)

Counts

4 → 88

Calls

4 calls:

75.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
29.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
28.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
7.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
55×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`

Counts

4 → 151

Calls

4 calls:

9.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
8.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
8.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify149.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
381×	`fma-neg_binary64`
215×	`associate-r_binary64`
196×	`*-commutative_binary64`
194×	`associate-/r/_binary64`

Counts

239 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	4527
1	704	4412
2	2293	4278
3	4840	4278
4	5019	4278

prune316.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	297	2	299
Fresh	3	2	5
Picked	0	1	1
Done	1	1	2
Total	301	6	307

Error

Counts

307 → 6

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)))
	0.5b	(.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 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
	0.4b	(/.f64 (.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2)))) 2)
	0.5b	(.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))))
	0.4b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 8610 to 4733 computations (45% saved)

regimes2.5s (21.1%)

Accuracy

Total 0.3b remaining (93.3%)

Threshold costs 0.3b (93.3%)

Counts

262 → 1

Compiler

Compiled 53670 to 36950 computations (31.2% saved)

simplify2.0ms (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

end114.0ms (1%)

Remove: (sort a1 a2)
Compiler: Compiled 202 to 137 computations (32.2% saved)

Details

analyze1.2s (10.2%)

sample4.8s (40.7%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series93.0ms (0.8%)

rewrite21.0ms (0.2%)

simplify112.0ms (1%)

prune169.0ms (1.4%)

localize16.0ms (0.1%)

series677.0ms (5.8%)

rewrite63.0ms (0.5%)

simplify252.0ms (2.2%)

prune443.0ms (3.8%)

localize10.0ms (0.1%)

series215.0ms (1.8%)

rewrite27.0ms (0.2%)

simplify148.0ms (1.3%)

prune234.0ms (2%)

localize14.0ms (0.1%)

series140.0ms (1.2%)

rewrite40.0ms (0.3%)

simplify149.0ms (1.3%)

prune316.0ms (2.7%)

regimes2.5s (21.1%)

simplify2.0ms (0%)

end114.0ms (1%)

Profiling