Details

analyze1.1s (9.1%)

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)

sample4.6s (38.6%)

Symmetry

(sort a1 a2)

Results

1.3s	1867×	body	1024	valid
1.1s	1574×	body	1024	invalid
857.0ms	5004×	body	128	valid
423.0ms	936×	body	512	valid
383.0ms	781×	body	512	invalid
130.0ms	443×	body	256	valid
128.0ms	408×	body	256	invalid
113.0ms	660×	body	128	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify56.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1095×	`rules-42_binary64`
878×	`fma-neg_binary64`
794×	`rules-41_binary64`
794×	`rules-43_binary64`
454×	`rules-40_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	86	18
2	320	18
3	1543	18
4	3917	18
5	26	18

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))

Compiler

Compiled 64 to 40 computations (37.5% 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))
✓	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series64.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

52.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
6.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
6.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite84.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

764×	`fma-neg_binary64`
439×	`fma-def_binary64`
249×	`prod-diff_binary64`
204×	`egg-rr`
186×	`expm1-udef_binary64`

Counts

3 → 204

Calls

3 calls:

79.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))
79.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
77.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	249	32
2	2903	32
3	5070	32
0	0	0
1	0	0

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

725×	`rules-40_binary64`
725×	`rules-41_binary64`
725×	`rules-42_binary64`
725×	`rules-43_binary64`
293×	`rules-21_binary64`

Counts

268 → 234

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	82	1389
1	507	1235
2	2501	1235
3	4977	1235

prune250.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	223	11	234
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	224	11	235

Error

0.0b

Counts

235 → 11

Alt Table

Status	Error	Program
	1.4b	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)) 0)
	0.7b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2)))
	1.8b	(fma.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 2)) 0)
▶	0.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 3)
	1.0b	(.f64 (log.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (fma.f64 a1 a1 (.f64 a2 a2)))
	0.9b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2))) (fma.f64 a1 a1 (*.f64 a2 a2)))
	1.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)))
	0.7b	(.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) (fma.f64 a1 a1 (.f64 a2 a2)))
	0.6b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (fma.f64 a1 a1 (*.f64 a2 a2)))
	17.2b	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)

Compiler

Compiled 5844 to 3627 computations (37.9% saved)

localize8.0ms (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)
✓	0.4b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
✓	0.4b	(/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))

series190.0ms (1.6%)

Counts

4 → 108

Calls

4 calls:

103.0ms	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
47.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
28.0ms	(/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))
12.0ms	(hypot.f64 a1 a2)

rewrite73.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

723×	`fma-neg_binary64`
386×	`fma-def_binary64`
261×	`prod-diff_binary64`
194×	`egg-rr`
188×	`expm1-udef_binary64`

Counts

4 → 194

Calls

4 calls:

70.0ms	(hypot.f64 a1 a2)
70.0ms	(pow.f64 (hypot.f64 a1 a2) 2)
70.0ms	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
70.0ms	(/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	252	40
2	2901	40
3	4959	40
0	0	0
1	0	0

simplify117.0ms (1%)

Algorithm

1×	egg-herbie

Rules

453×	`rules-21_binary64`
278×	`fma-neg_binary64`
256×	`rules-7-rev_binary64`
223×	`rules-40_binary64`
223×	`rules-41_binary64`

Counts

302 → 261

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	135	2601
1	892	2388
2	4291	2388
3	4960	2388
4	4904	2388

prune248.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	257	4	261
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	261	11	272

Error

0.0b

Counts

272 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) (fma.f64 a1 a1 (.f64 a2 a2)))
	0.6b	(*.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))
	1.0b	(.f64 (log.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (fma.f64 a1 a1 (.f64 a2 a2)))
	0.7b	(/.f64 (cos.f64 th) (pow.f64 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)) 2))
	0.7b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2)))
	1.8b	(fma.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 2)) 0)
	0.9b	(*.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))
	0.9b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2))) (fma.f64 a1 a1 (*.f64 a2 a2)))
	1.4b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (hypot.f64 a1 a2)) (.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2)))))
▶	0.6b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (fma.f64 a1 a1 (*.f64 a2 a2)))
	17.2b	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)

Compiler

Compiled 5500 to 3270 computations (40.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (cos.f64 th) 3)
✓	0.3b	(cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (*.f64 2 (sqrt.f64 2))))
✓	0.4b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (fma.f64 a1 a1 (*.f64 a2 a2)))
✓	0.7b	(/.f64 (pow.f64 (cos.f64 th) 3) (*.f64 2 (sqrt.f64 2)))

series746.0ms (6.3%)

Counts

4 → 64

Calls

4 calls:

498.0ms	(.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (fma.f64 a1 a1 (*.f64 a2 a2)))
222.0ms	(cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (*.f64 2 (sqrt.f64 2))))
19.0ms	(/.f64 (pow.f64 (cos.f64 th) 3) (*.f64 2 (sqrt.f64 2)))
6.0ms	(pow.f64 (cos.f64 th) 3)

rewrite139.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

355×	`prod-diff_binary64`
238×	`log1p-udef_binary64`
236×	`expm1-udef_binary64`
199×	`egg-rr`
137×	`add-sqr-sqrt_binary64`

Counts

4 → 199

Calls

4 calls:

