Details

sample2.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 26.794434%

Guaranteed chance to sample good point: 45.585293%

Results

22.0ms	46×	body	1280	valid
12.0ms	41×	body	640	valid
8.0ms	134×	body	80	valid
4.0ms	21×	body	320	valid
3.0ms	10×	body	640	invalid
2.0ms	14×	body	160	valid
2.0ms	8×	body	320	invalid
0.0ms	1×	body	1280	invalid
0.0ms	4×	body	80	invalid
0.0ms	5×	body	80	nan
0.0ms	1×	body	160	invalid

simplify114.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (6.0ms)

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

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: 12.5b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
7.5b	(pow (/ x (+ x y)) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

10.0ms	(/ (pow (/ x (+ x y)) x) x)
7.0ms	(/ x (+ x y))
6.0ms	(pow (/ x (+ x y)) x)

series43.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
18.0ms	(pow (/ x (+ x y)) x)

simplify103.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	752	1628
1	3787	1586
2	5001	1586

prune222.0ms

Filtered

134 candidates to 181 candidates (-35.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	173	8	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	8	182

Merged error: 0.8b

Counts

182 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.4b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
3.3b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`frac-times` `prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series108.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
22.0ms	(cbrt x)
26.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
38.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify90.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	977	1596
1	3500	1507
2	5002	1470

prune178.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	130	6	136

Merged error: 0.8b

Counts

136 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.4b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
3.7b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
85×	`*-un-lft-identity`
84×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`unpow-prod-down` `log-prod`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`cbrt-div` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `pow1/3` `div-exp` `rem-log-exp` `pow-exp` `flip-+` `div-inv`
1×	`pow-to-exp` `log-div` `pow-pow` `log-pow` `sqr-pow`

Counts

4 → 144

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt x)
22.0ms	(cbrt x)
25.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
26.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify75.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	778	1627
1	2653	1569
2	5001	1544

prune198.0ms

Filtered

103 candidates to 156 candidates (-51.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	156	6	162

Merged error: 0.8b

Counts

162 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (pow (/ x (+ x y)) x) 3))
0.0b	(/ x (+ x y))
0.0b	(pow (pow (/ x (+ x y)) x) 3)
7.5b	(pow (/ x (+ x y)) x)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

134×	`unpow-prod-down`
98×	`*-un-lft-identity`
72×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt`
50×	`cbrt-prod`
44×	`cube-prod`
19×	`distribute-lft-out`
13×	`add-exp-log`
12×	`associate-/r/`
8×	`pow-exp`
7×	`add-cbrt-cube` `sqr-pow`
6×	`pow-unpow` `flip3-+` `flip-+` `div-inv`
5×	`pow1`
4×	`associate-/r*` `add-log-exp`
3×	`pow-to-exp` `div-exp` `associate-/l*`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`cbrt-undiv` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

10.0ms	(cbrt (pow (pow (/ x (+ x y)) x) 3))
5.0ms	(/ x (+ x y))
11.0ms	(pow (pow (/ x (+ x y)) x) 3)
7.0ms	(pow (/ x (+ x y)) x)

series73.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (pow (pow (/ x (+ x y)) x) 3))
5.0ms	(/ x (+ x y))
30.0ms	(pow (pow (/ x (+ x y)) x) 3)
18.0ms	(pow (/ x (+ x y)) x)

simplify106.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	876	1754
1	4044	1712
2	5002	1706

prune204.0ms

Filtered

109 candidates to 201 candidates (-84.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	201	6	207

Merged error: 0.8b

Counts

207 → 6

regimes119.0ms

Accuracy

18.7% (4.0b remaining)

Error of 4.7b against oracle of 0.7b and baseline of 5.6b

bsearch87.0ms

Steps

Iters	Range		Point
10	4.867704170634238e+136	1.2718203681462129e+153	3.9859222443176736e+145
7	5047065388.793183	87808597248.4344	6217199369.632938

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	21
1	32	21

end0.0ms

sample4.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 26.794434%

Guaranteed chance to sample good point: 45.585293%

Results

722.0ms	1448×	body	1280	valid
369.0ms	1197×	body	640	valid
243.0ms	4371×	body	80	valid
135.0ms	659×	body	320	valid
73.0ms	251×	body	640	invalid
41.0ms	325×	body	160	valid
37.0ms	84×	body	1280	invalid
37.0ms	190×	body	320	invalid
12.0ms	101×	body	160	invalid
7.0ms	111×	body	80	invalid
6.0ms	137×	body	80	nan

Details

sample2.2s

simplify114.0ms

prune7.0ms

localize7.0ms

rewrite32.0ms

series43.0ms

simplify103.0ms

prune222.0ms

localize16.0ms

rewrite33.0ms

series108.0ms

simplify90.0ms

prune178.0ms

localize16.0ms

rewrite27.0ms

series96.0ms

simplify75.0ms

prune198.0ms

localize9.0ms

rewrite42.0ms

series73.0ms

simplify106.0ms

prune204.0ms

regimes119.0ms

bsearch87.0ms

simplify1.0ms

end0.0ms

sample4.0s

Profiling