Details

analyze1.2s (9.8%)

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)

sample4.6s (37%)

Symmetry

(sort a1 a2)

Results

1.3s	1795×	body	1024	valid
1.1s	1575×	body	1024	invalid
927.0ms	5114×	body	128	valid
442.0ms	934×	body	512	valid
374.0ms	800×	body	512	invalid
137.0ms	411×	body	256	valid
126.0ms	626×	body	128	invalid
120.0ms	360×	body	256	invalid
3.0ms	2×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify9.0ms (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

prune5.0ms (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

0.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.8b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.8b	(.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 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.8b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series133.0ms (1.1%)

Counts

4 → 88

Calls

4 calls:

71.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
27.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
26.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
8.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
55×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`

Counts

4 → 151

Calls

4 calls:

10.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
8.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
7.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify144.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
381×	`fma-neg_binary64`
215×	`associate-r_binary64`
196×	`*-commutative_binary64`
194×	`associate-/r/_binary64`

Counts

239 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	4527
1	704	4412
2	2293	4278
3	4840	4278
4	5019	4278

prune455.0ms (3.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	287	12	299
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	288	13	301

Error

Counts

301 → 13

Alt Table

Status	Error	Program
	15.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 a2 a2))))
	15.7b	(+.f64 (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	0.7b	(+.f64 (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.8b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	0.8b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	1.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))) (*.f64 a2 a2)))
	28.1b	(+.f64 (fma.f64 1/24 (.f64 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (.f64 a1 a1)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) (fma.f64 (.f64 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (.f64 a1 a1)) -1/720 (.f64 (.f64 (/.f64 (.f64 th th) (sqrt.f64 2)) (.f64 a1 a1)) -1/2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.9b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (.f64 a2 a2))))
	15.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 a2 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))
	0.7b	(/.f64 (.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2)))) 2)
▶	0.5b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	27.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (fma.f64 1/24 (.f64 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (.f64 a2 a2)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (fma.f64 (.f64 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (.f64 a2 a2)) -1/720 (.f64 (.f64 (/.f64 (.f64 th th) (sqrt.f64 2)) (.f64 a2 a2)) -1/2)))))

Compiler

Compiled 9272 to 5196 computations (44% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1)
	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.3b	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)
	0.8b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series50.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1)
21.0ms	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`associate-l_binary64`
20×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 67

Calls

2 calls:

6.0ms	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)
6.0ms	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1)

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
552×	`associate-/r*_binary64`
490×	`associate-*l/_binary64`
392×	`times-frac_binary64`
352×	`associate-*r/_binary64`

Counts

115 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1936
1	351	1751
2	1033	1743
3	2836	1737
4	4951	1737
5	5273	1737

prune370.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	303	11	314

Error

Counts

314 → 11

Alt Table

Status	Error	Program
▶	0.5b	(+.f64 (.f64 (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(+.f64 (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.8b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	1.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))) (*.f64 a2 a2)))
	15.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 a2 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))
	15.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 a2 a2))))
	0.7b	(/.f64 (.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2)))) 2)
✓	0.5b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	27.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (fma.f64 1/24 (.f64 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (.f64 a2 a2)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (fma.f64 (.f64 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (.f64 a2 a2)) -1/720 (.f64 (.f64 (/.f64 (.f64 th th) (sqrt.f64 2)) (.f64 a2 a2)) -1/2)))))
	0.9b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (.f64 a2 a2))))

Compiler

Compiled 8917 to 5241 computations (41.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) a1)
✓	0.6b	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
✓	0.7b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
	0.8b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series36.0ms (0.3%)

Counts

3 → 48

Calls

3 calls:

20.0ms

(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) a1)

9.0ms

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

7.0ms

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

rewrite238.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

1137×	`sqrt-prod_binary64`
1119×	`times-frac_binary64`
624×	`add-sqr-sqrt_binary64`
577×	`*-un-lft-identity_binary64`
577×	`add-cube-cbrt_binary64`

Counts

3 → 706

Calls

3 calls:

48.0ms

(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) a1)

