Details

analyze952.0ms (8.8%)

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)

sample85.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms	55×	body	1024	valid
15.0ms	39×	body	1024	invalid
12.0ms	157×	body	128	valid
7.0ms	32×	body	512	valid
6.0ms	28×	body	512	invalid
2.0ms	12×	body	256	valid
1.0ms	17×	body	128	invalid
1.0ms	9×	body	256	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify11.0ms (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

prune6.0ms (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

0.4b

Counts

2 → 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 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 92 to 63 computations (31.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 th)
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.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))

rewrite156.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 101

Calls

4 calls:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
1.0ms	(cos.f64 th)

Compiler

Compiled 2219 to 800 computations (63.9% saved)

series179.0ms (1.7%)

Error

0.3b

Counts

4 → 46

Calls

4 calls:

86.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
39.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
24.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
8.0ms	(cos.f64 th)

Compiler

Compiled 1622 to 1291 computations (20.4% saved)

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

867×	`distribute-rgt-in_binary64`
318×	`cancel-sign-sub-inv_binary64`
309×	`associate-/l*_binary64`
282×	`*-commutative_binary64`
273×	`unswap-sqr_binary64`

Counts

147 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	3223
1	419	2977
2	1348	2944
3	3386	2944
4	5740	2944

prune117.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Error

0.0b

Counts

130 → 8

Alt Table

Status	Error	Program
	0.6b	(.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))))
	14.7b	(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))))
	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))))
	0.6b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	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 (.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 (.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 (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))))

Compiler

Compiled 2062 to 921 computations (55.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.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))))
6.5b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.5b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite368.0ms (3.4%)

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:

30.0ms	(.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))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 7992 to 3469 computations (56.6% saved)

series287.0ms (2.7%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

87.0ms	(.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))))
75.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
37.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
37.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3910 to 3017 computations (22.8% saved)

simplify223.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

620×	`associate-/r*_binary64`
351×	`associate-/r/_binary64`
326×	`associate-l_binary64`
277×	`associate-r_binary64`
241×	`cancel-sign-sub-inv_binary64`

Counts

254 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	9967
1	747	8043
2	2969	7948
3	5281	7948

prune167.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	191	7	198

Error

Counts

198 → 7

Alt Table

Status	Error	Program
	0.6b	(.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 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.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))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.8b	(.f64 (.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))) (/.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
✓	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 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

Compiler

Compiled 4364 to 2127 computations (51.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite106.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 67

Calls

4 calls:

10.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
1.0ms	(cos.f64 th)

Compiler

Compiled 1404 to 435 computations (69% saved)

series197.0ms (1.8%)

Error

Counts

4 → 51

Calls

4 calls:

86.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
58.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
26.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
8.0ms	(cos.f64 th)

Compiler

Compiled 1923 to 1510 computations (21.5% saved)

simplify145.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/l*_binary64`
355×	`times-frac_binary64`
280×	`cancel-sign-sub-inv_binary64`
259×	`distribute-rgt-in_binary64`
242×	`distribute-lft-in_binary64`

Counts

118 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	2348
1	403	2063
2	1458	1982
3	4559	1982
4	4749	1982
5	5033	1982

prune80.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	98	7	105

Error

Counts

105 → 7

Alt Table

Status	Error	Program
	0.6b	(.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 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.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))))
▶	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.8b	(.f64 (.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))) (/.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
✓	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 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

Compiler

Compiled 1460 to 678 computations (53.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
0.6b	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

rewrite315.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

150×	`sqrt-prod_binary64`
142×	`add-sqr-sqrt_binary64`
132×	`times-frac_binary64`
86×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`

Counts

4 → 213

Calls

4 calls:

36.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
6.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 5156 to 2688 computations (47.9% saved)

series213.0ms (2%)

Error

Counts

4 → 46

Calls

4 calls:

85.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
52.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
29.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
20.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 2081 to 1740 computations (16.4% saved)

simplify243.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

449×	`associate-/l/_binary64`
402×	`times-frac_binary64`
351×	`distribute-rgt-in_binary64`
335×	`distribute-lft-in_binary64`
179×	`associate-*l/_binary64`

Counts

259 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	254	7637
1	681	7025
2	2205	6891
3	4755	6693
4	4962	6693

prune126.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	151	7	158

Error

Counts

158 → 7

Alt Table

Status	Error	Program
	0.6b	(.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 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.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))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.8b	(.f64 (.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))) (/.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
	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 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

Compiler

Compiled 2127 to 1077 computations (49.4% saved)

regimes4.0s (36.8%)

Accuracy

Total 0.3b remaining (90.7%)

Threshold costs 0.3b (90.7%)

Compiler

Compiled 67570 to 45676 computations (32.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	22	32
2	21	32

end11.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 69 to 54 computations (21.7% saved)

sample2.6s (24.5%)

Algorithm

1×

intervals

Results

554.0ms	1757×	body	1024	valid
498.0ms	1592×	body	1024	invalid
361.0ms	4879×	body	128	valid
210.0ms	914×	body	512	valid
170.0ms	755×	body	512	invalid
67.0ms	446×	body	256	valid
60.0ms	409×	body	256	invalid
49.0ms	626×	body	128	invalid
2.0ms	4×	body	2048	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 273 to 182 computations (33.3% saved)

Details

analyze952.0ms (8.8%)

sample85.0ms (0.8%)

simplify11.0ms (0.1%)

prune6.0ms (0.1%)

localize14.0ms (0.1%)

rewrite156.0ms (1.4%)

series179.0ms (1.7%)

simplify128.0ms (1.2%)

prune117.0ms (1.1%)

localize18.0ms (0.2%)

rewrite368.0ms (3.4%)

series287.0ms (2.7%)

simplify223.0ms (2.1%)

prune167.0ms (1.6%)

localize10.0ms (0.1%)

rewrite106.0ms (1%)

series197.0ms (1.8%)

simplify145.0ms (1.3%)

prune80.0ms (0.7%)

localize12.0ms (0.1%)

rewrite315.0ms (2.9%)

series213.0ms (2%)

simplify243.0ms (2.3%)

prune126.0ms (1.2%)

regimes4.0s (36.8%)

simplify3.0ms (0%)

end11.0ms (0.1%)

sample2.6s (24.5%)

Profiling