Details

analyze1.0s (12.4%)

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)

sample4.2s (51.7%)

Symmetry

(sort a1 a2)

Results

1.2s	1796×	body	1024	valid
1.0s	1583×	body	1024	invalid
845.0ms	5056×	body	128	valid
417.0ms	941×	body	512	valid
367.0ms	871×	body	512	invalid
136.0ms	462×	body	256	valid
120.0ms	727×	body	128	invalid
104.0ms	366×	body	256	invalid
1.0ms	1×	body	2048	valid

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`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	58	18
3	88	18
4	115	18
5	135	18
6	152	18
7	170	18
8	172	18

Stop Event

1×

saturated

Counts

1 → 2

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))

series70.0ms (0.9%)

Counts

3 → 84

Calls

3 calls:

47.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
18.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
6.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite47.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
182×	`pow3_binary64`
181×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	224	36
2	2744	36

Stop Event

1×	node limit

Counts

3 → 94

Calls

3 calls:

46.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))
46.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
46.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1517
1	201	1427
2	604	1383
3	2757	1341

Stop Event

1×	node limit

Counts

178 → 122

prune120.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	117	7	124

Error

0.0b

Counts

124 → 7

Alt Table

Status	Error	Program
	1.2b	(*.f64 (cos.f64 th) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3))
	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 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	0.5b	(.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))
	0.6b	(.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))))
	0.5b	(+.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 2349 to 1519 computations (35.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
✓	0.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	0.3b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓	0.4b	(/.f64 a1 (sqrt.f64 2))

series75.0ms (0.9%)

Counts

4 → 60

Calls

4 calls:

55.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
7.0ms	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
7.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
6.0ms	(/.f64 a1 (sqrt.f64 2))

rewrite66.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
222×	`fma-neg_binary64`
143×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	286	47
2	4127	47

Stop Event

1×	node limit

Counts

4 → 115

Calls

4 calls:

64.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
64.0ms	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
64.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
64.0ms	(/.f64 a1 (sqrt.f64 2))

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1250
1	196	1250
2	598	1076
3	2745	1046

Stop Event

1×	node limit

Counts

175 → 134

prune127.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Error

0.0b

Counts

141 → 7

Alt Table

Status	Error	Program
	1.2b	(*.f64 (cos.f64 th) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3))
	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 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.6b	(.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))))
▶	0.4b	(.f64 (cos.f64 th) (+.f64 (pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	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 3162 to 2087 computations (34% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 a2 (pow.f64 2 1/4))
	0.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	0.3b	(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
	0.4b	(/.f64 a1 (sqrt.f64 2))

series73.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

43.0ms	(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
30.0ms	(/.f64 a2 (pow.f64 2 1/4))

rewrite36.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`log1p-expm1-u_binary64`
621×	`expm1-log1p-u_binary64`
300×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	155	16
2	1784	16

Stop Event

1×	node limit

Counts

2 → 78

Calls

2 calls:

35.0ms	(/.f64 a2 (pow.f64 2 1/4))
35.0ms	(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

785×	`sqr-pow_binary64`
422×	`associate-l_binary64`
336×	`cube-prod_binary64`
332×	`pow-sqr_binary64`
311×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	192
1	21	192
2	40	192
3	94	192
4	313	192
5	1469	192
6	1663	192
7	1781	192
8	1927	192
9	2117	192
10	2367	192
11	2697	192
12	3129	192
13	3665	192
14	4357	192

Stop Event

1×	node limit

Counts

102 → 82

prune133.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	139	7	146

Error

0.0b

Counts

146 → 7

Alt Table

Status	Error	Program
	1.2b	(*.f64 (cos.f64 th) (pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3))
	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 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.6b	(.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))))
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
▶	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 3198 to 2294 computations (28.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series113.0ms (1.4%)

Counts

4 → 88

Calls

4 calls:

60.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
23.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
23.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
6.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite69.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`fma-def_binary64`
246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
243×	`fma-neg_binary64`
164×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	283	54
2	3898	54

Stop Event

1×	node limit

Counts

4 → 164

Calls

4 calls:

66.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
66.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
66.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
66.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-neg_binary64`
398×	`sub-neg_binary64`
338×	`unswap-sqr_binary64`
221×	`associate-r_binary64`
193×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	2134
1	297	2126
2	859	1810
3	3448	1806

Stop Event

1×	node limit

Counts

252 → 201

prune214.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	240	8	248

Error

Counts

248 → 8

Alt Table

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

Compiler

Compiled 6254 to 3577 computations (42.8% saved)

regimes1.3s (15.3%)

Accuracy

Total 0.4b remaining (91.5%)

Threshold costs 0.4b (91.5%)

Counts

151 → 1

Compiler

Compiled 22831 to 17395 computations (23.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	15	25

Stop Event

1×

saturated

end292.0ms (3.6%)

Compiler: Compiled 231 to 176 computations (23.8% saved)

Details

analyze1.0s (12.4%)

sample4.2s (51.7%)

simplify8.0ms (0.1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series70.0ms (0.9%)

rewrite47.0ms (0.6%)

simplify44.0ms (0.5%)

prune120.0ms (1.5%)

localize10.0ms (0.1%)

series75.0ms (0.9%)

rewrite66.0ms (0.8%)

simplify38.0ms (0.5%)

prune127.0ms (1.5%)

localize11.0ms (0.1%)

series73.0ms (0.9%)

rewrite36.0ms (0.4%)

simplify64.0ms (0.8%)

prune133.0ms (1.6%)

localize10.0ms (0.1%)

series113.0ms (1.4%)

rewrite69.0ms (0.8%)

simplify65.0ms (0.8%)

prune214.0ms (2.6%)

regimes1.3s (15.3%)

simplify2.0ms (0%)

end292.0ms (3.6%)

Profiling