135.0ms	(pow.f64 (cos.f64 th) 3)
135.0ms	(cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (*.f64 2 (sqrt.f64 2))))
135.0ms	(.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (fma.f64 a1 a1 (*.f64 a2 a2)))
135.0ms	(/.f64 (pow.f64 (cos.f64 th) 3) (*.f64 2 (sqrt.f64 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	46
1	338	42
2	3808	42
3	4994	42
4	5136	42
0	0	0
1	0	0

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

441×	`rules-14-rev_binary64`
375×	`rules-21_binary64`
342×	`fma-neg_binary64`
227×	`rules-20_binary64`
226×	`rules-7-rev_binary64`

Counts

263 → 240

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	116	2010
1	826	1819
2	4091	1819
3	5208	1819

prune240.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	235	5	240
Fresh	7	3	10
Picked	0	1	1
Done	0	0	0
Total	242	9	251

Error

0.0b

Counts

251 → 9

Alt Table

Status	Error	Program
	0.7b	(.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) (fma.f64 a1 a1 (.f64 a2 a2)))
	0.4b	(.f64 (.f64 (.f64 (cos.f64 th) (cbrt.f64 1/2)) (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3)) (fma.f64 a1 a1 (.f64 a2 a2)))
	0.6b	(.f64 (/.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) 1/2)) (cbrt.f64 (sqrt.f64 2))) (fma.f64 a1 a1 (*.f64 a2 a2)))
▶	0.4b	(.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (*.f64 (cos.f64 th) (cbrt.f64 1/2))) (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3))
	0.7b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2)))
	17.1b	(.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3)) 1/3)) (fma.f64 a1 a1 (*.f64 a2 a2)))
	1.4b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (hypot.f64 a1 a2)) (.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2)))))
	0.5b	(.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.6b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (fma.f64 a1 a1 (*.f64 a2 a2)))

Compiler

Compiled 6916 to 4407 computations (36.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (*.f64 (cos.f64 th) (cbrt.f64 1/2))) (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3))
✓	0.4b	(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (cos.f64 th) (cbrt.f64 1/2)))
✓	1.0b	(/.f64 1 (sqrt.f64 2))
✓	1.0b	(pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3)

series496.0ms (4.2%)

Counts

4 → 64

Calls

4 calls:

444.0ms	(.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (*.f64 (cos.f64 th) (cbrt.f64 1/2))) (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3))
52.0ms	(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (cos.f64 th) (cbrt.f64 1/2)))
0.0ms	(pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3)
0.0ms	(/.f64 1 (sqrt.f64 2))

rewrite135.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

636×	`prod-diff_binary64`
232×	`egg-rr`
172×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`

Counts

4 → 232

Calls

4 calls:

129.0ms	(.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (*.f64 (cos.f64 th) (cbrt.f64 1/2))) (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3))
129.0ms	(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (cos.f64 th) (cbrt.f64 1/2)))
129.0ms	(/.f64 1 (sqrt.f64 2))
129.0ms	(pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	64
1	436	41
2	4800	41
3	5874	41
0	0	0
1	0	0

simplify222.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1435×	`rules-43_binary64`
495×	`rules-14-rev_binary64`
420×	`rules-21_binary64`
291×	`fma-def_binary64`
257×	`fma-neg_binary64`

Counts

296 → 262

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	2554
1	666	1724
2	3637	1724
3	4768	1690
4	4844	1690
5	4975	1690
6	4990	1690
7	4995	1690
8	6148	1690

prune320.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	264	7	271

Error

Counts

271 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (fma.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 1/2)) 0) (pow.f64 (/.f64 1 (sqrt.f64 2)) 1/3))
✓	0.6b	(.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2)))) (fma.f64 a1 a1 (*.f64 a2 a2)))
	0.7b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2)))
	0.8b	(.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (*.f64 (cos.f64 th) (cbrt.f64 1/2))) (sqrt.f64 (cbrt.f64 1/2)))
	0.7b	(.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) (fma.f64 a1 a1 (.f64 a2 a2)))
	0.4b	(+.f64 (.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 1/2)) 0)
	0.6b	(.f64 (/.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) 1/2)) (cbrt.f64 (sqrt.f64 2))) (fma.f64 a1 a1 (*.f64 a2 a2)))

Compiler

Compiled 8632 to 6384 computations (26% saved)

regimes2.5s (20.8%)

Accuracy

Total 0.4b remaining (84.5%)

Threshold costs 0.4b (84.5%)

Counts

233 → 1

Compiler

Compiled 40317 to 30686 computations (23.9% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	19	26
2	18	26

end145.0ms (1.2%)

Remove: (sort a1 a2)
Compiler: Compiled 214 to 175 computations (18.2% saved)

Details

analyze1.1s (9.1%)

sample4.6s (38.6%)

simplify56.0ms (0.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series64.0ms (0.5%)

rewrite84.0ms (0.7%)

simplify59.0ms (0.5%)

prune250.0ms (2.1%)

localize8.0ms (0.1%)

series190.0ms (1.6%)

rewrite73.0ms (0.6%)

simplify117.0ms (1%)

prune248.0ms (2.1%)

localize12.0ms (0.1%)

series746.0ms (6.3%)

rewrite139.0ms (1.2%)

simplify84.0ms (0.7%)

prune240.0ms (2%)

localize16.0ms (0.1%)

series496.0ms (4.2%)

rewrite135.0ms (1.1%)

simplify222.0ms (1.9%)

prune320.0ms (2.7%)

regimes2.5s (20.8%)

simplify1.0ms (0%)

end145.0ms (1.2%)

Profiling