Details

analyze264.0ms

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

sample50.0ms

Algorithm

intervals

Results

18.0ms	116×	body	320	valid
10.0ms	102×	body	160	valid
8.0ms	281×	pre	80	true
2.0ms	13×	body	640	valid
1.0ms	25×	body	80	valid
1.0ms	25×	body	80	nan

simplify226.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (223.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

prune5.0ms

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: 53.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.5b	(-.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)))
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)

series72.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(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)

simplify64.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4900	1294
1	4900	1294

prune67.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 0.1b

Counts

83 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.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)))))

rewrite43.0ms

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:

7.0ms	(+.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))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

series145.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
48.0ms	(/.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)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4949	2008
1	4949	2008

prune93.0ms

Filtered

75 candidates to 110 candidates (-46.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Merged error: 0b

Counts

114 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(-.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:

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

series95.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
18.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
52.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
10.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify70.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4904	1292
1	4904	1292

prune68.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Merged error: 0b

Counts

89 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
0.2b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))

rewrite39.0ms

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:

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)))
9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c)
12.0ms	(/.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)))))
9.0ms	(-.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)
37.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))) c))

simplify72.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5006	3188

prune99.0ms

Filtered

99 candidates to 156 candidates (-57.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	157	5	162

Merged error: 0b

Counts

162 → 5

regimes105.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	16
1	62	16

end0.0ms

sample1.5s

Algorithm

intervals

Results

521.0ms	3634×	body	320	valid
290.0ms	2976×	body	160	valid
258.0ms	8867×	pre	80	true
90.0ms	484×	body	640	valid
45.0ms	906×	body	80	valid
41.0ms	867×	body	80	nan

Details

analyze264.0ms

sample50.0ms

simplify226.0ms

prune5.0ms

localize10.0ms

rewrite31.0ms

series72.0ms

simplify64.0ms

prune67.0ms

localize14.0ms

rewrite43.0ms

series145.0ms

simplify54.0ms

prune93.0ms

localize15.0ms

rewrite27.0ms

series95.0ms

simplify70.0ms

prune68.0ms

localize13.0ms

rewrite39.0ms

series82.0ms

simplify72.0ms

prune99.0ms

regimes105.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling