Details

analyze652.0ms

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
0%	99.9%	0.1%	5
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample64.0ms

Algorithm

intervals

Results

20.0ms	39×	body	1280	valid
14.0ms	44×	body	640	valid
7.0ms	137×	body	80	valid
5.0ms	26×	body	320	valid
3.0ms	12×	body	640	invalid
2.0ms	11×	body	320	invalid
1.0ms	3×	body	1280	invalid
1.0ms	10×	body	160	valid
0.0ms	6×	body	80	nan
0.0ms	4×	body	80	invalid

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (7.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune8.0ms

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: 11.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
6.5b	(pow (/ x (+ x y)) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 66

Calls

2 calls:

5.0ms	(/ x (+ x y))
6.0ms	(pow (/ x (+ x y)) x)

series22.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ x (+ x y))
17.0ms	(pow (/ x (+ x y)) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	451	502
1	2027	479
2	5002	474

prune111.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 0.9b

Counts

73 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
1.9b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
13×	`unpow-prod-down`
12×	`cbrt-div`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/r/`
6×	`flip3-+` `flip-+`
5×	`pow1` `pow-exp`
4×	`frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-pow` `times-frac` `div-inv` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series100.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
24.0ms	(cbrt x)
21.0ms	(cbrt x)
34.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	540	774
1	1876	714
2	5002	668

prune109.0ms

Filtered

55 candidates to 76 candidates (-38.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 0.7b

Counts

81 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-div`
1×	`flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 47

Calls

4 calls:

3.0ms	(cbrt (+ x y))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series233.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(cbrt (+ x y))
26.0ms	(cbrt x)
27.0ms	(cbrt x)
24.0ms	(cbrt x)

simplify204.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	167	258
1	354	240
2	998	202
3	4983	195
4	5003	195

prune94.0ms

Filtered

47 candidates to 59 candidates (-25.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	59	4	63

Merged error: 0.7b

Counts

63 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
22.5b	(pow (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))) x)

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
111×	`unpow-prod-down`
92×	`cbrt-div`
89×	`*-un-lft-identity`
72×	`cbrt-prod`
58×	`associate-/r/`
53×	`add-sqr-sqrt` `add-cube-cbrt`
46×	`flip3-+` `flip-+`
28×	`frac-times`
18×	`distribute-lft-out`
14×	`add-exp-log` `associate-r/` `associate-l/`
8×	`div-inv`
5×	`pow1` `div-exp`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3`
1×	`pow-to-exp` `pow-pow` `prod-exp` `sqr-pow`

Counts

4 → 170

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
32.0ms	(pow (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))) x)

series119.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt (+ x y))
34.0ms	(cbrt (+ x y))
31.0ms	(cbrt (+ x y))
22.0ms	(pow (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))) x)

simplify116.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1247	3137
1	4460	3096
2	5001	3018

prune210.0ms

Filtered

120 candidates to 182 candidates (-51.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	182	4	186

Merged error: 0.7b

Counts

186 → 4

regimes120.0ms

Accuracy

21.3% (3.7b remaining)

Error of 5.1b against oracle of 1.4b and baseline of 6.0b

bsearch317.0ms

Steps

Iters	Range		Point
10	2.5526541520170116e+98	9.507644868689494e+113	1.0393444200088786e+111
5	3563493.4329553843	8954449.085065203	3608328.164803992

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	29
1	26	29

end0.0ms

analyze670.0ms

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
0%	99.9%	0.1%	5
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample2.2s

Algorithm

intervals

Results

829.0ms	1437×	body	1280	valid
442.0ms	1234×	body	640	valid
268.0ms	4300×	body	80	valid
156.0ms	671×	body	320	valid
83.0ms	245×	body	640	invalid
51.0ms	358×	body	160	valid
49.0ms	88×	body	1280	invalid
41.0ms	182×	body	320	invalid
14.0ms	95×	body	160	invalid
10.0ms	156×	body	80	invalid
9.0ms	197×	body	80	nan

Details

analyze652.0ms

sample64.0ms

simplify112.0ms

prune8.0ms

localize6.0ms

rewrite13.0ms

series22.0ms

simplify53.0ms

prune111.0ms

localize18.0ms

rewrite20.0ms

series100.0ms

simplify57.0ms

prune109.0ms

localize12.0ms

rewrite8.0ms

series233.0ms

simplify204.0ms

prune94.0ms

localize15.0ms

rewrite60.0ms

series119.0ms

simplify116.0ms

prune210.0ms

regimes120.0ms

bsearch317.0ms

simplify2.0ms

end0.0ms

analyze670.0ms

sample2.2s

Profiling