Details

analyze1.3s (13.1%)

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)

sample117.0ms (1.2%)

Algorithm

1×

intervals

Results

31.0ms	59×	body	1024	valid
19.0ms	36×	body	1024	invalid
18.0ms	160×	body	128	valid
8.0ms	26×	body	512	valid
7.0ms	19×	body	512	invalid
3.0ms	14×	body	256	invalid
3.0ms	23×	body	128	invalid
2.0ms	11×	body	256	valid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify14.0ms (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

prune4.0ms (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

0.3b

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)

localize11.0ms (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))

rewrite132.0ms (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)))
6.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
3.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2099 to 762 computations (63.7% saved)

series151.0ms (1.5%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

77.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
35.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
23.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1499 to 1222 computations (18.5% saved)

simplify174.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

383×	`sub-neg_binary64`
345×	`associate-/l*_binary64`
289×	`associate-*l/_binary64`
287×	`associate-*r/_binary64`
156×	`distribute-rgt-in_binary64`

Counts

136 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	3277
1	448	3029
2	1516	2993
3	4384	2993
4	4766	2993
5	4948	2993
6	4952	2993

prune81.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	121	7	128

Error

0.0b

Counts

128 → 7

Alt Table

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

Compiler

Compiled 2044 to 911 computations (55.4% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.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 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
7.4b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
7.4b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite272.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

149×	`add-sqr-sqrt_binary64`
146×	`times-frac_binary64`
127×	`sqrt-prod_binary64`
90×	`cbrt-prod_binary64`
87×	`*-un-lft-identity_binary64`

Counts

4 → 226

Calls

4 calls:

35.0ms	(.f64 (/.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 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
3.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 8394 to 3621 computations (56.9% saved)

series178.0ms (1.8%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

58.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
37.0ms	(.f64 (/.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 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
28.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
27.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3463 to 2660 computations (23.2% saved)

simplify289.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

749×	`times-frac_binary64`
379×	`associate-/r*_binary64`
201×	`associate-*r/_binary64`
199×	`associate-*l/_binary64`
179×	`associate-/r/_binary64`

Counts

274 → 252

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	10532
1	633	9576
2	2249	9112
3	4650	8892
4	5026	8892

prune153.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	252	7	259

Error

0.0b

Counts

259 → 7

Alt Table

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

Compiler

Compiled 5964 to 2856 computations (52.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
0.2b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))

rewrite274.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

177×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
85×	`add-cube-cbrt_binary64`
80×	`cbrt-prod_binary64`

Counts

4 → 209

Calls

4 calls:

21.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
14.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
3.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 7016 to 3864 computations (44.9% saved)

series239.0ms (2.4%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

84.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
73.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
35.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
27.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2344 to 2003 computations (14.5% saved)

simplify230.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-/r/_binary64`
507×	`associate-/l/_binary64`
194×	`associate-l_binary64`
157×	`cancel-sign-sub-inv_binary64`
151×	`associate-*r/_binary64`

Counts

263 → 250

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	8317
1	733	7529
2	2552	7489
3	4673	7489
4	4958	7489

prune153.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	249	1	250
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	249	8	257

Error

Counts

257 → 8

Alt Table

Status	Error	Program
	17.9b	(.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))) (.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))))
	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 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.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))))
	0.6b	(.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 (cos.f64 th) (.f64 (/.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 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))))

Compiler

Compiled 5351 to 2915 computations (45.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))))
0.2b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))

rewrite228.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

101×	`add-exp-log_binary64`
62×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
46×	`prod-exp_binary64`
43×	`add-cbrt-cube_binary64`

Counts

4 → 153

Calls

4 calls:

21.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))))
18.0ms	(.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
3.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 5184 to 3228 computations (37.7% saved)

series249.0ms (2.5%)

Error

Counts

4 → 54

Calls

4 calls:

101.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
72.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))))
36.0ms	(.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
23.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2412 to 2071 computations (14.1% saved)

simplify142.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

492×	`associate-/r*_binary64`
288×	`distribute-rgt-in_binary64`
265×	`distribute-lft-in_binary64`
239×	`associate-/l/_binary64`
233×	`associate-r_binary64`

Counts

207 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	7249
1	607	4968
2	2220	4932
3	5101	4932

prune107.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	192	2	194
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	195	7	202

Error

Counts

202 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (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))))
	17.9b	(.f64 (.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))) (.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))))
	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 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
	0.3b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	0.4b	(.f64 (cos.f64 th) (.f64 (/.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 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))

Compiler

Compiled 2986 to 1775 computations (40.6% saved)

regimes1.7s (17%)

Accuracy

Total 0.4b remaining (86.8%)

Threshold costs 0.4b (86.8%)

Compiler

Compiled 34806 to 24487 computations (29.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	30
1	24	30
2	23	30

end10.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 66 to 51 computations (22.7% saved)

sample3.6s (36.6%)

Algorithm

1×

intervals

Results

894.0ms	1813×	body	1024	valid
823.0ms	1482×	body	1024	invalid
511.0ms	4852×	body	128	valid
297.0ms	917×	body	512	valid
229.0ms	739×	body	512	invalid
87.0ms	413×	body	256	valid
86.0ms	403×	body	256	invalid
65.0ms	634×	body	128	invalid
4.0ms	5×	body	2048	valid

Compiler

Compiled 248 to 176 computations (29% saved)

Details

analyze1.3s (13.1%)

sample117.0ms (1.2%)

simplify14.0ms (0.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite132.0ms (1.3%)

series151.0ms (1.5%)

simplify174.0ms (1.8%)

prune81.0ms (0.8%)

localize27.0ms (0.3%)

rewrite272.0ms (2.8%)

series178.0ms (1.8%)

simplify289.0ms (2.9%)

prune153.0ms (1.6%)

localize14.0ms (0.1%)

rewrite274.0ms (2.8%)

series239.0ms (2.4%)

simplify230.0ms (2.3%)

prune153.0ms (1.6%)

localize15.0ms (0.1%)

rewrite228.0ms (2.3%)

series249.0ms (2.5%)

simplify142.0ms (1.5%)

prune107.0ms (1.1%)

regimes1.7s (17%)

simplify3.0ms (0%)

end10.0ms (0.1%)

sample3.6s (36.6%)

Profiling