Details

analyze487.0ms

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	30×	body	2560	valid
9.0ms	172×	body	80	valid
7.0ms	26×	body	1280	valid
3.0ms	16×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	17×	body	80	nan
0.0ms	3×	body	80	invalid
0.0ms	1×	body	160	valid

simplify313.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (304.0ms)

Iter	Nodes	Cost
0	1835	24
1	1835	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: 33.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

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:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
59.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify74.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5308	1975

prune106.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 6.8b

Counts

83 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

693×	`times-frac_binary64`
438×	`add-sqr-sqrt_binary64`
363×	`*-un-lft-identity_binary64`
289×	`add-cube-cbrt_binary64`
74×	`difference-of-squares_binary64`
71×	`associate-/r*_binary64`
40×	`sqrt-prod_binary64`
37×	`distribute-lft-out--_binary64`
25×	`add-exp-log_binary64`
17×	`div-inv_binary64`
15×	`div-exp_binary64`
13×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64`
5×	`associate-/r/_binary64`
3×	`flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 352

Calls

4 calls:

22.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify198.0ms

Algorithm

egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5027	16279

prune388.0ms

Filtered

197 candidates to 364 candidates (-84.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	362	2	364
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	363	9	372

Merged error: 6.7b

Counts

372 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`difference-of-squares_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
17.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
104.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
67.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify137.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4941	2222
1	4941	2222

prune85.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	91	9	100

Merged error: 6.7b

Counts

100 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 58

Calls

4 calls:

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

series239.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
59.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify71.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4975	1536
1	4975	1536

prune81.0ms

Filtered

56 candidates to 70 candidates (-25.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	70	9	79

Merged error: 6.7b

Counts

79 → 9

regimes128.0ms

Accuracy

79.1% (6.0b remaining)

Error of 11.7b against oracle of 5.6b and baseline of 34.3b

bsearch125.0ms

Steps

Iters	Range		Point
3	50652223729.90005	62648093782.67851	51401965608.1987
10	1.4277311006459849e-25	1.3407713151514111e-14	9.228060049895551e-15
9	8.377315405567149e-167	1.009656993309182e-160	9.395550020877812e-161
9	-2.2869187191943033e+141	-9.368748744329815e+133	-1.1322680089054584e+134

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	111	69
1	111	69

end0.0ms

sample1.3s

Algorithm

intervals

Results

326.0ms	1035×	body	2560	valid
282.0ms	5181×	body	80	valid
224.0ms	865×	body	1280	valid
99.0ms	470×	body	640	valid
46.0ms	112×	body	5120	valid
39.0ms	258×	body	320	valid
36.0ms	662×	body	80	nan
25.0ms	390×	body	80	invalid
8.0ms	79×	body	160	valid

Details

analyze487.0ms

sample41.0ms

simplify313.0ms

prune4.0ms

localize11.0ms

rewrite31.0ms

series257.0ms

simplify74.0ms

prune106.0ms

localize15.0ms

rewrite71.0ms

series505.0ms

simplify198.0ms

prune388.0ms

localize11.0ms

rewrite35.0ms

series269.0ms

simplify137.0ms

prune85.0ms

localize14.0ms

rewrite26.0ms

series239.0ms

simplify71.0ms

prune81.0ms

regimes128.0ms

bsearch125.0ms

simplify5.0ms

end0.0ms

sample1.3s

Profiling