Details

analyze1.1s (11.3%)

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)

sample4.3s (44.4%)

Symmetry

(sort a1 a2)

Results

1.3s	1888×	body	1024	valid
966.0ms	1508×	body	1024	invalid
812.0ms	4963×	body	128	valid
407.0ms	964×	body	512	valid
384.0ms	842×	body	512	invalid
147.0ms	436×	body	256	valid
117.0ms	655×	body	128	invalid
113.0ms	369×	body	256	invalid
5.0ms	5×	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

prune4.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	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)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series77.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

56.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
20.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 85

Calls

2 calls:

8.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
3.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-l_binary64`
410×	`associate-r_binary64`
396×	`fma-neg_binary64`
332×	`associate-/l*_binary64`
299×	`sub-neg_binary64`

Counts

145 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3315
1	365	3012
2	1289	2968
3	4359	2968
4	5076	2968

prune155.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	146	7	153

Error

Counts

153 → 7

Alt Table

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

Compiler

Compiled 3761 to 1776 computations (52.8% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

series82.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

54.0ms	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
28.0ms	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

4.0ms	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
3.0ms	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))

simplify90.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

640×	`associate-/l*_binary64`
436×	`fma-def_binary64`
359×	`times-frac_binary64`
315×	`cancel-sign-sub-inv_binary64`
247×	`distribute-rgt-in_binary64`

Counts

123 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	2546
1	386	2329
2	1540	2260
3	4953	2258
4	5065	2258

prune89.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	106	6	112

Error

Counts

112 → 6

Alt Table

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

Compiler

Compiled 2470 to 1220 computations (50.6% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.3b	(/.f64 (/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
✓	0.3b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

series747.0ms (7.7%)

Counts

2 → 72

Calls

2 calls:

689.0ms

(/.f64 (*.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

58.0ms

(/.f64 (/.f64 (*.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`times-frac_binary64`
36×	`cbrt-prod_binary64`
32×	`add-exp-log_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

2 → 105

Calls

2 calls:

9.0ms

(/.f64 (/.f64 (*.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

8.0ms

(/.f64 (*.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

simplify167.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
405×	`cancel-sign-sub-inv_binary64`
293×	`fma-neg_binary64`
212×	`unswap-sqr_binary64`
186×	`times-frac_binary64`

Counts

177 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	6668
1	630	6058
2	2605	5972
3	4521	5608
4	4980	5608

prune228.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	236	6	242

Error

Counts

242 → 6

Alt Table

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

Compiler

Compiled 8013 to 4920 computations (38.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cos.f64 th))
✓	0.3b	(/.f64 (.f64 (cbrt.f64 1/2) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (cbrt.f64 (sqrt.f64 2)))
✓	0.4b	(.f64 (cbrt.f64 1/2) (.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))

series501.0ms (5.2%)

Counts

3 → 108

Calls

3 calls:

426.0ms

(/.f64 (*.f64 (cbrt.f64 1/2) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (cbrt.f64 (sqrt.f64 2)))

47.0ms

(*.f64 (cbrt.f64 1/2) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))

27.0ms

(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64`
15×	`cbrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 80

Calls

3 calls:

6.0ms

(/.f64 (*.f64 (cbrt.f64 1/2) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))) (cbrt.f64 (sqrt.f64 2)))

4.0ms

(*.f64 (cbrt.f64 1/2) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))

3.0ms

(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))

simplify159.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

922×	`fma-neg_binary64`
798×	`cancel-sign-sub-inv_binary64`
281×	`associate-r_binary64`
257×	`associate-l_binary64`
211×	`distribute-rgt-neg-in_binary64`

Counts

188 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	5213
1	595	4253
2	2559	4247
3	4181	4221
4	4989	4221
5	5364	4221

prune160.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	171	6	177

Error

Counts

177 → 6

Alt Table

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

Compiler

Compiled 4622 to 2670 computations (42.2% saved)

regimes1.3s (13.6%)

Accuracy

Total 0.4b remaining (85.6%)

Threshold costs 0.4b (85.6%)

Counts

154 → 1

Compiler

Compiled 27026 to 19107 computations (29.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	15	30
2	15	30

end271.0ms (2.8%)

Compiler: Compiled 215 to 163 computations (24.2% saved)

Details

analyze1.1s (11.3%)

sample4.3s (44.4%)

simplify9.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series77.0ms (0.8%)

rewrite17.0ms (0.2%)

simplify104.0ms (1.1%)

prune155.0ms (1.6%)

localize8.0ms (0.1%)

series82.0ms (0.9%)

rewrite10.0ms (0.1%)

simplify90.0ms (0.9%)

prune89.0ms (0.9%)

localize13.0ms (0.1%)

series747.0ms (7.7%)

rewrite31.0ms (0.3%)

simplify167.0ms (1.7%)

prune228.0ms (2.4%)

localize11.0ms (0.1%)

series501.0ms (5.2%)

rewrite18.0ms (0.2%)

simplify159.0ms (1.7%)

prune160.0ms (1.7%)

regimes1.3s (13.6%)

simplify2.0ms (0%)

end271.0ms (2.8%)

Profiling