Details

analyze282.0ms

Algorithm

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample40.0ms

Algorithm

intervals

Results

16.0ms	141×	body	160	valid
8.0ms	282×	pre	80	true
6.0ms	115×	body	80	valid
1.0ms	26×	body	80	nan

simplify233.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (230.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 28.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
28.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

series73.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
31.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
17.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

simplify66.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4900	1294
1	4900	1294

prune69.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.4b

Counts

83 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

series147.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
52.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
69.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4949	2008
1	4949	2008

prune118.0ms

Filtered

75 candidates to 110 candidates (-46.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	12	110
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 0.0b

Counts

115 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
0.3b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.3b	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

242×	`times-frac_binary64`
114×	`*-un-lft-identity_binary64`
106×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
61×	`add-exp-log_binary64`
47×	`add-cbrt-cube_binary64`
37×	`div-exp_binary64`
26×	`div-inv_binary64`
25×	`cbrt-undiv_binary64`
19×	`associate-/l*_binary64`
18×	`associate-/r/_binary64`
15×	`associate-*r/_binary64`
13×	`associate-/r*_binary64`
8×	`prod-exp_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64`
4×	`pow1_binary64` `distribute-lft-out_binary64` `1-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 225

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
20.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
12.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
51.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
56.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
56.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))

simplify95.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4893	5612
1	4893	5612

prune170.0ms

Filtered

138 candidates to 237 candidates (-71.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	239	10	249

Merged error: 0b

Counts

249 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.3b	(.f64 (/.f64 (.f64 -2 c) a) (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64` `times-frac_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
23×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
8×	`add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
10.0ms	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
16.0ms	(.f64 (/.f64 (.f64 -2 c) a) (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
55.0ms	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
59.0ms	(.f64 (/.f64 (.f64 -2 c) a) (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4949	2081
1	4949	2081

prune76.0ms

Filtered

86 candidates to 119 candidates (-38.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	119	10	129

Merged error: 0b

Counts

129 → 10

regimes158.0ms

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	62	20
1	62	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

456.0ms	4455×	body	160	valid
249.0ms	8839×	pre	80	true
190.0ms	3545×	body	80	valid
46.0ms	839×	body	80	nan

Details

analyze282.0ms

sample40.0ms

simplify233.0ms

prune6.0ms

localize11.0ms

rewrite32.0ms

series73.0ms

simplify66.0ms

prune69.0ms

localize14.0ms

rewrite41.0ms

series147.0ms

simplify53.0ms

prune118.0ms

localize14.0ms

rewrite56.0ms

series174.0ms

simplify95.0ms

prune170.0ms

localize13.0ms

rewrite41.0ms

series140.0ms

simplify63.0ms

prune76.0ms

regimes158.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling