Details

analyze765.0ms

Algorithm

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

sample95.0ms

Algorithm

intervals

Results

19.0ms	38×	body	1280	valid
17.0ms	40×	body	1280	invalid
11.0ms	154×	body	80	valid
11.0ms	36×	body	640	valid
10.0ms	33×	body	640	invalid
4.0ms	20×	body	320	valid
4.0ms	17×	body	320	invalid
1.0ms	17×	body	80	invalid
1.0ms	8×	body	160	invalid
1.0ms	8×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	105	13
1	105	13

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.4b

Counts

2 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2.0)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64` `sqrt-prod_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 94

Calls

3 calls:

4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2.0)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2.0))

series65.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
49.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2.0)))
11.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune120.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Merged error: 0b

Counts

105 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2.0) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
0.5b	(/.f64 (sqrt.f64 2.0) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
4.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

540×	`times-frac_binary64`
429×	`sqrt-prod_binary64`
297×	`add-sqr-sqrt_binary64`
295×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
48×	`associate-/r*_binary64`
22×	`sqrt-div_binary64`
17×	`associate-/r/_binary64`
12×	`associate-/l*_binary64`
11×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`sqrt-undiv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 411

Calls

4 calls:

20.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2.0) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
10.0ms	(/.f64 (sqrt.f64 2.0) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2.0) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
33.0ms	(/.f64 (sqrt.f64 2.0) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify125.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5081	11244

prune211.0ms

Filtered

163 candidates to 423 candidates (-159.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	423	7	430

Merged error: 0b

Counts

430 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (sqrt.f64 (sqrt.f64 2.0))))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0)))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (sqrt.f64 (sqrt.f64 2.0)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod_binary64`
1119×	`times-frac_binary64`
625×	`add-sqr-sqrt_binary64`
578×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
283×	`associate-r_binary64`
34×	`associate-/l*_binary64`
22×	`div-inv_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-/r*_binary64`
13×	`unswap-sqr_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 713

Calls

4 calls:

5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
71.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (sqrt.f64 (sqrt.f64 2.0))))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0)))
19.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (sqrt.f64 (sqrt.f64 2.0)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
45.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (sqrt.f64 (sqrt.f64 2.0))))
21.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0)))
19.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (sqrt.f64 (sqrt.f64 2.0)))

simplify143.0ms

Algorithm

egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5384	16199

prune428.0ms

Filtered

251 candidates to 725 candidates (-188.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	724	1	725
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	726	6	732

Merged error: 0b

Counts

732 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 th) (/.f64 (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (fabs.f64 (cbrt.f64 (sqrt.f64 2.0)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2.0)))))
0.2b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (fabs.f64 (cbrt.f64 (sqrt.f64 2.0))))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0)))
0.3b	(/.f64 (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (fabs.f64 (cbrt.f64 (sqrt.f64 2.0)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2.0))))

rewrite849.0ms

Algorithm

rewrite-expression-head

Rules

6954×	`times-frac_binary64`
4541×	`sqrt-prod_binary64`
3231×	`add-sqr-sqrt_binary64`
3141×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
1180×	`cbrt-prod_binary64`
1168×	`associate-r_binary64`
131×	`associate-/l*_binary64`
108×	`div-inv_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`associate-/r*_binary64`
21×	`unswap-sqr_binary64`
16×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`pow1_binary64`
4×	`associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 2695

Calls

4 calls:

255.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (fabs.f64 (cbrt.f64 (sqrt.f64 2.0)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2.0)))))
15.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (fabs.f64 (cbrt.f64 (sqrt.f64 2.0))))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0)))
49.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (fabs.f64 (cbrt.f64 (sqrt.f64 2.0)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2.0))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (fabs.f64 (cbrt.f64 (sqrt.f64 2.0)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2.0)))))
36.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (fabs.f64 (cbrt.f64 (sqrt.f64 2.0))))
21.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0)))
78.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2.0))) (fabs.f64 (cbrt.f64 (sqrt.f64 2.0)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2.0))))

simplify646.0ms

Algorithm

egg-herbie

Counts

2707 → 2707

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4988	95226
1	4988	95226

prune7.0s

Filtered

1154 candidates to 2707 candidates (-134.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	2707	0	2707
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	2707	6	2713

Merged error: 0b

Counts

2713 → 6

regimes415.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	24
1	19	24

end0.0ms

sample2.7s

Algorithm

intervals

Results

575.0ms	1314×	body	1280	valid
517.0ms	1144×	body	1280	invalid
348.0ms	1136×	body	640	valid
348.0ms	4722×	body	80	valid
296.0ms	989×	body	640	invalid
127.0ms	559×	body	320	valid
111.0ms	495×	body	320	invalid
45.0ms	527×	body	80	invalid
40.0ms	269×	body	160	valid
35.0ms	238×	body	160	invalid

Details

analyze765.0ms

sample95.0ms

simplify7.0ms

prune10.0ms

localize13.0ms

rewrite27.0ms

series65.0ms

simplify67.0ms

prune120.0ms

localize13.0ms

rewrite66.0ms

series59.0ms

simplify125.0ms

prune211.0ms

localize12.0ms

rewrite167.0ms

series91.0ms

simplify143.0ms

prune428.0ms

localize16.0ms

rewrite849.0ms

series271.0ms

simplify646.0ms

prune7.0s

regimes415.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling