Details

analyze733.0ms

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

sample80.0ms

Algorithm

intervals

Results

18.0ms	53×	body	1024	invalid
18.0ms	45×	body	1024	valid
11.0ms	156×	body	128	valid
9.0ms	40×	body	512	valid
5.0ms	20×	body	512	invalid
3.0ms	15×	body	256	valid
2.0ms	22×	body	128	invalid
1.0ms	8×	body	256	invalid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune5.0ms

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

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 83

Calls

2 calls:

13.0ms	(.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))

series436.0ms

Counts

2 → 6

Calls

2 calls:

328.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
108.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify69.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5014	2187

prune93.0ms

Filtered

59 candidates to 89 candidates (-50.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 0b

Counts

91 → 9

localize15.0ms

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))
6.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite62.0ms

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:

23.0ms	(.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)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
104.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
51.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
48.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify78.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5141	4549

prune128.0ms

Filtered

104 candidates to 180 candidates (-73.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	181	8	189

Merged error: 0b

Counts

189 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
0.3b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
6.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.0b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
39×	`sqrt-prod_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
21×	`times-frac_binary64`
17×	`associate-r_binary64` `sqrt-div_binary64`
15×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-l_binary64`
7×	`associate-*r/_binary64`
6×	`pow-prod-down_binary64` `unswap-sqr_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `prod-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`rem-sqrt-square_binary64`
2×	`div-inv_binary64` `*-commutative_binary64`
1×	`sqrt-unprod_binary64`

Counts

4 → 110

Calls

4 calls:

15.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
16.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

series480.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
87.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
47.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
76.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5270	3295

prune117.0ms

Filtered

96 candidates to 122 candidates (-27.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	122	8	130

Merged error: 0b

Counts

130 → 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 1/2)))
0.4b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
6.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 1/2)))
9.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 1/2)))
77.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
56.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
47.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify113.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4926	2023
1	4926	2023

prune80.0ms

Filtered

75 candidates to 106 candidates (-41.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	106	8	114

Merged error: 0b

Counts

114 → 8

regimes110.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

end0.0ms

sample2.5s

Algorithm

intervals

Results

642.0ms	1807×	body	1024	valid
540.0ms	1535×	body	1024	invalid
365.0ms	4823×	body	128	valid
212.0ms	888×	body	512	valid
189.0ms	810×	body	512	invalid
74.0ms	475×	body	256	valid
61.0ms	398×	body	256	invalid
49.0ms	608×	body	128	invalid
4.0ms	7×	body	2048	valid

Details

analyze733.0ms

sample80.0ms

simplify10.0ms

prune5.0ms

localize10.0ms

rewrite32.0ms

series436.0ms

simplify69.0ms

prune93.0ms

localize15.0ms

rewrite62.0ms

series312.0ms

simplify78.0ms

prune128.0ms

localize12.0ms

rewrite56.0ms

series480.0ms

simplify57.0ms

prune117.0ms

localize12.0ms

rewrite44.0ms

series255.0ms

simplify113.0ms

prune80.0ms

regimes110.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling