Details

analyze1.1s (15.4%)

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 (61.4%)

Symmetry

(sort a1 a2)

Results

1.2s	1860×	body	1024	valid
1.1s	1660×	body	1024	invalid
842.0ms	4980×	body	128	valid
438.0ms	946×	body	512	valid
364.0ms	797×	body	512	invalid
151.0ms	467×	body	256	valid
124.0ms	404×	body	256	invalid
118.0ms	663×	body	128	invalid
3.0ms	3×	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
▶	0.4b	(.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))

series68.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

50.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
17.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite52.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
198×	`pow1/3_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
181×	`pow3_binary64`

Counts

2 → 70

Calls

2 calls:

50.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
50.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	223	29
2	2595	29
3	5006	29
0	0	0
1	0	0

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Rules

492×	`associate-/r/_binary64`
338×	`unswap-sqr_binary64`
331×	`fma-neg_binary64`
276×	`sub-neg_binary64`
206×	`associate-/l/_binary64`

Counts

130 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1313
1	165	1259
2	547	1215
3	2202	1173
4	4857	1173
5	5023	1173

prune85.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	88	6	94

Error

0.0b

Counts

94 → 6

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.5b	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2))

Compiler

Compiled 1802 to 1199 computations (33.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a1 a2) 2)
✓	0.1b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
✓	0.4b	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))

series160.0ms (2.2%)

Counts

3 → 84

Calls

3 calls:

79.0ms	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
44.0ms	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
37.0ms	(pow.f64 (hypot.f64 a1 a2) 2)

rewrite58.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

534×	`log-prod_binary64`
298×	`pow2_binary64`
208×	`pow1/3_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`

Counts

3 → 84

Calls

3 calls:

57.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
57.0ms	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
57.0ms	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	248	36
2	2605	36
3	5054	36
0	0	0
1	0	0

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-def_binary64`
529×	`distribute-rgt-neg-in_binary64`
495×	`distribute-lft-neg-in_binary64`
460×	`associate-l_binary64`
446×	`associate-r_binary64`

Counts

168 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	1417
1	187	1226
2	695	1194
3	3350	1194
4	5262	1194

prune84.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	112	6	118

Error

Counts

118 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
▶	0.4b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	0.5b	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 2118 to 1316 computations (37.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series41.0ms (0.6%)

Counts

2 → 44

Calls

2 calls:

37.0ms	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
3.0ms	(*.f64 (sqrt.f64 1/2) (cos.f64 th))

rewrite46.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

902×	`log1p-expm1-u_binary64`
902×	`expm1-log1p-u_binary64`
106×	`add-sqr-sqrt_binary64`
102×	`prod-diff_binary64`
99×	`add-log-exp_binary64`

Counts

2 → 34

Calls

2 calls:

45.0ms	(*.f64 (sqrt.f64 1/2) (cos.f64 th))
45.0ms	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	217	25
2	2374	25
3	5703	25
0	0	0
1	0	0

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-def_binary64`
580×	`distribute-rgt-neg-in_binary64`
512×	`associate-l_binary64`
460×	`associate-r_binary64`
432×	`cancel-sign-sub-inv_binary64`

Counts

78 → 60

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	1145
1	223	892
2	798	852
3	3699	852
4	5161	852

prune49.0ms (0.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	60	6	66

Error

Counts

66 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))
▶	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
✓	0.4b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	0.5b	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 1279 to 805 computations (37.1% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series74.0ms (1%)

Counts

2 → 64

Calls

2 calls:

49.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
25.0ms	(*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th))

rewrite59.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

634×	`prod-diff_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
125×	`add-sqr-sqrt_binary64`
122×	`log1p-expm1-u_binary64`

Counts

2 → 68

Calls

2 calls:

57.0ms	(*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th))
57.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	258	29
2	3128	29
3	4924	29
0	0	0
1	0	0

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

585×	`sub-neg_binary64`
376×	`fma-def_binary64`
338×	`unswap-sqr_binary64`
293×	`cancel-sign-sub-inv_binary64`
280×	`associate--l+_binary64`

Counts

132 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	1622
1	230	1538
2	852	1205
3	3869	1205
4	4889	1205
5	4979	1205

prune68.0ms (0.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	1	2
Picked	1	0	1
Done	0	3	3
Total	99	5	104

Error

Counts

104 → 5

Alt Table

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

Compiler

Compiled 1962 to 1229 computations (37.4% saved)

regimes429.0ms (5.9%)

Accuracy

Total 0.4b remaining (83.9%)

Threshold costs 0.4b (83.9%)

Counts

53 → 1

Compiler

Compiled 6835 to 5247 computations (23.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	14	17
2	14	17

end93.0ms (1.3%)

Remove: (sort a1 a2)
Compiler: Compiled 131 to 100 computations (23.7% saved)

Details

analyze1.1s (15.4%)

sample4.5s (61.4%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series68.0ms (0.9%)

rewrite52.0ms (0.7%)

simplify74.0ms (1%)

prune85.0ms (1.2%)

localize9.0ms (0.1%)

series160.0ms (2.2%)

rewrite58.0ms (0.8%)

simplify62.0ms (0.9%)

prune84.0ms (1.2%)

localize8.0ms (0.1%)

series41.0ms (0.6%)

rewrite46.0ms (0.6%)

simplify56.0ms (0.8%)

prune49.0ms (0.7%)

localize11.0ms (0.1%)

series74.0ms (1%)

rewrite59.0ms (0.8%)

simplify81.0ms (1.1%)

prune68.0ms (0.9%)

regimes429.0ms (5.9%)

simplify2.0ms (0%)

end93.0ms (1.3%)

Profiling