Details

analyze770.0ms

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

sample103.0ms

Algorithm

intervals

Results

22.0ms	44×	body	1280	valid
19.0ms	44×	body	1280	invalid
15.0ms	48×	body	640	valid
10.0ms	143×	body	80	valid
10.0ms	34×	body	640	invalid
6.0ms	26×	body	320	invalid
3.0ms	16×	body	320	valid
1.0ms	17×	body	80	invalid
1.0ms	7×	body	160	invalid
1.0ms	5×	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

prune8.0ms

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: 0.6b

Counts

2 → 2

localize11.0ms

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)))
0.6b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

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:

5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series61.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
42.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
12.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify39.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5138	1529

prune87.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 0.3b

Counts

105 → 9

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.6b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
9.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

series54.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
17.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
31.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4986	841
1	4986	841

prune51.0ms

Filtered

47 candidates to 69 candidates (-46.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	70	8	78

Merged error: 0.3b

Counts

78 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
8.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
8.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64`
146×	`times-frac_binary64`
127×	`sqrt-prod_binary64`
90×	`cbrt-prod_binary64`
87×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
58×	`associate-r_binary64`
27×	`add-exp-log_binary64`
21×	`unswap-sqr_binary64`
19×	`add-cbrt-cube_binary64`
10×	`associate-l_binary64`
9×	`associate-/r*_binary64`
8×	`pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
6×	`associate-/l*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 226

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
37.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
13.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
6.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify104.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4903	5008
1	4903	5008

prune162.0ms

Filtered

140 candidates to 238 candidates (-70.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	238	8	246

Merged error: 0.3b

Counts

246 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
8.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
8.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

100×	`sqrt-prod_binary64`
91×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
61×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
40×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`unswap-sqr_binary64` `sqrt-div_binary64`
8×	`pow1_binary64`
6×	`associate-/r_binary64` `associate-l_binary64` `associate-/l_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 168

Calls

4 calls:

24.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
12.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify52.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5059	2892

prune70.0ms

Filtered

104 candidates to 180 candidates (-73.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	180	8	188

Merged error: 0.0b

Counts

188 → 8

regimes429.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	16
1	16	16

end0.0ms

sample2.8s

Algorithm

intervals

Results

620.0ms	1396×	body	1280	valid
523.0ms	1184×	body	1280	invalid
353.0ms	1127×	body	640	valid
348.0ms	4677×	body	80	valid
309.0ms	1011×	body	640	invalid
126.0ms	542×	body	320	valid
109.0ms	496×	body	320	invalid
41.0ms	533×	body	80	invalid
39.0ms	258×	body	160	valid
35.0ms	230×	body	160	invalid

Details

analyze770.0ms

sample103.0ms

simplify7.0ms

prune8.0ms

localize11.0ms

rewrite27.0ms

series61.0ms

simplify39.0ms

prune87.0ms

localize10.0ms

rewrite23.0ms

series54.0ms

simplify52.0ms

prune51.0ms

localize16.0ms

rewrite67.0ms

series50.0ms

simplify104.0ms

prune162.0ms

localize12.0ms

rewrite48.0ms

series38.0ms

simplify52.0ms

prune70.0ms

regimes429.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling