Details

analyze488.0ms

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

sample41.0ms

Algorithm

intervals

Results

9.0ms	174×	body	128	valid
9.0ms	33×	body	2048	valid
6.0ms	12×	body	4096	valid
5.0ms	24×	body	1024	valid
1.0ms	6×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	11×	body	128	invalid

simplify266.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (259.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms

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: 33.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite35.0ms

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:

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

series508.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
59.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5315	1975

prune112.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 5.5b

Counts

83 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
0.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
1.0b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
23.6b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite37.0ms

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`
3×	`distribute-lft-out--_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_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` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
120.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
60.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
118.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify70.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4920	1956
1	4920	1956

prune74.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	82	9	91

Merged error: 5.4b

Counts

91 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
2.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
9.8b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
23.6b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`flip3-+_binary64` `associate-/r*_binary64` `pow1_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
4×	`div-inv_binary64`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 102

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series898.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
290.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
370.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
117.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify90.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4950	3121
1	4950	3121

prune110.0ms

Filtered

77 candidates to 114 candidates (-48.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	116	7	123

Merged error: 5.4b

Counts

123 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
1.0b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.7b	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
23.6b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite31.0ms

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×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`associate-/r/_binary64` `+-commutative_binary64` `sqrt-div_binary64` `sum-log_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 → 71

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
7.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series604.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(/.f64 c (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
62.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
110.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
113.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify77.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4920	1958
1	4920	1958

prune75.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	82	8	90

Merged error: 5.4b

Counts

90 → 8

regimes145.0ms

Accuracy

94.1% (1.4b remaining)

Error of 6.8b against oracle of 5.4b and baseline of 29.3b

bsearch98.0ms

Steps

Iters	Range	Point
10	9.647093947483041e+27	3.402460884552278e+42	2.6022400513499554e+42
7	5.6559512677487335e-273	2.8572442025107414e-271	9.329496704353122e-273
8	-1.0467654810113616e+124	-1.55099810732216e+120	-9.653953438506672e+122

Iters

Range

Point

9.647093947483041e+27

3.402460884552278e+42

2.6022400513499554e+42

5.6559512677487335e-273

2.8572442025107414e-271

9.329496704353122e-273

-1.0467654810113616e+124

-1.55099810732216e+120

-9.653953438506672e+122

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	82
1	72	82

end0.0ms

sample1.2s

Algorithm

intervals

Results

293.0ms	1108×	body	2048	valid
282.0ms	5243×	body	128	valid
153.0ms	713×	body	1024	valid
138.0ms	420×	body	4096	valid
53.0ms	348×	body	512	valid
38.0ms	666×	body	128	nan
21.0ms	399×	body	128	invalid
17.0ms	168×	body	256	valid

Details

analyze488.0ms

sample41.0ms

simplify266.0ms

prune4.0ms

localize11.0ms

rewrite35.0ms

series508.0ms

simplify59.0ms

prune112.0ms

localize11.0ms

rewrite37.0ms

series510.0ms

simplify70.0ms

prune74.0ms

localize12.0ms

rewrite49.0ms

series898.0ms

simplify90.0ms

prune110.0ms

localize14.0ms

rewrite31.0ms

series604.0ms

simplify77.0ms

prune75.0ms

regimes145.0ms

bsearch98.0ms

simplify3.0ms

end0.0ms

sample1.2s

Profiling