Details

analyze1.0s (12.3%)

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)

sample4.8s (56.5%)

Results

1.2s	1778×	body	1024	valid
1.0s	1552×	body	1024	invalid
988.0ms	956×	body	512	valid
818.0ms	5029×	body	128	valid
361.0ms	837×	body	512	invalid
153.0ms	486×	body	256	valid
118.0ms	384×	body	256	invalid
117.0ms	662×	body	128	invalid
7.0ms	7×	body	2048	valid

Compiler

Compiled 46 to 32 computations (30.4% saved)

preprocess30.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

96×	`fma-def_binary64`
70×	`*-commutative_binary64`
57×	`associate-/l*_binary64`
30×	`associate-/r/_binary64`
26×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	69	72
2	160	72
3	243	72
4	321	72
5	375	72
6	420	72
7	474	72
8	480	72
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort a1 a2)

Compiler

Compiled 22 to 15 computations (31.8% saved)

simplify10.0ms (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)

localize10.0ms (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))

series69.0ms (0.8%)

Counts

3 → 84

Calls

21 calls:

8.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))	th	-inf
6.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))	th	inf
5.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))	th	0
5.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))	a1	-inf
4.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))	a1	inf

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	224	36
2	2729	36

Stop Event

1×	node limit

Counts

3 → 94

simplify49.0ms (0.6%)

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

prune108.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	5	124

Error

Counts

124 → 5

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.4b	(/.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 2265 to 1449 computations (36% saved)

localize12.0ms (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)))
✓	0.1b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	0.3b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓	0.5b	(/.f64 a1 (sqrt.f64 2))

series78.0ms (0.9%)

Counts

4 → 60

Calls

18 calls:

9.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))	a2	0
8.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))	th	-inf
7.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))	th	inf
6.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))	th	0
6.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))	a1	0

rewrite67.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
222×	`fma-neg_binary64`
147×	`add-sqr-sqrt_binary64`
143×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	286	47
2	4136	47

Stop Event

1×	node limit

Counts

4 → 115

simplify43.0ms (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

prune105.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.4b	(/.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 3068 to 2009 computations (34.5% saved)

localize10.0ms (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)
✓	0.1b	(.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))

series161.0ms (1.9%)

Counts

4 → 108

Calls

27 calls:

9.0ms	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))	a1	-inf
9.0ms	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))	a2	inf
9.0ms	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))	th	-inf
8.0ms	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))	a2	-inf
8.0ms	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))	th	inf

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`log-prod_binary64`
208×	`pow1/3_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
189×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	249	40
2	2782	40

Stop Event

1×	node limit

Counts

4 → 105

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
546×	`associate-r_binary64`
530×	`associate-l_binary64`
451×	`cancel-sign-sub-inv_binary64`
184×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	1905
1	365	1696
2	1259	1648

Stop Event

1×	node limit

Counts

213 → 163

prune125.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	163	5	168

Error

Counts

168 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
▶	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.4b	(/.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 3227 to 2032 computations (37% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series72.0ms (0.9%)

Counts

3 → 70

Calls

24 calls:

6.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))	th	-inf
6.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))	th	inf
5.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))	th	0
5.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))	a1	inf
5.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))	a2	-inf

rewrite64.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

634×	`prod-diff_binary64`
220×	`log1p-udef_binary64`
130×	`add-sqr-sqrt_binary64`
128×	`pow1_binary64`
126×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	261	36
2	3419	36

Stop Event

1×	node limit

Counts

3 → 101

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

375×	`fma-def_binary64`
293×	`cancel-sign-sub-inv_binary64`
280×	`associate--l+_binary64`
257×	`associate-r_binary64`
238×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	1646
1	265	1562
2	931	1229
3	4917	1229

Stop Event

1×	node limit

Counts

171 → 134

prune104.0ms (1.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
✓	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.4b	(/.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 2603 to 1613 computations (38% saved)

regimes1.1s (12.7%)

Accuracy

Total 0.4b remaining (93%)

Threshold costs 0.4b (93%)

Counts

131 → 1

Compiler

Compiled 17253 to 13466 computations (21.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	16	25

Stop Event

1×

saturated

end237.0ms (2.8%)

Stop Event

1×

fuel

Compiler

Compiled 162 to 122 computations (24.7% saved)

Details

analyze1.0s (12.3%)

sample4.8s (56.5%)

preprocess30.0ms (0.4%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series69.0ms (0.8%)

rewrite50.0ms (0.6%)

simplify49.0ms (0.6%)

prune108.0ms (1.3%)

localize12.0ms (0.1%)

series78.0ms (0.9%)

rewrite67.0ms (0.8%)

simplify43.0ms (0.5%)

prune105.0ms (1.2%)

localize10.0ms (0.1%)

series161.0ms (1.9%)

rewrite50.0ms (0.6%)

simplify48.0ms (0.6%)

prune125.0ms (1.5%)

localize10.0ms (0.1%)

series72.0ms (0.9%)

rewrite64.0ms (0.8%)

simplify54.0ms (0.6%)

prune104.0ms (1.2%)

regimes1.1s (12.7%)

simplify2.0ms (0%)

end237.0ms (2.8%)

Profiling