Details

analyze460.0ms

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

sample49.0ms

Algorithm

intervals

Results

13.0ms	43×	body	2560	valid
10.0ms	152×	body	80	valid
8.0ms	34×	body	1280	valid
3.0ms	14×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	15×	body	80	nan
0.0ms	7×	body	80	invalid
0.0ms	3×	body	160	valid

simplify251.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (248.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	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: 36.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) (.f64 a 2.0))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite30.0ms

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 4.0 (.f64 a c)))) b) (.f64 a 2.0))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) (.f64 a 2.0))
17.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
13.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5340	1316

prune132.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 6.5b

Counts

83 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite21.0ms

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
11.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5246	824

prune98.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	64	10	74

Merged error: 6.5b

Counts

74 → 10

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify5.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune21.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	2	2
Total	10	10

Merged error: 6.5b

Counts

10 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))))
24.3b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
24.3b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
24.3b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div_binary64`
30×	`flip3--_binary64` `flip--_binary64`
28×	`frac-times_binary64`
26×	`sqrt-div_binary64`
24×	`pow1_binary64`
15×	`sqrt-pow1_binary64`
14×	`associate-*l/_binary64`
12×	`pow1/3_binary64`
9×	`pow-prod-up_binary64` `cbrt-prod_binary64`
8×	`associate-*r/_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`pow-plus_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow-sqr_binary64`
2×	`pow2_binary64`
1×	`pow1/2_binary64` `pow3_binary64` `sqrt-prod_binary64`

Counts

4 → 89

Calls

4 calls:

18.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))))
26.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
29.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
26.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify81.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4933	2546
1	4933	2546

prune110.0ms

Filtered

67 candidates to 101 candidates (-50.7%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	101	10	111

Merged error: 6.5b

Counts

111 → 10

regimes341.0ms

Accuracy

83.5% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 34.1b

bsearch122.0ms

Steps

Iters	Range		Point
8	19632.042828082296	11222340.51519018	477515.78107987816
9	6.191562960307448e-31	3.849886770774018e-24	4.162966466628992e-26
8	1.8735819436265453e-63	7.090452779956445e-59	1.4820993962288012e-59
8	-6.217592569728448e+112	-1.141697663647829e+110	-2.0801679587946785e+111

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	106	47
1	106	47

end0.0ms

sample1.3s

Algorithm

intervals

Results

346.0ms	1087×	body	2560	valid
278.0ms	5080×	body	80	valid
226.0ms	898×	body	1280	valid
105.0ms	491×	body	640	valid
45.0ms	108×	body	5120	valid
37.0ms	244×	body	320	valid
33.0ms	637×	body	80	nan
21.0ms	383×	body	80	invalid
9.0ms	92×	body	160	valid

Details

analyze460.0ms

sample49.0ms

simplify251.0ms

prune7.0ms

localize10.0ms

rewrite30.0ms

series80.0ms

simplify45.0ms

prune132.0ms

localize14.0ms

rewrite21.0ms

series57.0ms

simplify42.0ms

prune98.0ms

localize3.0ms

rewrite0.0ms

series0.0ms

simplify5.0ms

prune21.0ms

localize18.0ms

rewrite37.0ms

series100.0ms

simplify81.0ms

prune110.0ms

regimes341.0ms

bsearch122.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling