Details

analyze1.1s (12.5%)

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 (49.7%)

Symmetry

(sort a1 a2)

Results

1.2s	1802×	body	1024	valid
1.0s	1565×	body	1024	invalid
828.0ms	5057×	body	128	valid
384.0ms	910×	body	512	valid
331.0ms	788×	body	512	invalid
143.0ms	384×	body	256	invalid
142.0ms	474×	body	256	valid
107.0ms	642×	body	128	invalid
14.0ms	13×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% 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`

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
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.4b	(+.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 2 expressions with local error:

New	Error	Program
✓	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))

series120.0ms (1.4%)

Counts

2 → 60

Calls

2 calls:

99.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
21.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite53.0ms (0.6%)

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

2 → 70

Calls

2 calls:

51.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
51.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	223	29
2	2595	29
3	5006	29

simplify72.0ms (0.8%)

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

130 → 92

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

prune98.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Error

Counts

94 → 8

Alt Table

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

Compiler

Compiled 1905 to 1269 computations (33.4% 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))
✓	0.1b	(*.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))

series83.0ms (1%)

Counts

3 → 70

Calls

3 calls:

51.0ms	(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
25.0ms	(*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th))
7.0ms	(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))

rewrite69.0ms (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

3 → 103

Calls

3 calls:

67.0ms	(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
67.0ms	(*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th))
67.0ms	(/.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	45
1	258	36
2	3128	36
3	4924	36

simplify83.0ms (1%)

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

173 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	1646
1	230	1562
2	852	1229
3	3869	1229
4	4889	1229
5	4979	1229

prune114.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	138	6	144

Error

Counts

144 → 6

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))) 1)
	0.5b	(.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cos.f64 th) (pow.f64 2 -1/2)))
	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	13.7b	(pow.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 2)
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 2745 to 1704 computations (37.9% saved)

localize9.0ms (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)
✓	0.2b	(/.f64 (sqrt.f64 2) (cos.f64 th))
✓	0.3b	(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))

series146.0ms (1.7%)

Counts

4 → 88

Calls

4 calls:

91.0ms	(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
38.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
9.0ms	(hypot.f64 a1 a2)
7.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))

rewrite70.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`log-prod_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
184×	`log-pow_binary64`
151×	`egg-rr`

Counts

4 → 151

Calls

4 calls:

65.0ms	(hypot.f64 a1 a2)
65.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
65.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
65.0ms	(/.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	36
1	233	36
2	2792	36
3	5124	36

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-neg_binary64`
350×	`associate-r_binary64`
318×	`fma-def_binary64`
303×	`associate-l_binary64`
254×	`associate-/l*_binary64`

Counts

239 → 208

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	1937
1	341	1879
2	1108	1505
3	4817	1505
4	5694	1505

prune168.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	208	6	214

Error

Counts

214 → 6

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))) 1)
	0.5b	(.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cos.f64 th) (pow.f64 2 -1/2)))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	13.7b	(pow.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 2)
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 4440 to 2907 computations (34.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a1 a2)
✓	0.1b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
✓	0.3b	(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
✓	0.4b	(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

series155.0ms (1.8%)

Counts

3 → 84

Calls

3 calls:

88.0ms

(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))

50.0ms

(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))

17.0ms

(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

rewrite65.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`log-prod_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
188×	`log-pow_binary64`
132×	`log-div_binary64`

Counts

3 → 109

Calls

3 calls:

64.0ms

(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))

64.0ms

(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))

64.0ms

(/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	250	38
2	2876	38
3	5123	38

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-neg_binary64`
478×	`times-frac_binary64`
376×	`associate-/l*_binary64`
349×	`associate-r_binary64`
297×	`associate-l_binary64`

Counts

193 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	2107
1	333	2029
2	1133	1969
3	4798	1969
4	5267	1969

prune232.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	270	6	276

Error

Counts

276 → 6

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))) 1)
	0.5b	(.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cos.f64 th) (pow.f64 2 -1/2)))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	13.7b	(pow.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 2)
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 6074 to 3655 computations (39.8% saved)

regimes1.4s (16.2%)

Accuracy

Total 0.4b remaining (89.8%)

Threshold costs 0.4b (89.8%)

Counts

153 → 1

Compiler

Compiled 20272 to 15736 computations (22.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	17	21
2	16	21

end109.0ms (1.3%)

Remove: (sort a1 a2)
Compiler: Compiled 171 to 123 computations (28.1% saved)

Details

analyze1.1s (12.5%)

sample4.2s (49.7%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series120.0ms (1.4%)

rewrite53.0ms (0.6%)

simplify72.0ms (0.8%)

prune98.0ms (1.2%)

localize10.0ms (0.1%)

series83.0ms (1%)

rewrite69.0ms (0.8%)

simplify83.0ms (1%)

prune114.0ms (1.3%)

localize9.0ms (0.1%)

series146.0ms (1.7%)

rewrite70.0ms (0.8%)

simplify73.0ms (0.9%)

prune168.0ms (2%)

localize9.0ms (0.1%)

series155.0ms (1.8%)

rewrite65.0ms (0.8%)

simplify78.0ms (0.9%)

prune232.0ms (2.7%)

regimes1.4s (16.2%)

simplify2.0ms (0%)

end109.0ms (1.3%)

Profiling