Details

analyze967.0ms (9.4%)

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)

sample87.0ms (0.8%)

Algorithm

1×

intervals

Results

17.0ms	173×	body	128	valid
16.0ms	51×	body	1024	valid
12.0ms	39×	body	1024	invalid
5.0ms	22×	body	512	valid
5.0ms	22×	body	512	invalid
3.0ms	17×	body	256	invalid
2.0ms	26×	body	128	invalid
2.0ms	10×	body	256	valid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify10.0ms (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

prune5.0ms (0%)

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
	0.4b	(+.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)

localize9.0ms (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))

rewrite138.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

11.0ms	(.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))

Compiler

Compiled 2099 to 762 computations (63.7% saved)

series162.0ms (1.6%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

81.0ms	(.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))
23.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1486 to 1213 computations (18.4% saved)

simplify122.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

360×	`sub-neg_binary64`
341×	`unswap-sqr_binary64`
336×	`associate-/l*_binary64`
303×	`*-commutative_binary64`
272×	`associate-*r/_binary64`

Counts

136 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3337
1	445	3089
2	1498	2993
3	4158	2993
4	5024	2993

prune102.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	118	8	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	120	8	128

Error

0.0b

Counts

128 → 8

Alt Table

Status	Error	Program
	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))))
	0.5b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	1.4b	(.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))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))))
	0.4b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (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))))))
	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 2094 to 933 computations (55.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
7.0b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
7.0b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite653.0ms (6.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

540×	`times-frac_binary64`
429×	`sqrt-prod_binary64`
302×	`add-sqr-sqrt_binary64`
295×	`*-un-lft-identity_binary64`
295×	`add-cube-cbrt_binary64`

Counts

4 → 413

Calls

4 calls:

21.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
8.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 12677 to 3357 computations (73.5% saved)

series190.0ms (1.8%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

49.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
39.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
36.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
35.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 2951 to 2043 computations (30.8% saved)

simplify533.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

320×	`distribute-rgt-in_binary64`
309×	`associate-/r/_binary64`
304×	`associate-/l/_binary64`
230×	`cancel-sign-sub-inv_binary64`
196×	`associate-*l/_binary64`

Counts

467 → 436

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	381	21842
1	872	20630
2	2670	19112
3	3428	18539
4	4969	18539

prune221.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	434	2	436
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	436	8	444

Error

Counts

444 → 8

Alt Table

Status	Error	Program
	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 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	1.4b	(.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 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
✓	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))))))
	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 7079 to 2284 computations (67.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (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)))

rewrite200.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

84×	`sqrt-prod_binary64`
72×	`times-frac_binary64`
63×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
59×	`add-cube-cbrt_binary64`

Counts

4 → 158

Calls

4 calls:

21.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 4795 to 1205 computations (74.9% saved)

series249.0ms (2.4%)

Error

Counts

4 → 60

Calls

4 calls:

86.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
50.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
35.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
35.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 3534 to 2482 computations (29.8% saved)

simplify234.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

794×	`times-frac_binary64`
242×	`associate-l_binary64`
207×	`associate-r_binary64`
189×	`cancel-sign-sub-inv_binary64`
186×	`distribute-rgt-in_binary64`

Counts

218 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	278	5983
1	692	5674
2	2399	5578
3	4721	5578
4	4991	5578
5	4963	5578

prune115.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	157	8	165

Error

Counts

165 → 8

Alt Table

Status	Error	Program
	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 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	1.4b	(.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 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
✓	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))))))
▶	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 3310 to 1221 computations (63.1% saved)

localize12.0ms (0.1%)

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))))
0.2b	(/.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)))

rewrite398.0ms (3.9%)

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:

31.0ms	(.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))))
14.0ms	(/.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)))
10.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 7820 to 4642 computations (40.6% saved)

series287.0ms (2.8%)

Error

Counts

4 → 54

Calls

4 calls:

111.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
82.0ms	(.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))))
38.0ms	(/.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)))
31.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2315 to 1978 computations (14.6% saved)

simplify335.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

467×	`associate-/r/_binary64`
203×	`associate-l_binary64`
198×	`associate-r_binary64`
181×	`associate-/l/_binary64`
180×	`associate--l+_binary64`

Counts

279 → 268

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	311	9936
1	777	9305
2	2796	9209
3	4706	8623
4	4964	8623
5	4946	8623

prune224.0ms (2.2%)

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
	0.6b	(.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 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	0.4b	(/.f64 (.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))) (cbrt.f64 (sqrt.f64 2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (sqrt.f64 2)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
	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 5474 to 3087 computations (43.6% saved)

regimes2.4s (22.9%)

Accuracy

Total 0.3b remaining (83.8%)

Threshold costs 0.3b (83.8%)

Compiler

Compiled 41755 to 27680 computations (33.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	17	34
2	17	34

end8.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 75 to 39 computations (48% saved)

sample2.6s (25.6%)

Algorithm

1×

intervals

Results

571.0ms	1783×	body	1024	valid
486.0ms	1552×	body	1024	invalid
365.0ms	4878×	body	128	valid
210.0ms	872×	body	512	valid
177.0ms	785×	body	512	invalid
70.0ms	465×	body	256	valid
61.0ms	403×	body	256	invalid
55.0ms	649×	body	128	invalid
1.0ms	2×	body	2048	valid

Compiler

Compiled 228 to 147 computations (35.5% saved)

Details

analyze967.0ms (9.4%)

sample87.0ms (0.8%)

simplify10.0ms (0.1%)

prune5.0ms (0%)

localize9.0ms (0.1%)

rewrite138.0ms (1.3%)

series162.0ms (1.6%)

simplify122.0ms (1.2%)

prune102.0ms (1%)

localize13.0ms (0.1%)

rewrite653.0ms (6.3%)

series190.0ms (1.8%)

simplify533.0ms (5.2%)

prune221.0ms (2.1%)

localize14.0ms (0.1%)

rewrite200.0ms (1.9%)

series249.0ms (2.4%)

simplify234.0ms (2.3%)

prune115.0ms (1.1%)

localize12.0ms (0.1%)

rewrite398.0ms (3.9%)

series287.0ms (2.8%)

simplify335.0ms (3.3%)

prune224.0ms (2.2%)

regimes2.4s (22.9%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample2.6s (25.6%)

Profiling