Details

analyze1.1s (13.3%)

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)

sample4.4s (55.3%)

Symmetry

(sort a1 a2)

Results

1.2s	1849×	body	1024	valid
1.1s	1602×	body	1024	invalid
823.0ms	5012×	body	128	valid
406.0ms	917×	body	512	valid
357.0ms	831×	body	512	invalid
140.0ms	470×	body	256	valid
118.0ms	698×	body	128	invalid
116.0ms	390×	body	256	invalid
8.0ms	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

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
	0.5b	(+.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 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize30.0ms (0.4%)

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))

series64.0ms (0.8%)

Counts

3 → 64

Calls

3 calls:

46.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
16.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
1.0ms	(cos.f64 th)

rewrite56.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
198×	`pow1/3_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
181×	`pow3_binary64`

Counts

3 → 90

Calls

3 calls:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	223	32
2	2595	32
3	5006	32

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

478×	`associate-/r/_binary64`
446×	`fma-neg_binary64`
338×	`unswap-sqr_binary64`
316×	`sub-neg_binary64`
212×	`associate-/l/_binary64`

Counts

154 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	1369
1	197	1311
2	628	1263
3	2455	1221
4	5311	1221

prune98.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	7	119
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	113	8	121

Error

Counts

121 → 8

Alt Table

Status	Error	Program
	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))))
▶	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	17.7b	(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 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	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))
	1.1b	(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 2369 to 1490 computations (37.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 th)
✓	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))

series71.0ms (0.9%)

Counts

2 → 64

Calls

2 calls:

48.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
23.0ms	(*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th))

rewrite61.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

634×	`prod-diff_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
125×	`add-sqr-sqrt_binary64`
122×	`log1p-expm1-u_binary64`

Counts

2 → 66

Calls

2 calls:

60.0ms	(*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th))
60.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	258	29
2	3128	29
3	4924	29

simplify136.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

585×	`sub-neg_binary64`
376×	`fma-def_binary64`
338×	`unswap-sqr_binary64`
293×	`cancel-sign-sub-inv_binary64`
280×	`associate--l+_binary64`

Counts

130 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	1622
1	230	1538
2	852	1205
3	3869	1205
4	4889	1205
5	4979	1205

prune99.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	126	7	133

Error

Counts

133 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 -1/2))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	17.7b	(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
	0.6b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
▶	0.4b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))) 1)

Compiler

Compiled 2598 to 1697 computations (34.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series132.0ms (1.7%)

Counts

3 → 64

Calls

3 calls:

87.0ms	(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
38.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
7.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))

rewrite67.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`log-prod_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
184×	`log-pow_binary64`
150×	`prod-diff_binary64`

Counts

3 → 123

Calls

3 calls:

64.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
64.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
64.0ms	(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	233	32
2	2792	32
3	5124	32

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

492×	`associate-/r/_binary64`
338×	`unswap-sqr_binary64`
331×	`fma-neg_binary64`
276×	`sub-neg_binary64`
246×	`associate-r_binary64`

Counts

187 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1449
1	201	1409
2	652	1051
3	2525	1004
4	5266	1004

prune146.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	179	7	186

Error

Counts

186 → 7

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 -1/2))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	15.7b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) 1)
✓	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.6b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
✓	0.4b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))) 1)

Compiler

Compiled 3719 to 2418 computations (35% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series145.0ms (1.8%)

Counts

2 → 72

Calls

2 calls:

81.0ms	(.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 -1/2))
63.0ms	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))

rewrite51.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`log-prod_binary64`
298×	`pow2_binary64`
208×	`pow1/3_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`

Counts

2 → 40

Calls

2 calls:

50.0ms	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))
49.0ms	(.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 -1/2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	248	29
2	2603	29
3	5055	29

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
593×	`cancel-sign-sub-inv_binary64`
531×	`associate-l_binary64`
522×	`associate-r_binary64`
341×	`associate--l+_binary64`

Counts

112 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	1532
1	261	1323
2	1011	1266
3	4308	1266
4	5031	1266

prune120.0ms (1.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	147	7	154

Error

Counts

154 → 7

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 -1/2))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	15.7b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) 1)
✓	0.4b	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.6b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
✓	0.4b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))) 1)

Compiler

Compiled 2878 to 1786 computations (37.9% saved)

regimes876.0ms (11%)

Accuracy

Total 0.4b remaining (90.7%)

Threshold costs 0.4b (90.7%)

Counts

100 → 1

Compiler

Compiled 13071 to 10275 computations (21.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	12	18
2	12	18

end121.0ms (1.5%)

Remove: (sort a1 a2)
Compiler: Compiled 176 to 130 computations (26.1% saved)

Details

analyze1.1s (13.3%)

sample4.4s (55.3%)

simplify9.0ms (0.1%)

prune4.0ms (0%)

localize30.0ms (0.4%)

series64.0ms (0.8%)

rewrite56.0ms (0.7%)

simplify57.0ms (0.7%)

prune98.0ms (1.2%)

localize10.0ms (0.1%)

series71.0ms (0.9%)

rewrite61.0ms (0.8%)

simplify136.0ms (1.7%)

prune99.0ms (1.2%)

localize10.0ms (0.1%)

series132.0ms (1.7%)

rewrite67.0ms (0.8%)

simplify53.0ms (0.7%)

prune146.0ms (1.8%)

localize11.0ms (0.1%)

series145.0ms (1.8%)

rewrite51.0ms (0.6%)

simplify71.0ms (0.9%)

prune120.0ms (1.5%)

regimes876.0ms (11%)

simplify2.0ms (0%)

end121.0ms (1.5%)

Profiling