Details

analyze1.1s (14.3%)

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)

sample4.3s (56.5%)

Symmetry

(sort a1 a2)

Results

1.2s	1887×	body	1024	valid
1.1s	1574×	body	1024	invalid
807.0ms	4966×	body	128	valid
430.0ms	916×	body	512	valid
344.0ms	827×	body	512	invalid
139.0ms	479×	body	256	valid
120.0ms	399×	body	256	invalid
111.0ms	668×	body	128	invalid
8.0ms	8×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify8.0ms (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

prune5.0ms (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

0.4b

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)))
	0.6b	(+.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)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series68.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

49.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
19.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite82.0ms (1.1%)

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 → 68

Calls

2 calls:

81.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
81.0ms	(/.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

simplify71.0ms (0.9%)

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

prune135.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Error

Counts

92 → 7

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.6b	(+.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 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (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 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4))))
	0.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))

Compiler

Compiled 1857 to 1237 computations (33.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.3b	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
✓	0.4b	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

series160.0ms (2.1%)

Counts

3 → 84

Calls

3 calls:

89.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
54.0ms	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
17.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

rewrite110.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

577×	`log-prod_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
192×	`pow3_binary64`
191×	`log-pow_binary64`

Counts

3 → 54

Calls

3 calls:

109.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
109.0ms	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
109.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	247	38
2	2718	38
3	4945	38
4	4977	38
5	4943	38
0	0	0
1	0	0

simplify78.0ms (1%)

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

138 → 107

Iterations

Useful iterations: 2 (0.0ms)

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

prune79.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
	0.5b	(.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 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.6b	(+.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 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))
	0.4b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))

Compiler

Compiled 2512 to 1614 computations (35.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a2 a2 (*.f64 a1 a1))
✓	0.2b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
✓	0.4b	(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))

series61.0ms (0.8%)

Counts

3 → 84

Calls

3 calls:

40.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
14.0ms	(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
7.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))

rewrite53.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 57

Calls

3 calls:

52.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))
52.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
52.0ms	(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	217	36
2	2380	36
3	5725	36
0	0	0
1	0	0

simplify58.0ms (0.8%)

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

141 → 86

Iterations

Useful iterations: 2 (0.0ms)

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

prune92.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	86	6	92

Error

Counts

92 → 6

Alt Table

Status	Error	Program
	0.5b	(.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 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.6b	(+.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 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))
▶	0.4b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))

Compiler

Compiled 1609 to 1010 computations (37.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a2 a2 (*.f64 a1 a1))
✓	0.2b	(*.f64 (sqrt.f64 1/2) (cos.f64 th))
✓	0.4b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))

series95.0ms (1.3%)

Counts

2 → 44

Calls

2 calls:

90.0ms	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
5.0ms	(*.f64 (sqrt.f64 1/2) (cos.f64 th))

rewrite50.0ms (0.7%)

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 → 32

Calls

2 calls:

49.0ms	(*.f64 (sqrt.f64 1/2) (cos.f64 th))
49.0ms	(.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

simplify55.0ms (0.7%)

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

76 → 58

Iterations

Useful iterations: 2 (0.0ms)

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

prune60.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	87	6	93

Error

Counts

93 → 6

Alt Table

Status	Error	Program
	0.5b	(.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 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.6b	(+.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 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))
✓	0.4b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))

Compiler

Compiled 1643 to 993 computations (39.6% saved)

regimes767.0ms (10.1%)

Accuracy

Total 0.4b remaining (94.5%)

Threshold costs 0.4b (94.5%)

Counts

85 → 1

Compiler

Compiled 11222 to 8847 computations (21.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	15	21
2	15	21

end96.0ms (1.3%)

Remove: (sort a1 a2)
Compiler: Compiled 171 to 115 computations (32.7% saved)

Details

analyze1.1s (14.3%)

sample4.3s (56.5%)

simplify8.0ms (0.1%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

series68.0ms (0.9%)

rewrite82.0ms (1.1%)

simplify71.0ms (0.9%)

prune135.0ms (1.8%)

localize9.0ms (0.1%)

series160.0ms (2.1%)

rewrite110.0ms (1.4%)

simplify78.0ms (1%)

prune79.0ms (1%)

localize8.0ms (0.1%)

series61.0ms (0.8%)

rewrite53.0ms (0.7%)

simplify58.0ms (0.8%)

prune92.0ms (1.2%)

localize8.0ms (0.1%)

series95.0ms (1.3%)

rewrite50.0ms (0.7%)

simplify55.0ms (0.7%)

prune60.0ms (0.8%)

regimes767.0ms (10.1%)

simplify2.0ms (0%)

end96.0ms (1.3%)

Profiling