Details

analyze265.0ms

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

sample38.0ms

Algorithm

intervals

Results

14.0ms	154×	body	160	valid
8.0ms	281×	pre	80	true
5.0ms	102×	body	80	valid
1.0ms	25×	body	80	nan

simplify225.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (222.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

prune9.0ms

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: 29.8b

Counts

2 → 1

localize10.0ms

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 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
29.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite31.0ms

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

series72.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt.f64 (-.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))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

simplify62.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4900	1294
1	4900	1294

prune101.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Merged error: 0.3b

Counts

83 → 6

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

rewrite44.0ms

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))))
17.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
51.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
65.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4949	2008
1	4949	2008

prune147.0ms

Filtered

75 candidates to 110 candidates (-46.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	107	9	116

Merged error: 0b

Counts

116 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
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)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

4.0ms	(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))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
54.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
10.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify68.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4904	1292
1	4904	1292

prune110.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Merged error: 0b

Counts

92 → 9

localize12.0ms

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac_binary64`
96×	`*-un-lft-identity_binary64`
62×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
19×	`associate-/r*_binary64`
17×	`distribute-lft-out_binary64` `add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `div-exp_binary64`
7×	`associate-/l*_binary64`
6×	`div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/r/_binary64` `inv-pow_binary64` `+-commutative_binary64` `flip--_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 144

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
11.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))

series82.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
20.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
36.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))

simplify69.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5006	3188

prune140.0ms

Filtered

99 candidates to 156 candidates (-57.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	156	9	165

Merged error: 0b

Counts

165 → 9

regimes183.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	16
1	62	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

420.0ms	4483×	body	160	valid
266.0ms	8914×	pre	80	true
171.0ms	3517×	body	80	valid
42.0ms	914×	body	80	nan

Details

analyze265.0ms

sample38.0ms

simplify225.0ms

prune9.0ms

localize10.0ms

rewrite31.0ms

series72.0ms

simplify62.0ms

prune101.0ms

localize14.0ms

rewrite44.0ms

series143.0ms

simplify52.0ms

prune147.0ms

localize11.0ms

rewrite27.0ms

series96.0ms

simplify68.0ms

prune110.0ms

localize12.0ms

rewrite37.0ms

series82.0ms

simplify69.0ms

prune140.0ms

regimes183.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling