Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample2.6s (38.6%)

Symmetry

(sort a1 a2)

Results

1.2s	1884×	body	1024	valid
766.0ms	4840×	body	128	valid
394.0ms	1041×	body	512	valid
181.0ms	489×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify10.0ms (0.2%)

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 (0.1%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.2b	(.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 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)))
✓	0.2b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series85.0ms (1.3%)

Counts

2 → 60

Calls

2 calls:

62.0ms	(.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))

rewrite20.0ms (0.3%)

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:

7.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
4.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify105.0ms (1.5%)

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

prune191.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	146	7	153

Error

Counts

153 → 7

Alt Table

Status	Error	Program
	0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
▶	0.2b	(.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))))
	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.2b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.2b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.3b	(+.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 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 3709 to 1752 computations (52.8% saved)

localize15.0ms (0.2%)

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))))
✓	0.1b	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
✓	0.1b	(/.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)))

series452.0ms (6.6%)

Counts

3 → 84

Calls

3 calls:

365.0ms

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

63.0ms

(*.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))))

23.0ms

(/.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)))

rewrite68.0ms (1%)

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:

21.0ms

(*.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))))

8.0ms

(/.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)))

6.0ms

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

simplify240.0ms (3.5%)

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

prune445.0ms (6.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	366	6	372

Error

Counts

372 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.2b	(.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 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.2b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.3b	(+.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 12706 to 8027 computations (36.8% saved)

localize9.0ms (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)))
✓	0.2b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

series93.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

62.0ms	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
31.0ms	(.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2)))

rewrite10.0ms (0.2%)

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)))

simplify91.0ms (1.3%)

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

prune105.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	105	6	111

Error

Counts

111 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.2b	(.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 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
▶	0.2b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.3b	(+.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 2441 to 1188 computations (51.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.1b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
✓	0.4b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
✓	28.4b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series337.0ms (5%)

Counts

4 → 120

Calls

4 calls:

212.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
88.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
23.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
14.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`sqrt-prod_binary64`
72×	`times-frac_binary64`
65×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64`

Counts

4 → 162

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
4.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
3.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify222.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-def_binary64`
376×	`cancel-sign-sub-inv_binary64`
345×	`associate-l_binary64`
317×	`sub-neg_binary64`
308×	`fma-neg_binary64`

Counts

282 → 332

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	347	7564
1	936	6108
2	3364	6008
3	4799	6003
4	4932	6003
5	5038	6003

prune325.0ms (4.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	331	1	332
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	332	6	338

Error

Counts

338 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.2b	(.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 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
✓	0.2b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
✓	0.2b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 9184 to 3854 computations (58% saved)

regimes1.2s (17.3%)

Accuracy

Total 0.2b remaining (85.9%)

Threshold costs 0.2b (85.9%)

Counts

140 → 1

Compiler

Compiled 24853 to 16418 computations (33.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	15	24
2	15	24

end111.0ms (1.6%)

Remove: (sort a1 a2)
Compiler: Compiled 194 to 130 computations (33% saved)

Details

analyze2.0ms (0%)

sample2.6s (38.6%)

simplify10.0ms (0.2%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series85.0ms (1.3%)

rewrite20.0ms (0.3%)

simplify105.0ms (1.5%)

prune191.0ms (2.8%)

localize15.0ms (0.2%)

series452.0ms (6.6%)

rewrite68.0ms (1%)

simplify240.0ms (3.5%)

prune445.0ms (6.5%)

localize9.0ms (0.1%)

series93.0ms (1.4%)

rewrite10.0ms (0.2%)

simplify91.0ms (1.3%)

prune105.0ms (1.6%)

localize14.0ms (0.2%)

series337.0ms (5%)

rewrite35.0ms (0.5%)

simplify222.0ms (3.3%)

prune325.0ms (4.8%)

regimes1.2s (17.3%)

simplify2.0ms (0%)

end111.0ms (1.6%)

Profiling