Details

analyze4.0ms (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)

sample4.1s (35.5%)

Symmetry

(sort a1 a2)

Results

2.0s	1951×	body	1024	valid
1.2s	4878×	body	128	valid
679.0ms	948×	body	512	valid
201.0ms	477×	body	256	valid
4.0ms	2×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify15.0ms (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

prune7.0ms (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)))
	0.3b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize28.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series89.0ms (0.8%)

Counts

3 → 52

Calls

3 calls:

41.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
33.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
15.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 135

Calls

3 calls:

8.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
8.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
4.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify188.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-*l/_binary64`
511×	`associate-/l*_binary64`
431×	`fma-def_binary64`
425×	`associate-*r/_binary64`
240×	`fma-neg_binary64`

Counts

187 → 212

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	3496
1	559	3164
2	1620	3148
3	4427	3146
4	4999	3146
5	4986	3146

prune564.0ms (4.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	258	5	263
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	259	6	265

Error

Counts

265 → 6

Alt Table

Status	Error	Program
	0.4b	(+.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)))
▶	0.2b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
	0.2b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
	0.3b	(+.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)))
	0.3b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.3b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 7624 to 4205 computations (44.8% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 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)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series28.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
13.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite87.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

594×	`sqrt-prod_binary64`
576×	`times-frac_binary64`
310×	`*-un-lft-identity_binary64`
310×	`add-sqr-sqrt_binary64`
310×	`add-cube-cbrt_binary64`

Counts

2 → 389

Calls

2 calls:

16.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
12.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

simplify778.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
502×	`times-frac_binary64`
463×	`cancel-sign-sub-inv_binary64`
440×	`associate-/r*_binary64`
426×	`fma-neg_binary64`

Counts

413 → 385

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	318	13544
1	692	12676
2	1320	12060
3	3059	11869
4	4523	11860
5	4996	11860
6	4966	11860

prune963.0ms (8.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	517	0	517
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	517	6	523

Error

Counts

523 → 6

Alt Table

Status	Error	Program
	0.4b	(+.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)))
✓	0.2b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
▶	0.2b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
	0.3b	(+.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)))
	0.3b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.3b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 18849 to 12082 computations (35.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 th) (pow.f64 a2 2))
✓	0.2b	(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
	0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

series46.0ms (0.4%)

Counts

2 → 8

Calls

2 calls:

32.0ms	(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
14.0ms	(*.f64 (cos.f64 th) (pow.f64 a2 2))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 60

Calls

2 calls:

7.0ms	(*.f64 (cos.f64 th) (pow.f64 a2 2))
5.0ms	(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

628×	`associate-/l*_binary64`
497×	`fma-def_binary64`
468×	`associate-l_binary64`
462×	`associate-r_binary64`
460×	`times-frac_binary64`

Counts

68 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	1255
1	290	1069
2	996	1045
3	4623	1039
4	5234	1039

prune518.0ms (4.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	239	6	245

Error

Counts

245 → 6

Alt Table

Status	Error	Program
	0.4b	(+.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)))
✓	0.2b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
✓	0.2b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
	0.3b	(+.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)))
▶	0.3b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.3b	(+.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 6678 to 4058 computations (39.2% saved)

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	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))

series163.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

111.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
37.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
14.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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 → 95

Calls

3 calls:

15.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
6.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
0.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

simplify193.0ms (1.6%)

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

179 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3607
1	368	3275
2	1296	3231
3	4370	3231
4	5109	3231

prune348.0ms (3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	174	6	180

Error

Counts

180 → 6

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
	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 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
	0.3b	(+.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)))
	0.2b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) 1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2)))
✓	0.3b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 3902 to 1766 computations (54.7% saved)

regimes2.9s (24.7%)

Accuracy

Total 0.2b remaining (88.7%)

Threshold costs 0.2b (88.7%)

Counts

181 → 1

Compiler

Compiled 37638 to 26777 computations (28.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	19	32
2	18	32

end391.0ms (3.3%)

Compiler: Compiled 233 to 143 computations (38.6% saved)

Details

analyze4.0ms (0%)

sample4.1s (35.5%)

simplify15.0ms (0.1%)

prune7.0ms (0.1%)

localize28.0ms (0.2%)

series89.0ms (0.8%)

rewrite34.0ms (0.3%)

simplify188.0ms (1.6%)

prune564.0ms (4.8%)

localize27.0ms (0.2%)

series28.0ms (0.2%)

rewrite87.0ms (0.7%)

simplify778.0ms (6.7%)

prune963.0ms (8.2%)

localize13.0ms (0.1%)

series46.0ms (0.4%)

rewrite18.0ms (0.2%)

simplify97.0ms (0.8%)

prune518.0ms (4.4%)

localize19.0ms (0.2%)

series163.0ms (1.4%)

rewrite31.0ms (0.3%)

simplify193.0ms (1.6%)

prune348.0ms (3%)

regimes2.9s (24.7%)

simplify4.0ms (0%)

end391.0ms (3.3%)

Profiling