Details

analyze1.0s (8.8%)

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)

sample4.6s (39%)

Symmetry

(sort a1 a2)

Results

1.3s	1845×	body	1024	valid
1.1s	1646×	body	1024	invalid
871.0ms	4984×	body	128	valid
455.0ms	855×	body	512	invalid
423.0ms	938×	body	512	valid
150.0ms	487×	body	256	valid
118.0ms	655×	body	128	invalid
116.0ms	389×	body	256	invalid
2.0ms	2×	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

prune6.0ms (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)))
▶	0.5b	(.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 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 th)
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	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))

series108.0ms (0.9%)

Counts

4 → 88

Calls

4 calls:

77.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
23.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
6.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))
2.0ms	(cos.f64 th)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

4 → 104

Calls

4 calls:

9.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
3.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
1.0ms	(cos.f64 th)
0.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

simplify159.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-l_binary64`
420×	`associate-r_binary64`
336×	`associate-/l*_binary64`
297×	`fma-neg_binary64`
276×	`associate-*r/_binary64`

Counts

192 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3723
1	401	3380
2	1380	3332
3	4425	3332
4	4788	3332
5	4979	3332
6	4971	3332

prune188.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	184	7	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	185	8	193

Error

Counts

193 → 8

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)))
	1.3b	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2)))) (/.f64 (sqrt.f64 2) (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (cos.f64 th))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.8b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
	17.7b	(.f64 (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))) (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))))

Compiler

Compiled 4451 to 2054 computations (53.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series137.0ms (1.2%)

Counts

4 → 88

Calls

4 calls:

74.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
30.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
26.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
6.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
55×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`

Counts

4 → 151

Calls

4 calls:

14.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
9.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
8.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify146.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
381×	`fma-neg_binary64`
215×	`associate-r_binary64`
196×	`*-commutative_binary64`
194×	`associate-/r/_binary64`

Counts

239 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	4527
1	704	4412
2	2293	4278
3	4840	4278
4	5019	4278

prune297.0ms (2.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	295	4	299
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	300	7	307

Error

Counts

307 → 7

Alt Table

Status	Error	Program
	0.6b	(.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (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 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2) a2))
▶	0.5b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.8b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
	0.5b	(+.f64 (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 8812 to 4866 computations (44.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1)
	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.4b	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series48.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1)
20.0ms	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`associate-l_binary64`
20×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 67

Calls

2 calls:

8.0ms	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1)
7.0ms	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
552×	`associate-/r*_binary64`
490×	`associate-*l/_binary64`
392×	`times-frac_binary64`
352×	`associate-*r/_binary64`

Counts

115 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1936
1	351	1751
2	1033	1743
3	2836	1737
4	4951	1737
5	5273	1737

prune306.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	301	7	308

Error

Counts

308 → 7

Alt Table

Status	Error	Program
	0.6b	(.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (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 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2) a2))
✓	0.5b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.8b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
▶	0.5b	(+.f64 (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 8631 to 5033 computations (41.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
✓	0.6b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
✓	0.6b	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series43.0ms (0.4%)

Counts

3 → 48

Calls

3 calls:

26.0ms

(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (*.f64 a1 a1))

10.0ms

(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

7.0ms

(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite192.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

1137×	`sqrt-prod_binary64`
1119×	`times-frac_binary64`
610×	`add-sqr-sqrt_binary64`
576×	`*-un-lft-identity_binary64`
576×	`add-cube-cbrt_binary64`

Counts

3 → 711

Calls

3 calls:

41.0ms

(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (*.f64 a1 a1))

13.0ms

(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

6.0ms

(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

simplify658.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
454×	`associate-*l/_binary64`
395×	`associate-/r/_binary64`
388×	`*-commutative_binary64`
387×	`associate-/l/_binary64`

Counts

759 → 794

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	464	21834
1	1309	20764
2	2726	19880
3	3965	19680
4	4981	19680
5	4971	19680

prune1.1s (9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	845	0	845
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	845	7	852

Error

Counts

852 → 7

Alt Table

Status	Error	Program
	0.6b	(.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 th) (cos.f64 th)) (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 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2) a2))
✓	0.5b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.8b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
✓	0.5b	(+.f64 (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 32267 to 21068 computations (34.7% saved)

regimes2.5s (20.8%)

Accuracy

Total 0.4b remaining (94.1%)

Threshold costs 0.4b (94.1%)

Counts

226 → 1

Compiler

Compiled 47317 to 32861 computations (30.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	16	26
2	16	26

end132.0ms (1.1%)

Remove: (sort a1 a2)
Compiler: Compiled 244 to 163 computations (33.2% saved)

Details

analyze1.0s (8.8%)

sample4.6s (39%)

simplify9.0ms (0.1%)

prune6.0ms (0%)

localize8.0ms (0.1%)

series108.0ms (0.9%)

rewrite19.0ms (0.2%)

simplify159.0ms (1.3%)

prune188.0ms (1.6%)

localize10.0ms (0.1%)

series137.0ms (1.2%)

rewrite46.0ms (0.4%)

simplify146.0ms (1.2%)

prune297.0ms (2.5%)

localize10.0ms (0.1%)

series48.0ms (0.4%)

rewrite19.0ms (0.2%)

simplify97.0ms (0.8%)

prune306.0ms (2.6%)

localize13.0ms (0.1%)

series43.0ms (0.4%)

rewrite192.0ms (1.6%)

simplify658.0ms (5.6%)

prune1.1s (9%)

regimes2.5s (20.8%)

simplify2.0ms (0%)

end132.0ms (1.1%)

Profiling