Details

analyze1.1s (8.4%)

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)

sample4.7s (35.9%)

Symmetry

(sort a1 a2)

Results

1.3s	1857×	body	1024	valid
1.2s	1591×	body	1024	invalid
877.0ms	4997×	body	128	valid
462.0ms	952×	body	512	valid
411.0ms	865×	body	512	invalid
161.0ms	442×	body	256	valid
129.0ms	406×	body	256	invalid
119.0ms	667×	body	128	invalid
8.0ms	8×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify12.0ms (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)

localize10.0ms (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)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series91.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

64.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
20.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
7.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite23.0ms (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:

9.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
7.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
0.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

simplify159.0ms (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

prune189.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	167	7	174
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	169	7	176

Error

Counts

176 → 7

Alt Table

Status	Error	Program
	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))))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))
	0.7b	(.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)))))
	0.5b	(.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))))
	0.5b	(.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))))
	0.6b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))

Compiler

Compiled 4135 to 1931 computations (53.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.2b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
✓	0.2b	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
✓	0.3b	(/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

series381.0ms (2.9%)

Counts

3 → 84

Calls

3 calls:

307.0ms

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

53.0ms

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

21.0ms

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

rewrite63.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
110×	`add-sqr-sqrt_binary64`
94×	`cbrt-prod_binary64`
90×	`*-un-lft-identity_binary64`
90×	`add-cube-cbrt_binary64`

Counts

3 → 218

Calls

3 calls:

21.0ms

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

8.0ms

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

6.0ms

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

simplify254.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
500×	`associate-/r/_binary64`
260×	`fma-def_binary64`
191×	`associate-/l*_binary64`
181×	`associate-/l/_binary64`

Counts

302 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	9806
1	697	8974
2	2581	8924
3	4583	8924
4	5353	8924

prune509.0ms (3.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	387	1	388
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	388	7	395

Error

Counts

395 → 7

Alt Table

Status	Error	Program
▶	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))))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))
	0.7b	(.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)))))
	0.5b	(.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))))
	0.5b	(.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))))
	0.6b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a2 a2 (.f64 a1 a1)))))

Compiler

Compiled 13365 to 8433 computations (36.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
✓	0.3b	(.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))))
✓	7.6b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series632.0ms (4.8%)

Counts

4 → 120

Calls

4 calls:

380.0ms	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
195.0ms	(.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))))
43.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
13.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite60.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64`
99×	`sqrt-prod_binary64`
91×	`add-sqr-sqrt_binary64`
86×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`

Counts

4 → 219

Calls

4 calls:

17.0ms	(.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))))
9.0ms	(.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
5.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify222.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

629×	`fma-def_binary64`
486×	`associate-l_binary64`
420×	`associate-r_binary64`
263×	`associate-*r/_binary64`
258×	`fma-neg_binary64`

Counts

339 → 404

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	424	12369
1	1171	9283
2	4493	9166
3	5108	9166

prune495.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	404	0	404
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	404	7	411

Error

Counts

411 → 7

Alt Table

Status	Error	Program
✓	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))))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))
	0.7b	(.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)))))
▶	0.5b	(.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))))
	0.5b	(.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))))
	0.6b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a2 a2 (.f64 a1 a1)))))

Compiler

Compiled 15690 to 9213 computations (41.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.3b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
✓	0.4b	(.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))))
✓	0.6b	(/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

series513.0ms (3.9%)

Counts

3 → 72

Calls

3 calls:

283.0ms

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

175.0ms

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

54.0ms

(*.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))))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`times-frac_binary64`
70×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
48×	`add-cube-cbrt_binary64`
46×	`cbrt-prod_binary64`

Counts

3 → 148

Calls

3 calls:

15.0ms

(*.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))))

6.0ms

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

5.0ms

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

simplify164.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
508×	`associate-/l/_binary64`
196×	`associate-*r/_binary64`
187×	`cancel-sign-sub-inv_binary64`
184×	`distribute-rgt-in_binary64`

Counts

220 → 217

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	6892
1	636	5433
2	2515	5371
3	4709	5361
4	5194	5361

prune286.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	240	7	247

Error

Counts

247 → 7

Alt Table

Status	Error	Program
✓	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))))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))
	0.7b	(.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)))))
✓	0.5b	(.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))))
	0.5b	(.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))))
	0.6b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a2 a2 (.f64 a1 a1)))))

Compiler

Compiled 7489 to 4607 computations (38.5% saved)

regimes2.9s (22.5%)

Accuracy

Total 0.4b remaining (85.6%)

Threshold costs 0.4b (85.6%)

Counts

277 → 1

Compiler

Compiled 59111 to 42997 computations (27.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	57
1	23	57
2	22	57

end171.0ms (1.3%)

Remove: (sort a1 a2)
Compiler: Compiled 333 to 258 computations (22.5% saved)

Details

analyze1.1s (8.4%)

sample4.7s (35.9%)

simplify12.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series91.0ms (0.7%)

rewrite23.0ms (0.2%)

simplify159.0ms (1.2%)

prune189.0ms (1.4%)

localize15.0ms (0.1%)

series381.0ms (2.9%)

rewrite63.0ms (0.5%)

simplify254.0ms (1.9%)

prune509.0ms (3.9%)

localize19.0ms (0.1%)

series632.0ms (4.8%)

rewrite60.0ms (0.5%)

simplify222.0ms (1.7%)

prune495.0ms (3.8%)

localize14.0ms (0.1%)

series513.0ms (3.9%)

rewrite42.0ms (0.3%)

simplify164.0ms (1.3%)

prune286.0ms (2.2%)

regimes2.9s (22.5%)

simplify3.0ms (0%)

end171.0ms (1.3%)

Profiling