Details

analyze787.0ms

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

sample98.0ms

Algorithm

intervals

Results

22.0ms	51×	body	1280	valid
16.0ms	44×	body	640	valid
14.0ms	32×	body	1280	invalid
11.0ms	36×	body	640	invalid
10.0ms	140×	body	80	valid
4.0ms	19×	body	320	invalid
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	invalid
1.0ms	12×	body	80	invalid
1.0ms	6×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	105	13
1	105	13

prune11.0ms

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
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))

rewrite28.0ms

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

series64.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
42.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
13.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5138	1529

prune85.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	0	1	1
Picked	0	1	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 (+.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))
5.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite47.0ms

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:

22.0ms	(.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))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
15.0ms	(/.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)))

simplify53.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5059	2892

prune86.0ms

Filtered

104 candidates to 180 candidates (-73.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	180	7	187

Merged error: 0b

Counts

187 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.2b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite171.0ms

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))
73.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
10.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
21.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
41.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
17.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
21.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

simplify147.0ms

Algorithm

egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5377	16199

prune300.0ms

Filtered

249 candidates to 725 candidates (-191.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	725	0	725
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	725	7	732

Merged error: 0b

Counts

732 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th))
0.3b	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
5.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

62×	`times-frac_binary64`
61×	`associate-r_binary64`
55×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
47×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
45×	`add-exp-log_binary64`
36×	`cbrt-prod_binary64`
35×	`add-cbrt-cube_binary64`
20×	`cbrt-unprod_binary64` `prod-exp_binary64`
13×	`pow1_binary64`
11×	`associate-l_binary64`
10×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
3×	`unswap-sqr_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`associate-*r/_binary64` `frac-times_binary64`

Counts

4 → 150

Calls

4 calls:

14.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th))
29.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th))
30.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.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)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify86.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4989	3312
1	4989	3312

prune99.0ms

Filtered

99 candidates to 162 candidates (-63.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	162	7	169

Merged error: 0b

Counts

169 → 7

regimes324.0ms

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	16	23
1	16	23

end0.0ms

sample2.8s

Algorithm

intervals

Results

615.0ms	1366×	body	1280	valid
526.0ms	1197×	body	1280	invalid
369.0ms	1142×	body	640	valid
339.0ms	4600×	body	80	valid
309.0ms	976×	body	640	invalid
135.0ms	577×	body	320	valid
112.0ms	508×	body	320	invalid
48.0ms	315×	body	160	valid
43.0ms	521×	body	80	invalid
36.0ms	217×	body	160	invalid

Details

analyze787.0ms

sample98.0ms

simplify8.0ms

prune11.0ms

localize11.0ms

rewrite28.0ms

series64.0ms

simplify44.0ms

prune85.0ms

localize13.0ms

rewrite47.0ms

series42.0ms

simplify53.0ms

prune86.0ms

localize13.0ms

rewrite171.0ms

series85.0ms

simplify147.0ms

prune300.0ms

localize16.0ms

rewrite62.0ms

series98.0ms

simplify86.0ms

prune99.0ms

regimes324.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling