Details

analyze448.0ms

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample38.0ms

Algorithm

intervals

Results

9.0ms	38×	body	2048	valid
8.0ms	170×	body	128	valid
5.0ms	25×	body	1024	valid
4.0ms	12×	body	4096	valid
1.0ms	22×	body	128	nan
1.0ms	6×	body	512	valid
1.0ms	11×	body	128	invalid
0.0ms	5×	body	256	valid

simplify262.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (255.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	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: 31.9b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

8.0ms	(.f64 (.f64 3 a) c)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(.f64 (.f64 3 a) c)
119.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
60.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5415	1210

prune91.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	59	11	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	11	71

Merged error: 10.0b

Counts

71 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 a (.f64 c -3))
0.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))) b)
1.4b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))
22.0b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`flip3-+_binary64` `difference-of-squares_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(.f64 a (.f64 c -3))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))) b)
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 a (.f64 c -3))
117.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))) b)
65.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -3)))
129.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -3))))

simplify87.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4963	1201
1	4963	1201

prune66.0ms

Filtered

47 candidates to 70 candidates (-48.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	70	11	81

Merged error: 10.0b

Counts

81 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5052	1222

prune93.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	67	8	75

Merged error: 10.0b

Counts

75 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
2.8b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
9.1b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
19×	`*-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×	`associate-/r*_binary64` `pow1_binary64`
4×	`distribute-lft-out_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_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 → 101

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
19.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
12.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series848.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
284.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
384.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4935	3147
1	4935	3147

prune123.0ms

Filtered

75 candidates to 113 candidates (-50.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	103	10	113
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	106	15	121

Merged error: 7.2b

Counts

121 → 15

regimes340.0ms

Accuracy

95.8% (0.9b remaining)

Error of 9.6b against oracle of 8.7b and baseline of 29.4b

bsearch111.0ms

Steps

Iters	Range	Point
8	4.635839778054971e+154	8.957423577250147e+157	4.6929395429942243e+154
8	-5.5462216848953775e-304	5.93424297922754e-309	-1.0583505148364568e-306
8	-1.8320773659964503e+141	-6.103416920230122e+136	-1.3543978985140437e+138

Iters

Range

Point

4.635839778054971e+154

8.957423577250147e+157

4.6929395429942243e+154

-5.5462216848953775e-304

5.93424297922754e-309

-1.0583505148364568e-306

-1.8320773659964503e+141

-6.103416920230122e+136

-1.3543978985140437e+138

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	152	186
1	152	186

end0.0ms

sample1.2s

Algorithm

intervals

Results

279.0ms	1119×	body	2048	valid
263.0ms	5210×	body	128	valid
139.0ms	730×	body	1024	valid
135.0ms	421×	body	4096	valid
52.0ms	352×	body	512	valid
31.0ms	665×	body	128	nan
22.0ms	399×	body	128	invalid
16.0ms	168×	body	256	valid

Details

analyze448.0ms

sample38.0ms

simplify262.0ms

prune4.0ms

localize9.0ms

rewrite31.0ms

series334.0ms

simplify60.0ms

prune91.0ms

localize11.0ms

rewrite28.0ms

series339.0ms

simplify87.0ms

prune66.0ms

localize12.0ms

rewrite27.0ms

series358.0ms

simplify61.0ms

prune93.0ms

localize13.0ms

rewrite54.0ms

series848.0ms

simplify79.0ms

prune123.0ms

regimes340.0ms

bsearch111.0ms

simplify5.0ms

end0.0ms

sample1.2s

Profiling