Details

analyze2.2s (15.2%)

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)

sample214.0ms (1.5%)

Algorithm

1×

intervals

Results

50.0ms	47×	body	1024	invalid
46.0ms	50×	body	1024	valid
28.0ms	171×	body	128	valid
22.0ms	31×	body	512	invalid
14.0ms	26×	body	512	valid
5.0ms	16×	body	256	invalid
4.0ms	25×	body	128	invalid
3.0ms	9×	body	256	valid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`
9×	`distribute-rgt-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	26	20
2	46	20
3	66	20
4	85	20
5	97	20
6	108	20
7	106	20
8	106	20

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.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 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 92 to 63 computations (31.5% saved)

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite247.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

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 → 94

Calls

3 calls:

68.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2099 to 762 computations (63.7% saved)

series271.0ms (1.9%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

132.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
74.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
34.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1499 to 1222 computations (18.5% saved)

simplify191.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

383×	`sub-neg_binary64`
346×	`associate-/l*_binary64`
302×	`associate-*r/_binary64`
298×	`associate-*l/_binary64`
157×	`distribute-rgt-in_binary64`

Counts

136 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	3537
1	454	3289
2	1540	3143
3	4404	3143
4	4792	3143
5	4960	3143

prune89.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	9	128

Error

Counts

128 → 9

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
	0.4b	(/.f64 (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2))
	0.4b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	1.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (fabs.f64 (cbrt.f64 2)))) (/.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 (cbrt.f64 2))))
	0.4b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))

Compiler

Compiled 2133 to 967 computations (54.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
7.0b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.0b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite297.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

108×	`times-frac_binary64`
102×	`sqrt-prod_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64`
84×	`add-cube-cbrt_binary64`

Counts

4 → 201

Calls

4 calls:

25.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
7.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
3.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 7992 to 3469 computations (56.6% saved)

series564.0ms (3.9%)

Error

Counts

4 → 75

Calls

4 calls:

163.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
152.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
83.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
72.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 5738 to 4414 computations (23.1% saved)

simplify372.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-l_binary64`
482×	`associate-r_binary64`
400×	`associate-*l/_binary64`
347×	`associate-*r/_binary64`
247×	`associate-/l*_binary64`

Counts

276 → 217

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	12942
1	1212	10938
2	5135	10938

prune273.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	217	9	226

Error

Counts

226 → 9

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
▶	0.4b	(/.f64 (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2))
	0.4b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	1.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (fabs.f64 (cbrt.f64 2)))) (/.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 (cbrt.f64 2))))
	0.4b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))

Compiler

Compiled 5181 to 2630 computations (49.2% saved)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.1b	(.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
0.4b	(/.f64 (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2))

rewrite141.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

15.0ms	(/.f64 (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2))
10.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
5.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1316 to 409 computations (68.9% saved)

series306.0ms (2.1%)

Error

Counts

3 → 48

Calls

3 calls:

144.0ms	(/.f64 (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2))
95.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
37.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1841 to 1478 computations (19.7% saved)

simplify241.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

359×	`times-frac_binary64`
357×	`cancel-sign-sub-inv_binary64`
324×	`distribute-rgt-in_binary64`
296×	`distribute-lft-in_binary64`
206×	`associate-/l/_binary64`

Counts

110 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2692
1	492	2396
2	1852	2345
3	4553	2332
4	4997	2332
5	4993	2332
6	4976	2332

prune116.0ms (0.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	100	8	108

Error

Counts

108 → 8

Alt Table

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

Compiler

Compiled 1498 to 686 computations (54.2% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

rewrite651.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 225

Calls

4 calls:

48.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
24.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
16.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 7820 to 4642 computations (40.6% saved)

series501.0ms (3.5%)

Error

Counts

4 → 54

Calls

4 calls:

189.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
157.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
66.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
50.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2328 to 1987 computations (14.6% saved)

simplify543.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-/r/_binary64`
224×	`associate-l_binary64`
214×	`associate-r_binary64`
206×	`associate-/l*_binary64`
186×	`associate-/l/_binary64`

Counts

279 → 268

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	339	10310
1	821	9649
2	2949	9503
3	4566	8917
4	4958	8917
5	4953	8917

prune305.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	269	7	276

Error

Counts

276 → 7

Alt Table

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

Compiler

Compiled 5393 to 3056 computations (43.3% saved)

regimes3.3s (22.7%)

Accuracy

Total 0.4b remaining (88%)

Threshold costs 0.4b (88%)

Compiler

Compiled 41699 to 29208 computations (30% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	19	27
2	19	27

end9.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 60 to 45 computations (25% saved)

sample3.6s (24.6%)

Algorithm

1×

intervals

Results

855.0ms	1773×	body	1024	valid
836.0ms	1545×	body	1024	invalid
563.0ms	4892×	body	128	valid
267.0ms	894×	body	512	valid
216.0ms	714×	body	512	invalid
93.0ms	440×	body	256	valid
78.0ms	394×	body	256	invalid
68.0ms	645×	body	128	invalid
2.0ms	1×	body	2048	valid

Compiler

Compiled 216 to 149 computations (31% saved)

Details

analyze2.2s (15.2%)

sample214.0ms (1.5%)

simplify20.0ms (0.1%)

prune7.0ms (0.1%)

localize19.0ms (0.1%)

rewrite247.0ms (1.7%)

series271.0ms (1.9%)

simplify191.0ms (1.3%)

prune89.0ms (0.6%)

localize19.0ms (0.1%)

rewrite297.0ms (2%)

series564.0ms (3.9%)

simplify372.0ms (2.6%)

prune273.0ms (1.9%)

localize22.0ms (0.2%)

rewrite141.0ms (1%)

series306.0ms (2.1%)

simplify241.0ms (1.7%)

prune116.0ms (0.8%)

localize27.0ms (0.2%)

rewrite651.0ms (4.5%)

series501.0ms (3.5%)

simplify543.0ms (3.7%)

prune305.0ms (2.1%)

regimes3.3s (22.7%)

simplify4.0ms (0%)

end9.0ms (0.1%)

sample3.6s (24.6%)

Profiling