Details

analyze749.0ms

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

sample90.0ms

Algorithm

intervals

Results

17.0ms	39×	body	1280	invalid
14.0ms	36×	body	640	invalid
12.0ms	29×	body	1280	valid
12.0ms	168×	body	80	valid
10.0ms	33×	body	640	valid
4.0ms	19×	body	320	invalid
4.0ms	17×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	12×	body	80	invalid
1.0ms	6×	body	160	invalid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	105	13
1	105	13

prune9.0ms

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

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

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))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2.0))
11.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2.0)))

series65.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
13.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2.0))
45.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune119.0ms

Filtered

67 candidates to 103 candidates (-53.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Merged error: 0.3b

Counts

105 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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-*r/_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` `distribute-lft-in_binary64` `distribute-rgt-in_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 → 62

Calls

3 calls:

4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
9.0ms	(/.f64 (.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2.0))
7.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

series78.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
45.0ms	(/.f64 (.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2.0))
27.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

simplify54.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4979	870
1	4979	870

prune70.0ms

Filtered

47 candidates to 71 candidates (-51.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	71	7	78

Merged error: 0.3b

Counts

78 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2.0)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2.0))
7.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 157

Calls

4 calls:

18.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2.0)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2.0))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2.0)))
13.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2.0))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify80.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4972	2849
1	4972	2849

prune127.0ms

Filtered

100 candidates to 169 candidates (-69.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	169	7	176

Merged error: 0.3b

Counts

176 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
0.2b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2.0)))
7.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.4b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

33×	`sqrt-prod_binary64`
31×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64`
19×	`times-frac_binary64`
13×	`pow1_binary64`
12×	`sqrt-div_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-*r/_binary64`
4×	`pow-prod-down_binary64` `flip3-+_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `flip-+_binary64`
3×	`rem-sqrt-square_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `div-inv_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

8.0ms	(.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
15.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2.0)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2.0))

series84.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
39.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2.0)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
11.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5399	1691

prune101.0ms

Filtered

87 candidates to 112 candidates (-28.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	3	1	4
Picked	0	1	1
Done	0	2	2
Total	113	6	119

Merged error: 0.3b

Counts

119 → 6

regimes304.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

end0.0ms

sample2.8s

Algorithm

intervals

Results

591.0ms	1333×	body	1280	valid
542.0ms	1236×	body	1280	invalid
352.0ms	4721×	body	80	valid
338.0ms	1115×	body	640	valid
309.0ms	1009×	body	640	invalid
132.0ms	558×	body	320	valid
100.0ms	463×	body	320	invalid
41.0ms	273×	body	160	valid
41.0ms	527×	body	80	invalid
36.0ms	229×	body	160	invalid

Details

analyze749.0ms

sample90.0ms

simplify7.0ms

prune9.0ms

localize10.0ms

rewrite26.0ms

series65.0ms

simplify68.0ms

prune119.0ms

localize10.0ms

rewrite22.0ms

series78.0ms

simplify54.0ms

prune70.0ms

localize15.0ms

rewrite41.0ms

series74.0ms

simplify80.0ms

prune127.0ms

localize15.0ms

rewrite36.0ms

series84.0ms

simplify37.0ms

prune101.0ms

regimes304.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling