Details

analyze1.1s (11.6%)

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)

sample4.5s (49%)

Symmetry

(sort a1 a2)

Results

1.4s	1869×	body	1024	valid
1.1s	1644×	body	1024	invalid
832.0ms	4976×	body	128	valid
409.0ms	926×	body	512	valid
340.0ms	779×	body	512	invalid
149.0ms	477×	body	256	valid
128.0ms	400×	body	256	invalid
116.0ms	692×	body	128	invalid
11.0ms	8×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify9.0ms (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

prune6.0ms (0.1%)

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 (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
✓	0.2b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.5b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series77.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

56.0ms	(.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))

rewrite54.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

68× egg-rr

Counts

2 → 68

Calls

2 calls:

53.0ms	((/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))))
0.0ms	()

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

simplify73.0ms (0.8%)

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

128 → 90

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

prune88.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Error

Counts

92 → 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))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (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 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 1785 to 1177 computations (34.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a1 a2)
✓	0.0b	(pow.f64 (hypot.f64 a1 a2) 2)
✓	0.2b	(.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))

series231.0ms (2.5%)

Counts

4 → 108

Calls

4 calls:

102.0ms	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
67.0ms	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
49.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
13.0ms	(hypot.f64 a1 a2)

rewrite57.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

105× egg-rr

Counts

4 → 105

Calls

2 calls:

55.0ms	((.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)) (.f64 (cos.f64 th) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))) (pow.f64 (hypot.f64 a1 a2) 2) (hypot.f64 a1 a2))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	248	40
2	2605	40
3	5054	40
0	0	0
1	0	0

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-neg_binary64`
658×	`fma-def_binary64`
556×	`associate-r_binary64`
537×	`associate-l_binary64`
451×	`cancel-sign-sub-inv_binary64`

Counts

213 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	1905
1	327	1696
2	1156	1648
3	4811	1648
4	5315	1648

prune130.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	163	5	168

Error

Counts

168 → 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))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (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 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 3212 to 2036 computations (36.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a1 a2)
✓	0.2b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
✓	0.2b	(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
✓	0.5b	(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

series241.0ms (2.6%)

Counts

3 → 84

Calls

3 calls:

153.0ms

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

66.0ms

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

21.0ms

(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

rewrite64.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

107× egg-rr

Counts

3 → 107

Calls

2 calls:

62.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	250	38
2	2876	38
3	5123	38
0	0	0
1	0	0

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-neg_binary64`
478×	`times-frac_binary64`
376×	`associate-/l*_binary64`
349×	`associate-r_binary64`
297×	`associate-l_binary64`

Counts

191 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	2107
1	333	2029
2	1133	1969
3	4798	1969
4	5267	1969

prune205.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	265	1	266
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	266	5	271

Error

Counts

271 → 5

Alt Table

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

Compiler

Compiled 6062 to 3672 computations (39.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (hypot.f64 a1 a2) 2)
✓	0.2b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))))
✓	0.2b	(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))
✓	5.5b	(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))

series181.0ms (2%)

Counts

3 → 84

Calls

3 calls:

103.0ms

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

58.0ms

(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))

20.0ms

(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))

rewrite67.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

87× egg-rr

Counts

3 → 87

Calls

2 calls:

65.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	53
1	274	38
2	2970	38
3	5215	38
0	0	0
1	0	0

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
676×	`fma-def_binary64`
608×	`associate-l_binary64`
419×	`cancel-sign-sub-inv_binary64`
302×	`times-frac_binary64`

Counts

171 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1983
1	355	1812
2	1301	1780
3	4968	1780
4	5577	1780

prune138.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	186	5	191

Error

Counts

191 → 5

Alt Table

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

Compiler

Compiled 4107 to 2489 computations (39.4% saved)

regimes1.6s (17.5%)

Accuracy

Total 0.3b remaining (81.9%)

Threshold costs 0.3b (81.9%)

Counts

182 → 1

Compiler

Compiled 25492 to 19461 computations (23.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	18	23
2	17	23

end103.0ms (1.1%)

Remove: (sort a1 a2)
Compiler: Compiled 166 to 117 computations (29.5% saved)

Details

analyze1.1s (11.6%)

sample4.5s (49%)

simplify9.0ms (0.1%)

prune6.0ms (0.1%)

localize8.0ms (0.1%)

series77.0ms (0.8%)

rewrite54.0ms (0.6%)

simplify73.0ms (0.8%)

prune88.0ms (1%)

localize9.0ms (0.1%)

series231.0ms (2.5%)

rewrite57.0ms (0.6%)

simplify79.0ms (0.9%)

prune130.0ms (1.4%)

localize10.0ms (0.1%)

series241.0ms (2.6%)

rewrite64.0ms (0.7%)

simplify85.0ms (0.9%)

prune205.0ms (2.2%)

localize12.0ms (0.1%)

series181.0ms (2%)

rewrite67.0ms (0.7%)

simplify82.0ms (0.9%)

prune138.0ms (1.5%)

regimes1.6s (17.5%)

simplify2.0ms (0%)

end103.0ms (1.1%)

Profiling