Details

analyze1.1s (10.6%)

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)

sample4.4s (43.2%)

Symmetry

(sort a1 a2)

Results

1.2s	1843×	body	1024	valid
1.1s	1625×	body	1024	invalid
836.0ms	5036×	body	128	valid
425.0ms	892×	body	512	valid
368.0ms	778×	body	512	invalid
139.0ms	479×	body	256	valid
131.0ms	390×	body	256	invalid
123.0ms	733×	body	128	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-def_binary64`
651×	`rules-20_binary64`
521×	`rules-33_binary64`
334×	`rules-13_binary64`
306×	`rules-14-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	32	18
2	100	18
3	393	18
4	1940	18
5	4569	18
6	5539	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 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	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))

series72.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

48.0ms	(.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))
6.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite85.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

830×	`fma-neg_binary64`
306×	`prod-diff_binary64`
191×	`egg-rr`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`

Counts

3 → 191

Calls

3 calls:

80.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))
80.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
80.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	253	36
2	3015	36
3	4924	36
0	0	0
1	0	0

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

595×	`fma-def_binary64`
348×	`rules-13_binary64`
293×	`rules-11_binary64`
252×	`rules-20_binary64`
203×	`fma-neg_binary64`

Counts

275 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1517
1	179	1421
2	865	1303
3	4948	1303
4	5013	1303

prune252.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	210	9	219
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	212	9	221

Error

0.0b

Counts

221 → 9

Alt Table

Status	Error	Program
	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))
	37.4b	(*.f64 (cos.f64 th) (cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))
	17.1b	(fma.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))) 0)
	0.6b	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	1.1b	(.f64 (cos.f64 th) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))))
	0.5b	(fma.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 1 (/.f64 (sqrt.f64 2) (cos.f64 th))) 0)
	1.2b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 3)

Compiler

Compiled 5252 to 3311 computations (37% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series160.0ms (1.6%)

Counts

4 → 108

Calls

4 calls:

86.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
47.0ms	(*.f64 (hypot.f64 a1 a2) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
17.0ms	(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))
9.0ms	(hypot.f64 a1 a2)

rewrite107.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

927×	`fma-neg_binary64`
358×	`prod-diff_binary64`
317×	`egg-rr`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`

Counts

4 → 317

Calls

4 calls:

101.0ms	(hypot.f64 a1 a2)
101.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
101.0ms	(*.f64 (hypot.f64 a1 a2) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
101.0ms	(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	257	42
2	3179	42
3	5324	42
0	0	0
1	0	0

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

755×	`fma-def_binary64`
504×	`rules-20_binary64`
479×	`rules-15-rev_binary64`
461×	`fma-neg_binary64`
371×	`rules-14-rev_binary64`

Counts

425 → 399

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	2779
1	449	2619
2	2002	2531
3	5264	2531

prune388.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	456	4	460
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	462	7	469

Error

Counts

469 → 7

Alt Table

Status	Error	Program
	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))
	0.6b	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2))
▶	0.3b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))))
	0.4b	(/.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
	0.4b	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) (cos.f64 th)))
	0.5b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2))))
	1.1b	(.f64 (cos.f64 th) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))))

Compiler

Compiled 11608 to 6648 computations (42.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a1 a2) 2)
✓	0.1b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))))
✓	0.2b	(*.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))
✓	8.5b	(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))

series174.0ms (1.7%)

Counts

4 → 108

Calls

4 calls:

77.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))))
45.0ms	(*.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))
36.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
15.0ms	(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))

rewrite117.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

978×	`fma-neg_binary64`
354×	`prod-diff_binary64`
333×	`egg-rr`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`

Counts

4 → 333

Calls

4 calls:

110.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
110.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))))
110.0ms	(*.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))
110.0ms	(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	60
1	279	45
2	3332	45
3	5564	45
0	0	0
1	0	0

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

935×	`fma-neg_binary64`
720×	`rules-13_binary64`
537×	`rules-20_binary64`
225×	`rules-21_binary64`
179×	`fma-def_binary64`

Counts

441 → 392

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	118	2189
1	384	2005
2	1843	2005
3	5264	2005

prune305.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	391	1	392
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	393	6	399

Error

Counts

399 → 6

Alt Table

Status	Error	Program
	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))
	0.6b	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2))
✓	0.3b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))))
	0.4b	(/.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
▶	0.4b	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) (cos.f64 th)))
	0.4b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))

Compiler

Compiled 10257 to 5848 computations (43% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a1 a2)
✓	0.2b	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) (cos.f64 th)))
✓	0.2b	(/.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) (cos.f64 th))
✓	0.5b	(/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))

series187.0ms (1.8%)

Counts

3 → 96

Calls

3 calls:

88.0ms	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) (cos.f64 th)))
80.0ms	(/.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) (cos.f64 th))
19.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))

rewrite104.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

847×	`fma-neg_binary64`
286×	`prod-diff_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
115×	`egg-rr`

Counts

3 → 115

Calls

3 calls:

101.0ms	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) (cos.f64 th)))
101.0ms	(/.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) (cos.f64 th))
101.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	252	43
2	3048	43
3	4967	43
4	4939	43
0	0	0
1	0	0

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

931×	`fma-neg_binary64`
661×	`rules-15-rev_binary64`
308×	`rules-21_binary64`
150×	`fma-def_binary64`
144×	`rules-20_binary64`

Counts

211 → 204

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	184	3537
1	612	3297
2	2908	3297
3	5631	3297

prune262.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	325	1	326
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	327	5	332

Error

Counts

332 → 5

Alt Table

Status	Error	Program
	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))
	0.4b	(/.f64 (*.f64 (cos.f64 th) (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (sqrt.f64 2))
✓	0.3b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))))
	0.4b	(/.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
	0.4b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))

Compiler

Compiled 7688 to 4380 computations (43% saved)

regimes2.0s (19.6%)

Accuracy

Total 0.3b remaining (94.5%)

Threshold costs 0.3b (94.5%)

Counts

227 → 1

Compiler

Compiled 33905 to 24390 computations (28.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	12	23

end93.0ms (0.9%)

Remove: (sort a1 a2)
Compiler: Compiled 156 to 109 computations (30.1% saved)

Details

analyze1.1s (10.6%)

sample4.4s (43.2%)

simplify48.0ms (0.5%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series72.0ms (0.7%)

rewrite85.0ms (0.8%)

simplify74.0ms (0.7%)

prune252.0ms (2.5%)

localize9.0ms (0.1%)

series160.0ms (1.6%)

rewrite107.0ms (1.1%)

simplify78.0ms (0.8%)

prune388.0ms (3.8%)

localize10.0ms (0.1%)

series174.0ms (1.7%)

rewrite117.0ms (1.2%)

simplify72.0ms (0.7%)

prune305.0ms (3%)

localize8.0ms (0.1%)

series187.0ms (1.8%)

rewrite104.0ms (1%)

simplify84.0ms (0.8%)

prune262.0ms (2.6%)

regimes2.0s (19.6%)

simplify3.0ms (0%)

end93.0ms (0.9%)

Profiling