Details

analyze1.1s (8.9%)

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)

sample4.5s (36.2%)

Symmetry

(sort a1 a2)

Results

1.3s	1852×	body	1024	valid
1.1s	1592×	body	1024	invalid
882.0ms	5042×	body	128	valid
449.0ms	935×	body	512	valid
376.0ms	846×	body	512	invalid
141.0ms	424×	body	256	valid
117.0ms	387×	body	256	invalid
110.0ms	645×	body	128	invalid
3.0ms	3×	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 (0.1%)

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)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.1b	(.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))

series82.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

55.0ms	(.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))
6.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

7.0ms	(.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))
0.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

simplify105.0ms (0.8%)

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

179 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3607
1	368	3275
2	1296	3231
3	4370	3231
4	5109	3231

prune165.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	166	8	174
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	168	8	176

Error

Counts

176 → 8

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	0.4b	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.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))))
	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))))))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	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))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))

Compiler

Compiled 4101 to 1889 computations (53.9% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series61.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

61.0ms

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

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 44

Calls

1 calls:

8.0ms

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

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

454×	`associate-l_binary64`
393×	`unswap-sqr_binary64`
389×	`associate-r_binary64`
331×	`fma-neg_binary64`
310×	`times-frac_binary64`

Counts

80 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2273
1	324	2099
2	994	1695
3	3622	1695
4	5155	1695

prune193.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	178	7	185

Error

Counts

185 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))) (cos.f64 th))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	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 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
▶	0.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) (cos.f64 th))

Compiler

Compiled 4136 to 1914 computations (53.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) (cos.f64 th))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
✓	0.4b	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
✓	6.6b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series366.0ms (2.9%)

Counts

4 → 108

Calls

4 calls:

194.0ms	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) (cos.f64 th))
134.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
25.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
13.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite103.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

526×	`times-frac_binary64`
306×	`add-sqr-sqrt_binary64`
281×	`*-un-lft-identity_binary64`
281×	`add-cube-cbrt_binary64`
272×	`sqrt-prod_binary64`

Counts

4 → 401

Calls

4 calls:

25.0ms	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) (cos.f64 th))
9.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
3.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify419.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
328×	`associate-/r/_binary64`
279×	`*-commutative_binary64`
274×	`cancel-sign-sub-inv_binary64`
268×	`associate-*l/_binary64`

Counts

509 → 607

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	476	16538
1	1176	13481
2	3565	12886
3	4770	12886
4	4997	12886
5	4924	12886

prune536.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	606	1	607
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	607	7	614

Error

Counts

614 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
▶	0.4b	(.f64 (/.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))) (cos.f64 th))
	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 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
✓	0.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) (cos.f64 th))

Compiler

Compiled 19399 to 7679 computations (60.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series297.0ms (2.4%)

Counts

4 → 108

Calls

4 calls:

111.0ms	(.f64 (/.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))) (cos.f64 th))
72.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
67.0ms	(/.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1)))
46.0ms	(/.f64 (cbrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))

rewrite201.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

1076×	`times-frac_binary64`
473×	`add-sqr-sqrt_binary64`
441×	`*-un-lft-identity_binary64`
441×	`add-cube-cbrt_binary64`
298×	`cbrt-prod_binary64`

Counts

4 → 617

Calls

4 calls:

43.0ms	(.f64 (/.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))) (cos.f64 th))
15.0ms	(/.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1)))
13.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
3.0ms	(/.f64 (cbrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))

simplify517.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

732×	`associate-/l/_binary64`
586×	`associate-/r/_binary64`
402×	`associate-/l*_binary64`
298×	`associate-/r*_binary64`
199×	`*-commutative_binary64`

Counts

725 → 1057

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	755	31336
1	2127	25513
2	5013	25513

prune1.2s (9.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1057	0	1057
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	1057	7	1064

Error

Counts

1064 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
✓	0.4b	(.f64 (/.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))) (cos.f64 th))
	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 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
✓	0.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) (cos.f64 th))

Compiler

Compiled 41218 to 25720 computations (37.6% saved)

regimes2.3s (18.7%)

Accuracy

Total 0.4b remaining (91.5%)

Threshold costs 0.4b (91.5%)

Counts

273 → 1

Compiler

Compiled 48696 to 33860 computations (30.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	15	25
2	15	25

end127.0ms (1%)

Remove: (sort a1 a2)
Compiler: Compiled 226 to 165 computations (27% saved)

Details

analyze1.1s (8.9%)

sample4.5s (36.2%)

simplify9.0ms (0.1%)

prune6.0ms (0.1%)

localize8.0ms (0.1%)

series82.0ms (0.7%)

rewrite18.0ms (0.1%)

simplify105.0ms (0.8%)

prune165.0ms (1.3%)

localize11.0ms (0.1%)

series61.0ms (0.5%)

rewrite12.0ms (0.1%)

simplify72.0ms (0.6%)

prune193.0ms (1.5%)

localize13.0ms (0.1%)

series366.0ms (2.9%)

rewrite103.0ms (0.8%)

simplify419.0ms (3.3%)

prune536.0ms (4.3%)

localize13.0ms (0.1%)

series297.0ms (2.4%)

rewrite201.0ms (1.6%)

simplify517.0ms (4.1%)

prune1.2s (9.5%)

regimes2.3s (18.7%)

simplify2.0ms (0%)

end127.0ms (1%)

Profiling