Details

analyze2.1s (19.2%)

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)

sample4.6s (42.5%)

Symmetry

(sort a1 a2)

Results

1.3s	1888×	body	1024	valid
1.1s	1710×	body	1024	invalid
828.0ms	4927×	body	128	valid
448.0ms	944×	body	512	valid
406.0ms	822×	body	512	invalid
167.0ms	491×	body	256	valid
131.0ms	410×	body	256	invalid
116.0ms	662×	body	128	invalid
6.0ms	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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.7b	(+.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)

localize11.0ms (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)))
✓	0.6b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series78.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

58.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
20.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite17.0ms (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:

7.0ms	(.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))

simplify110.0ms (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

prune144.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Error

Counts

153 → 8

Alt Table

Status	Error	Program
	0.9b	(.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 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
	1.2b	(.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))))
	0.8b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.8b	(.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))))
	0.7b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(.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 3771 to 1790 computations (52.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series198.0ms (1.8%)

Counts

4 → 108

Calls

4 calls:

104.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
61.0ms	(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
19.0ms	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))
13.0ms	(hypot.f64 a2 a1)

rewrite29.0ms (0.3%)

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:

7.0ms	(*.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 (1.4%)

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 → 218

Iterations

Useful iterations: 2 (0.0ms)

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

prune205.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	257	3	260
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	261	7	268

Error

Counts

268 → 7

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
▶	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
	0.9b	(.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 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.8b	(.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))))
	0.7b	(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
	0.6b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))))

Compiler

Compiled 6295 to 3365 computations (46.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series144.0ms (1.3%)

Counts

2 → 72

Calls

2 calls:

107.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
37.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`associate-r_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

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

simplify110.0ms (1%)

Algorithm

1×	egg-herbie

Rules

670×	`times-frac_binary64`
519×	`fma-neg_binary64`
367×	`fma-def_binary64`
298×	`associate-l_binary64`
246×	`associate-/r/_binary64`

Counts

136 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	3472
1	624	2973
2	2337	2869
3	4799	2867
4	5136	2867

prune228.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	314	1	315
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	316	6	322

Error

Counts

322 → 6

Alt Table

Status	Error	Program
	0.9b	(.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)))))
▶	0.6b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
✓	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
	0.8b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.8b	(.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))))
	0.7b	(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

Compiler

Compiled 7728 to 3872 computations (49.9% saved)

localize11.0ms (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 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)
✓	0.2b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
✓	5.4b	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

series119.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

89.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
19.0ms	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))
10.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`

Counts

3 → 90

Calls

3 calls:

9.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
2.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)
2.0ms	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

simplify146.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

767×	`times-frac_binary64`
619×	`fma-neg_binary64`
488×	`cancel-sign-sub-inv_binary64`
293×	`associate-r_binary64`
260×	`associate-l_binary64`

Counts

174 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	293	5151
1	752	4553
2	2741	3865
3	5000	3865
4	5283	3865

prune273.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	286	1	287
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	287	6	293

Error

Counts

293 → 6

Alt Table

Status	Error	Program
	0.8b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
✓	0.6b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
✓	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
	0.8b	(.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))))
	0.7b	(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

Compiler

Compiled 7864 to 3470 computations (55.9% saved)

regimes1.9s (18.1%)

Accuracy

Total 0.4b remaining (91.4%)

Threshold costs 0.4b (91.4%)

Counts

224 → 1

Compiler

Compiled 36297 to 24579 computations (32.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	14	20
2	14	20

end143.0ms (1.3%)

Remove: (sort a1 a2)
Compiler: Compiled 173 to 116 computations (32.9% saved)

Details

analyze2.1s (19.2%)

sample4.6s (42.5%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series78.0ms (0.7%)

rewrite17.0ms (0.2%)

simplify110.0ms (1%)

prune144.0ms (1.3%)

localize11.0ms (0.1%)

series198.0ms (1.8%)

rewrite29.0ms (0.3%)

simplify148.0ms (1.4%)

prune205.0ms (1.9%)

localize8.0ms (0.1%)

series144.0ms (1.3%)

rewrite15.0ms (0.1%)

simplify110.0ms (1%)

prune228.0ms (2.1%)

localize11.0ms (0.1%)

series119.0ms (1.1%)

rewrite19.0ms (0.2%)

simplify146.0ms (1.4%)

prune273.0ms (2.5%)

regimes1.9s (18.1%)

simplify2.0ms (0%)

end143.0ms (1.3%)

Profiling