Details

analyze1.1s (10.4%)

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)

sample4.9s (44.6%)

Symmetry

(sort a1 a2)

Results

1.4s	1841×	body	1024	valid
1.2s	1609×	body	1024	invalid
943.0ms	5056×	body	128	valid
482.0ms	907×	body	512	valid
422.0ms	840×	body	512	invalid
175.0ms	449×	body	256	valid
146.0ms	426×	body	256	invalid
133.0ms	666×	body	128	invalid
3.0ms	3×	body	2048	valid
1.0ms	1×	body	2048	invalid

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

prune5.0ms (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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.7b	(.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 3 expressions with local error:

New	Error	Program
✓	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)))
✓	0.6b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series99.0ms (0.9%)

Counts

3 → 84

Calls

3 calls:

62.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
30.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
8.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite22.0ms (0.2%)

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:

8.0ms	(.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))

simplify127.0ms (1.2%)

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

prune181.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	165	9	174
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	167	9	176

Error

Counts

176 → 9

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.8b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.9b	(.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))))
	0.7b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.9b	(.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 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
	0.7b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.7b	(.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))))
	0.8b	(.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 1 (sqrt.f64 2)))

Compiler

Compiled 4147 to 1945 computations (53.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series216.0ms (2%)

Counts

3 → 84

Calls

3 calls:

120.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
72.0ms	(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
24.0ms	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))

rewrite26.0ms (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`
23×	`associate-r_binary64`

Counts

3 → 110

Calls

3 calls:

8.0ms	(.f64 (cos.f64 th) (.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
8.0ms	(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
3.0ms	(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))

simplify109.0ms (1%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-/l*_binary64`
669×	`times-frac_binary64`
233×	`fma-def_binary64`
218×	`associate-/l/_binary64`
166×	`associate-r_binary64`

Counts

194 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	4340
1	586	4018
2	2016	3928
3	5092	3928

prune189.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	178	8	186

Error

Counts

186 → 8

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.8b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.9b	(.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))))
	0.7b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(.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))))
	0.7b	(/.f64 (*.f64 (cos.f64 th) (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (sqrt.f64 2))
▶	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))

Compiler

Compiled 4486 to 2444 computations (45.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series158.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

120.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
38.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`associate-r_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

8.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
3.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))

simplify115.0ms (1%)

Algorithm

1×	egg-herbie

Rules

670×	`times-frac_binary64`
519×	`fma-neg_binary64`
367×	`fma-def_binary64`
298×	`associate-l_binary64`
246×	`associate-/r/_binary64`

Counts

136 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	3472
1	624	2973
2	2337	2869
3	4799	2867
4	5136	2867

prune181.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	232	7	239

Error

Counts

239 → 7

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.8b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
▶	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.7b	(/.f64 (.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (hypot.f64 a2 a1)) (sqrt.f64 2))
	0.6b	(.f64 (/.f64 (.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))

Compiler

Compiled 5856 to 2920 computations (50.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series170.0ms (1.5%)

Counts

3 → 84

Calls

3 calls:

117.0ms

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

29.0ms

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

23.0ms

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

rewrite215.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

1116×	`sqrt-prod_binary64`
1098×	`times-frac_binary64`
576×	`*-un-lft-identity_binary64`
576×	`add-sqr-sqrt_binary64`
576×	`add-cube-cbrt_binary64`

Counts

3 → 700

Calls

3 calls:

46.0ms

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

14.0ms

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

6.0ms

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

simplify489.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

494×	`associate-l_binary64`
428×	`associate-/l/_binary64`
415×	`associate-/l*_binary64`
398×	`associate-r_binary64`
393×	`associate-*r/_binary64`

Counts

784 → 749

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	566	26295
1	1564	24420
2	5059	24420

prune731.0ms (6.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	824	1	825
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	825	7	832

Error

Counts

832 → 7

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
	0.7b	(/.f64 (.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (hypot.f64 a2 a1)) (sqrt.f64 2))
	0.8b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(/.f64 (.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2)))
	0.6b	(.f64 (/.f64 (.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))

Compiler

Compiled 27394 to 16644 computations (39.2% saved)

regimes1.7s (15.6%)

Accuracy

Total 0.4b remaining (96.7%)

Threshold costs 0.4b (96.7%)

Counts

180 → 1

Compiler

Compiled 32497 to 21265 computations (34.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	13	20
2	13	20

end119.0ms (1.1%)

Remove: (sort a1 a2)
Compiler: Compiled 199 to 134 computations (32.7% saved)

Details

analyze1.1s (10.4%)

sample4.9s (44.6%)

simplify10.0ms (0.1%)

prune5.0ms (0%)

localize9.0ms (0.1%)

series99.0ms (0.9%)

rewrite22.0ms (0.2%)

simplify127.0ms (1.2%)

prune181.0ms (1.7%)

localize8.0ms (0.1%)

series216.0ms (2%)

rewrite26.0ms (0.2%)

simplify109.0ms (1%)

prune189.0ms (1.7%)

localize8.0ms (0.1%)

series158.0ms (1.4%)

rewrite18.0ms (0.2%)

simplify115.0ms (1%)

prune181.0ms (1.6%)

localize10.0ms (0.1%)

series170.0ms (1.5%)

rewrite215.0ms (2%)

simplify489.0ms (4.5%)

prune731.0ms (6.7%)

regimes1.7s (15.6%)

simplify2.0ms (0%)

end119.0ms (1.1%)

Profiling