Details

analyze469.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample50.0ms

Algorithm

intervals

Results

14.0ms	46×	body	2560	valid
10.0ms	150×	body	80	valid
7.0ms	30×	body	1280	valid
3.0ms	15×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	30×	body	80	nan
1.0ms	7×	body	320	valid
0.0ms	9×	body	80	invalid
0.0ms	2×	body	160	valid

simplify246.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (243.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

prune7.0ms

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: 35.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite26.0ms

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-/l*_binary64`
3×	`associate-/r*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_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:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4931	1327
1	4931	1327

prune92.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 5.1b

Counts

84 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.8b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.7b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
14.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
14.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
53.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
73.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4997	3057
1	4997	3057

prune110.0ms

Filtered

102 candidates to 139 candidates (-36.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	140	8	148

Merged error: 5.0b

Counts

148 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.7b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
17.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify54.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5070	1600

prune73.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 5.0b

Counts

101 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac_binary64`
82×	`*-un-lft-identity_binary64`
57×	`add-sqr-sqrt_binary64`
56×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`div-exp_binary64`
6×	`pow1_binary64`
5×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 134

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify85.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4925	2928
1	4925	2928

prune81.0ms

Filtered

91 candidates to 146 candidates (-60.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	146	8	154

Merged error: 5.0b

Counts

154 → 8

regimes234.0ms

Accuracy

96.6% (0.8b remaining)

Error of 6.5b against oracle of 5.7b and baseline of 29.5b

bsearch103.0ms

Steps

Iters	Range	Point
10	1.0267243006130582e+139	7.587285064599763e+148	6.199083478586426e+140
9	-9.213095929507221e-268	-5.202379215210675e-277	-7.506137588580103e-277
10	-2.85588695931454e+160	-1.0894827457037006e+148	-1.6751224960373033e+149

Iters

Range

Point

1.0267243006130582e+139

7.587285064599763e+148

6.199083478586426e+140

-9.213095929507221e-268

-5.202379215210675e-277

-7.506137588580103e-277

-2.85588695931454e+160

-1.0894827457037006e+148

-1.6751224960373033e+149

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	106	64
1	106	64

end0.0ms

sample1.3s

Algorithm

intervals

Results

335.0ms	1085×	body	2560	valid
273.0ms	5163×	body	80	valid
224.0ms	882×	body	1280	valid
86.0ms	446×	body	640	valid
48.0ms	116×	body	5120	valid
34.0ms	692×	body	80	nan
32.0ms	209×	body	320	valid
20.0ms	387×	body	80	invalid
10.0ms	99×	body	160	valid

Details

analyze469.0ms

sample50.0ms

simplify246.0ms

prune7.0ms

localize11.0ms

rewrite26.0ms

series64.0ms

simplify51.0ms

prune92.0ms

localize12.0ms

rewrite43.0ms

series151.0ms

simplify43.0ms

prune110.0ms

localize13.0ms

rewrite30.0ms

series102.0ms

simplify54.0ms

prune73.0ms

localize14.0ms

rewrite33.0ms

series77.0ms

simplify85.0ms

prune81.0ms

regimes234.0ms

bsearch103.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling