Details

analyze1.2s (11.1%)

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)

sample4.4s (42.4%)

Symmetry

(sort a1 a2)

Results

1.2s	1844×	body	1024	valid
1.0s	1555×	body	1024	invalid
855.0ms	4955×	body	128	valid
439.0ms	945×	body	512	valid
368.0ms	817×	body	512	invalid
151.0ms	416×	body	256	invalid
151.0ms	508×	body	256	valid
102.0ms	610×	body	128	invalid
4.0ms	4×	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)

localize10.0ms (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))

series82.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

58.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
23.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite18.0ms (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:

9.0ms	(.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))

simplify109.0ms (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

prune212.0ms (2%)

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

0.0b

Counts

153 → 7

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))))
	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (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 (/.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 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (.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)))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))

Compiler

Compiled 3751 to 1778 computations (52.6% saved)

localize12.0ms (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))

series89.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

61.0ms	(/.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)))

rewrite12.0ms (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:

6.0ms	(/.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)))

simplify115.0ms (1.1%)

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

prune103.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	104	8	112

Error

Counts

112 → 8

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))))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (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 (/.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 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (.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)))))
	0.6b	(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2)))
	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)))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))

Compiler

Compiled 2555 to 1280 computations (49.9% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
✓	0.2b	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
✓	0.2b	(/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

series402.0ms (3.9%)

Counts

3 → 84

Calls

3 calls:

324.0ms

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

55.0ms

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

22.0ms

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

rewrite79.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
110×	`add-sqr-sqrt_binary64`
94×	`cbrt-prod_binary64`
90×	`*-un-lft-identity_binary64`
90×	`add-cube-cbrt_binary64`

Counts

3 → 218

Calls

3 calls:

33.0ms

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

10.0ms

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

5.0ms

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

simplify238.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
500×	`associate-/r/_binary64`
260×	`fma-def_binary64`
191×	`associate-/l*_binary64`
181×	`associate-/l/_binary64`

Counts

302 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	9806
1	697	8974
2	2581	8924
3	4583	8924
4	5353	8924

prune419.0ms (4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	365	8	373

Error

Counts

373 → 8

Alt Table

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

Compiler

Compiled 12775 to 8084 computations (36.7% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
✓	0.2b	(/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
✓	0.4b	(.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))

series654.0ms (6.3%)

Counts

3 → 84

Calls

3 calls:

420.0ms

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

215.0ms

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

18.0ms

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

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
19×	`add-exp-log_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`

Counts

3 → 96

Calls

3 calls:

11.0ms

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

5.0ms

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

4.0ms

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

simplify137.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-def_binary64`
452×	`fma-neg_binary64`
290×	`cancel-sign-sub-inv_binary64`
284×	`associate-l_binary64`
258×	`distribute-rgt-in_binary64`

Counts

180 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	4730
1	469	4129
2	1978	4012
3	4657	4010
4	4977	4010

prune206.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	183	6	189

Error

Counts

189 → 6

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))))
✓	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (.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)))))
	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)))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (.f64 (cbrt.f64 1/2) (cos.f64 th)) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 4616 to 2769 computations (40% saved)

regimes1.7s (16.7%)

Accuracy

Total 0.4b remaining (88%)

Threshold costs 0.4b (88%)

Counts

178 → 1

Compiler

Compiled 33434 to 23192 computations (30.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	17	25
2	17	25

end131.0ms (1.3%)

Remove: (sort a1 a2)
Compiler: Compiled 206 to 149 computations (27.7% saved)

Details

analyze1.2s (11.1%)

sample4.4s (42.4%)

simplify9.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series82.0ms (0.8%)

rewrite18.0ms (0.2%)

simplify109.0ms (1%)

prune212.0ms (2%)

localize12.0ms (0.1%)

series89.0ms (0.9%)

rewrite12.0ms (0.1%)

simplify115.0ms (1.1%)

prune103.0ms (1%)

localize12.0ms (0.1%)

series402.0ms (3.9%)

rewrite79.0ms (0.8%)

simplify238.0ms (2.3%)

prune419.0ms (4%)

localize12.0ms (0.1%)

series654.0ms (6.3%)

rewrite25.0ms (0.2%)

simplify137.0ms (1.3%)

prune206.0ms (2%)

regimes1.7s (16.7%)

simplify2.0ms (0%)

end131.0ms (1.3%)

Profiling