Details

analyze1.1s (13.8%)

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 (55.8%)

Symmetry

(sort a1 a2)

Results

1.3s	1892×	body	1024	valid
1.0s	1555×	body	1024	invalid
839.0ms	4983×	body	128	valid
410.0ms	925×	body	512	valid
343.0ms	778×	body	512	invalid
133.0ms	453×	body	256	valid
119.0ms	389×	body	256	invalid
112.0ms	651×	body	128	invalid
5.0ms	3×	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`

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

prune7.0ms (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
	0.6b	(+.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 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

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	(cos.f64 th)
✓	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))

series66.0ms (0.9%)

Counts

3 → 64

Calls

3 calls:

47.0ms	(.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))
2.0ms	(cos.f64 th)

rewrite51.0ms (0.7%)

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	34
1	224	32
2	2744	32

Stop Event

1×	node limit

Counts

3 → 87

Calls

3 calls:

50.0ms	(cos.f64 th)
49.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
49.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-neg_binary64`
338×	`unswap-sqr_binary64`
316×	`sub-neg_binary64`
210×	`associate-r_binary64`
206×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	1369
1	233	1311
2	693	1263
3	3075	1263

Stop Event

1×	node limit

Counts

151 → 116

prune105.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	108	8	116
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	110	8	118

Error

Counts

118 → 8

Alt Table

Status	Error	Program
	16.0b	(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
▶	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	28.5b	(*.f64 (cos.f64 th) (sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 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 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.5b	(/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.8b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))

Compiler

Compiled 2343 to 1487 computations (36.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
✓	0.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	0.4b	(/.f64 a1 (sqrt.f64 2))
✓	0.5b	(/.f64 (sqrt.f64 2) a2)

series77.0ms (1%)

Counts

4 → 48

Calls

4 calls:

59.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
8.0ms	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
6.0ms	(/.f64 a1 (sqrt.f64 2))
3.0ms	(/.f64 (sqrt.f64 2) a2)

rewrite70.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
148×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`
140×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	292	44
2	4335	44

Stop Event

1×	node limit

Counts

4 → 114

Calls

4 calls:

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

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	1142
1	196	1142
2	598	968
3	2745	938

Stop Event

1×	node limit

Counts

162 → 130

prune122.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	130	8	138

Error

Counts

138 → 8

Alt Table

Status	Error	Program
	16.0b	(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	28.5b	(*.f64 (cos.f64 th) (sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 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 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.5b	(/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.8b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))

Compiler

Compiled 3139 to 2058 computations (34.4% saved)

localize9.0ms (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 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.2b	(.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))

series163.0ms (2.1%)

Counts

4 → 108

Calls

4 calls:

88.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
46.0ms	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
19.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))
9.0ms	(hypot.f64 a1 a2)

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	247	42
2	2876	42

Stop Event

1×	node limit

Counts

4 → 76

Calls

4 calls:

48.0ms	(hypot.f64 a1 a2)
48.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
48.0ms	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
48.0ms	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
496×	`cancel-sign-sub-inv_binary64`
404×	`times-frac_binary64`
260×	`fma-neg_binary64`
171×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2471
1	494	2282
2	1776	2234

Stop Event

1×	node limit

Counts

184 → 159

prune173.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	212	7	219

Error

Counts

219 → 7

Alt Table

Status	Error	Program
	16.0b	(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	0.8b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
▶	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
	28.5b	(*.f64 (cos.f64 th) (sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)))
✓	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.5b	(/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))

Compiler

Compiled 4881 to 2936 computations (39.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series70.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

40.0ms	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
24.0ms	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
6.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))

rewrite55.0ms (0.7%)

Algorithm

1×	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`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	218	36
2	2526	36

Stop Event

1×	node limit

Counts

3 → 55

Calls

3 calls:

54.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))
54.0ms	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
54.0ms	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary64`
593×	`cancel-sign-sub-inv_binary64`
524×	`associate-l_binary64`
516×	`associate-r_binary64`
341×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	1736
1	299	1491
2	1118	1434

Stop Event

1×	node limit

Counts

151 → 93

prune97.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	122	7	129

Error

Counts

129 → 7

Alt Table

Status	Error	Program
	16.0b	(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	0.8b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
✓	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
	28.5b	(*.f64 (cos.f64 th) (sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)))
✓	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.5b	(/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))

Compiler

Compiled 2295 to 1355 computations (41% saved)

regimes743.0ms (9.6%)

Accuracy

Total 0.4b remaining (95.4%)

Threshold costs 0.4b (95.4%)

Counts

90 → 1

Compiler

Compiled 11747 to 8906 computations (24.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18

Stop Event

1×

saturated

end254.0ms (3.3%)

Compiler: Compiled 171 to 123 computations (28.1% saved)

Details

analyze1.1s (13.8%)

sample4.3s (55.8%)

simplify8.0ms (0.1%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

series66.0ms (0.9%)

rewrite51.0ms (0.7%)

simplify48.0ms (0.6%)

prune105.0ms (1.4%)

localize14.0ms (0.2%)

series77.0ms (1%)

rewrite70.0ms (0.9%)

simplify38.0ms (0.5%)

prune122.0ms (1.6%)

localize9.0ms (0.1%)

series163.0ms (2.1%)

rewrite50.0ms (0.6%)

simplify59.0ms (0.8%)

prune173.0ms (2.2%)

localize9.0ms (0.1%)

series70.0ms (0.9%)

rewrite55.0ms (0.7%)

simplify42.0ms (0.5%)

prune97.0ms (1.3%)

regimes743.0ms (9.6%)

simplify2.0ms (0%)

end254.0ms (3.3%)

Profiling