14.0ms

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

5.0ms

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

simplify649.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
626×	`associate-*r/_binary64`
470×	`*-commutative_binary64`
387×	`associate-/l/_binary64`
380×	`fma-neg_binary64`

Counts

754 → 787

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	457	21445
1	1116	19716
2	2249	18856
3	3780	18654
4	4873	18645
5	4959	18645

prune1.3s (10.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	838	0	838
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	838	11	849

Error

Counts

849 → 11

Alt Table

Status	Error	Program
✓	0.5b	(+.f64 (.f64 (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(+.f64 (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.8b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	1.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))) (*.f64 a2 a2)))
	15.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 a2 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))
	15.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 a2 a2))))
▶	0.7b	(/.f64 (.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2)))) 2)
✓	0.5b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	27.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (fma.f64 1/24 (.f64 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (.f64 a2 a2)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (fma.f64 (.f64 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (.f64 a2 a2)) -1/720 (.f64 (.f64 (/.f64 (.f64 th th) (sqrt.f64 2)) (.f64 a2 a2)) -1/2)))))
	0.9b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (.f64 a2 a2))))

Compiler

Compiled 32334 to 21956 computations (32.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 th)
✓	0.2b	(/.f64 (.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2)))) 2)
✓	0.3b	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.4b	(.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))

series121.0ms (1%)

Counts

4 → 112

Calls

4 calls:

52.0ms	(/.f64 (.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2)))) 2)
40.0ms	(.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
27.0ms	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
2.0ms	(cos.f64 th)

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))
6.0ms	(/.f64 (.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2)))) 2)
3.0ms	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
1.0ms	(cos.f64 th)

simplify175.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

810×	`cancel-sign-sub-inv_binary64`
531×	`fma-neg_binary64`
314×	`associate-r_binary64`
237×	`associate-l_binary64`
222×	`fma-def_binary64`

Counts

195 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	4283
1	625	3788
2	2608	3691
3	4357	3689
4	4983	3689
5	4967	3689

prune187.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	170	6	176
Fresh	7	1	8
Picked	1	0	1
Done	1	1	2
Total	179	8	187

Error

Counts

187 → 8

Alt Table

Status	Error	Program
	0.7b	(/.f64 (.f64 (sqrt.f64 2) (.f64 (log1p.f64 (expm1.f64 (cos.f64 th))) (fma.f64 a1 a1 (*.f64 a2 a2)))) 2)
	0.7b	(/.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))))) 2)
	0.7b	(/.f64 (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
✓	0.5b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	15.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 a2 a2))))
	0.7b	(/.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))))) 2)
	0.8b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))))) 2)
	0.7b	(/.f64 (.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 2))) 2)

Compiler

Compiled 4212 to 2204 computations (47.7% saved)

regimes2.3s (18.3%)

Accuracy

Total 0.5b remaining (94.9%)

Threshold costs 0.5b (94.9%)

Counts

226 → 1

Compiler

Compiled 47817 to 33667 computations (29.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	18	30
2	18	30

end305.0ms (2.5%)

Compiler: Compiled 262 to 188 computations (28.2% saved)

Details

analyze1.2s (9.8%)

sample4.6s (37%)

simplify9.0ms (0.1%)

prune5.0ms (0%)

localize10.0ms (0.1%)

series133.0ms (1.1%)

rewrite38.0ms (0.3%)

simplify144.0ms (1.2%)

prune455.0ms (3.7%)

localize10.0ms (0.1%)

series50.0ms (0.4%)

rewrite20.0ms (0.2%)

simplify91.0ms (0.7%)

prune370.0ms (3%)

localize14.0ms (0.1%)

series36.0ms (0.3%)

rewrite238.0ms (1.9%)

simplify649.0ms (5.2%)

prune1.3s (10.1%)

localize9.0ms (0.1%)

series121.0ms (1%)

rewrite20.0ms (0.2%)

simplify175.0ms (1.4%)

prune187.0ms (1.5%)

regimes2.3s (18.3%)

simplify2.0ms (0%)

end305.0ms (2.5%)

Profiling