Details

analyze751.0ms

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

sample97.0ms

Algorithm

intervals

Results

22.0ms	52×	body	1280	valid
14.0ms	33×	body	1280	invalid
13.0ms	137×	body	80	valid
11.0ms	35×	body	640	valid
10.0ms	32×	body	640	invalid
5.0ms	22×	body	320	valid
4.0ms	20×	body	320	invalid
2.0ms	21×	body	80	invalid
1.0ms	10×	body	160	valid
1.0ms	4×	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

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: 0.6b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.3b	(.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:

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

series64.0ms

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)))
16.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5138	1529

prune128.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0.3b

Counts

105 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (/.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))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite43.0ms

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` `associate-*l/_binary64`
5×	`flip3-+_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`
1×	`associate-r/_binary64` `associate-l_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 157

Calls

4 calls:

19.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (/.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)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
16.0ms	(/.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)))

simplify55.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5429	2865

prune136.0ms

Filtered

99 candidates to 169 candidates (-70.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	169	8	177

Merged error: 0.3b

Counts

177 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

522×	`times-frac_binary64`
403×	`sqrt-prod_binary64`
312×	`add-sqr-sqrt_binary64`
270×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
257×	`associate-r_binary64`
18×	`sqrt-div_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
11×	`unswap-sqr_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`pow1_binary64` `div-inv_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 380

Calls

4 calls:

68.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
8.0ms	(/.f64 (sqrt.f64 2) (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)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
11.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
12.0ms	(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

392 → 392

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4978	7394
1	4978	7394

prune220.0ms

Filtered

170 candidates to 392 candidates (-130.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	391	1	392
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	393	7	400

Merged error: 0.3b

Counts

400 → 7

localize15.0ms

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 (/.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))))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac_binary64`
102×	`sqrt-prod_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
78×	`cbrt-prod_binary64`
58×	`associate-r_binary64`
38×	`add-exp-log_binary64`
29×	`add-cbrt-cube_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
9×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/l*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`associate-r/_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `-commutative_binary64`

Counts

4 → 201

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
28.0ms	(.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)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
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))))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify91.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4958	4503
1	4958	4503

prune194.0ms

Filtered

127 candidates to 213 candidates (-67.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	213	7	220

Merged error: 0.3b

Counts

220 → 7

regimes465.0ms

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	23
1	16	23

end0.0ms

sample2.8s

Algorithm

intervals

Results

626.0ms	1429×	body	1280	valid
511.0ms	1141×	body	1280	invalid
347.0ms	1132×	body	640	valid
331.0ms	4645×	body	80	valid
295.0ms	964×	body	640	invalid
124.0ms	516×	body	320	invalid
117.0ms	540×	body	320	valid
41.0ms	511×	body	80	invalid
38.0ms	242×	body	160	invalid
38.0ms	254×	body	160	valid

Details

analyze751.0ms

sample97.0ms

simplify7.0ms

prune10.0ms

localize10.0ms

rewrite28.0ms

series64.0ms

simplify41.0ms

prune128.0ms

localize13.0ms

rewrite43.0ms

series60.0ms

simplify55.0ms

prune136.0ms

localize13.0ms

rewrite114.0ms

series72.0ms

simplify80.0ms

prune220.0ms

localize15.0ms

rewrite59.0ms

series69.0ms

simplify91.0ms

prune194.0ms

regimes465.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling