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)

sample145.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

Results

30.0ms	54×	body	1024	valid
30.0ms	57×	body	1024	invalid
15.0ms	162×	body	128	valid
9.0ms	27×	body	512	valid
7.0ms	26×	body	512	invalid
4.0ms	18×	body	128	invalid
3.0ms	13×	body	256	valid
2.0ms	7×	body	256	invalid

Compiler

Compiled 48 to 34 computations (29.2% 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

0.4b

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)

localize9.0ms (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))

series137.0ms (1.1%)

Counts

2 → 60

Calls

2 calls:

116.0ms	(.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))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 85

Calls

2 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))

simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-l_binary64`
410×	`associate-r_binary64`
396×	`fma-neg_binary64`
332×	`associate-/l*_binary64`
299×	`sub-neg_binary64`

Counts

145 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3315
1	365	3012
2	1289	2968
3	4359	2968
4	5076	2968

prune142.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Error

Counts

153 → 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)))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.4b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	1.2b	(.f64 (cos.f64 th) (.f64 (.f64 (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1)))) (/.f64 (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	38.1b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th)) 3))

Compiler

Compiled 3763 to 1772 computations (52.9% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
✓	0.2b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
✓	0.3b	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

series102.0ms (0.8%)

Counts

3 → 84

Calls

3 calls:

56.0ms

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

25.0ms

(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))

21.0ms

(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite233.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 706

Calls

3 calls:

56.0ms

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

14.0ms

(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

5.0ms

(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))

simplify669.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
722×	`associate-/r/_binary64`
428×	`associate-/l/_binary64`
297×	`associate-/l*_binary64`
226×	`associate-l_binary64`

Counts

790 → 735

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	474	28220
1	1079	24418
2	3065	23626
3	4504	23572
4	5188	23572

prune769.0ms (6.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	731	4	735
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	737	6	743

Error

Counts

743 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (cos.f64 th))
	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))))
	1.2b	(.f64 (cos.f64 th) (.f64 (.f64 (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1)))) (/.f64 (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 2))))
	0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (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)))
▶	0.3b	(.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (fma.f64 a2 a2 (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 25145 to 14694 computations (41.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (fma.f64 a2 a2 (.f64 a1 a1)))
✓	1.0b	(sqrt.f64 (/.f64 1 (sqrt.f64 2)))
✓	1.0b	(/.f64 1 (sqrt.f64 2))

series45.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

24.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (fma.f64 a2 a2 (.f64 a1 a1)))
21.0ms	(/.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))
0.0ms	(/.f64 1 (sqrt.f64 2))
0.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 2)))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`sqrt-prod_binary64`
74×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
57×	`*-un-lft-identity_binary64`
53×	`add-cube-cbrt_binary64`

Counts

4 → 176

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (fma.f64 a2 a2 (.f64 a1 a1)))
9.0ms	(/.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (fma.f64 a2 a2 (.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))
3.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 2)))
3.0ms	(/.f64 1 (sqrt.f64 2))

simplify172.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-def_binary64`
717×	`unswap-sqr_binary64`
542×	`associate-/l*_binary64`
512×	`times-frac_binary64`
283×	`associate-l_binary64`

Counts

224 → 232

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	155	4427
1	270	3775
2	893	3769
3	3351	3733
4	4082	3393
5	4045	3267
6	5318	3267

prune230.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	232	6	238

Error

Counts

238 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (cos.f64 th))
	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (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)))
✓	0.3b	(.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (fma.f64 a2 a2 (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2))))
▶	0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))))
	0.6b	(.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 (pow.f64 2 -1/2)) (fma.f64 a2 a2 (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 6104 to 4041 computations (33.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series247.0ms (2%)

Counts

4 → 60

Calls

4 calls:

191.0ms	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
56.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))))
0.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
0.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))

rewrite293.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

1479×	`sqrt-prod_binary64`
1473×	`times-frac_binary64`
776×	`*-un-lft-identity_binary64`
776×	`add-sqr-sqrt_binary64`
776×	`add-cube-cbrt_binary64`

Counts

4 → 966

Calls

4 calls:

62.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))))
16.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
4.0ms	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))

simplify864.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

394×	`associate-l_binary64`
353×	`associate-*r/_binary64`
342×	`associate-r_binary64`
309×	`*-commutative_binary64`
261×	`associate-*l/_binary64`

Counts

1026 → 942

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	421	34822
1	1045	32649
2	4022	32369
3	4976	32369
4	4968	32369

prune1.1s (9.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	942	0	942
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	942	6	948

Error

Counts

948 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (cos.f64 th))
	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (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)))
✓	0.3b	(.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (fma.f64 a2 a2 (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2))))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))))
	0.6b	(.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 (pow.f64 2 -1/2)) (fma.f64 a2 a2 (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 36308 to 28121 computations (22.5% saved)

regimes2.2s (17.9%)

Accuracy

Total 0.3b remaining (80.8%)

Threshold costs 0.3b (80.8%)

Counts

215 → 1

Compiler

Compiled 43734 to 32129 computations (26.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	30
1	20	30
2	19	30

end7.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 66 to 51 computations (22.7% saved)

sample3.4s (28.2%)

Algorithm

1×

intervals

Results

816.0ms	1698×	body	1024	valid
804.0ms	1620×	body	1024	invalid
518.0ms	4922×	body	128	valid
270.0ms	929×	body	512	valid
234.0ms	781×	body	512	invalid
87.0ms	449×	body	256	valid
83.0ms	373×	body	256	invalid
74.0ms	664×	body	128	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 186 to 142 computations (23.7% saved)

Details

analyze1.1s (9.1%)

sample145.0ms (1.2%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series137.0ms (1.1%)

rewrite19.0ms (0.2%)

simplify109.0ms (0.9%)

prune142.0ms (1.2%)

localize13.0ms (0.1%)

series102.0ms (0.8%)

rewrite233.0ms (1.9%)

simplify669.0ms (5.5%)

prune769.0ms (6.3%)

localize12.0ms (0.1%)

series45.0ms (0.4%)

rewrite37.0ms (0.3%)

simplify172.0ms (1.4%)

prune230.0ms (1.9%)

localize16.0ms (0.1%)

series247.0ms (2%)

rewrite293.0ms (2.4%)

simplify864.0ms (7.1%)

prune1.1s (9.4%)

regimes2.2s (17.9%)

simplify2.0ms (0%)

end7.0ms (0.1%)

sample3.4s (28.2%)

Profiling