Details

sample227.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.83728%

Guaranteed chance to sample good point: 97.451617%

Results

22.0ms	41×	body	1280	valid
11.0ms	36×	body	640	valid
8.0ms	142×	body	80	valid
7.0ms	12×	body	160	valid
5.0ms	25×	body	320	valid
2.0ms	8×	body	640	invalid
1.0ms	7×	body	320	invalid
1.0ms	20×	body	80	invalid
0.0ms	1×	body	1280	invalid
0.0ms	2×	body	160	invalid
0.0ms	3×	body	80	nan

simplify121.0ms

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

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: 11.3b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
6.1b	(pow (/ x (+ x y)) x)

rewrite30.0ms

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

series48.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
22.0ms	(pow (/ x (+ x y)) x)

simplify100.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (21.0ms)

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

prune215.0ms

Filtered

134 candidates to 181 candidates (-35.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	7	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	7	182

Merged error: 0.9b

Counts

182 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.5b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.2b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite35.0ms

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)
11.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
16.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series113.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt x)
23.0ms	(cbrt x)
30.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
37.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify94.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (77.0ms)

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

prune175.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	128	7	135

Merged error: 0.9b

Counts

135 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.5b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
3.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite28.0ms

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)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
22.0ms	(cbrt x)
31.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
24.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify79.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (61.0ms)

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

prune200.0ms

Filtered

103 candidates to 156 candidates (-51.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	156	7	163

Merged error: 0.9b

Counts

163 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (pow (/ x (+ x y)) x) x))
6.1b	(pow (/ x (+ x y)) x)
6.1b	(pow (/ x (+ x y)) x)
6.1b	(pow (/ x (+ x y)) x)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
117×	`*-un-lft-identity`
108×	`unpow-prod-down`
81×	`add-sqr-sqrt` `add-cube-cbrt`
70×	`cbrt-prod`
18×	`distribute-lft-out`
13×	`add-exp-log`
12×	`associate-/r/`
9×	`pow-unpow`
7×	`pow1` `div-inv`
6×	`flip3-+` `pow-exp` `flip-+` `sqr-pow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-exp`
1×	`cbrt-div` `pow1/3`

Counts

4 → 178

Calls

4 calls:

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

series97.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(cbrt (/ (pow (/ x (+ x y)) x) x))
18.0ms	(pow (/ x (+ x y)) x)
18.0ms	(pow (/ x (+ x y)) x)
19.0ms	(pow (/ x (+ x y)) x)

simplify112.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	919	2341
1	3802	2269
2	5002	2262

prune257.0ms

Filtered

142 candidates to 190 candidates (-33.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	189	8	197

Merged error: 0.9b

Counts

197 → 8

regimes127.0ms

Accuracy

1.5% (5.1b remaining)

Error of 5.9b against oracle of 0.8b and baseline of 6.0b

bsearch72.0ms

Steps

Iters	Range		Point
9	4.5468694725583477e+151	3.214759301000658e+160	4.870356022114595e+154
7	8.348533650331745e+99	1.0043784292405748e+102	5.686548380314168e+100

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	21
1	32	21

end0.0ms

sample2.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.83728%

Guaranteed chance to sample good point: 97.451617%

Results

708.0ms	1416×	body	1280	valid
380.0ms	1223×	body	640	valid
251.0ms	4358×	body	80	valid
134.0ms	651×	body	320	valid
78.0ms	270×	body	640	invalid
52.0ms	115×	body	1280	invalid
45.0ms	352×	body	160	valid
37.0ms	191×	body	320	invalid
26.0ms	470×	body	80	invalid
12.0ms	96×	body	160	invalid
6.0ms	144×	body	80	nan

Details

sample227.0ms

simplify121.0ms

prune7.0ms

localize6.0ms

rewrite30.0ms

series48.0ms

simplify100.0ms

prune215.0ms

localize18.0ms

rewrite35.0ms

series113.0ms

simplify94.0ms

prune175.0ms

localize19.0ms

rewrite28.0ms

series100.0ms

simplify79.0ms

prune200.0ms

localize11.0ms

rewrite45.0ms

series97.0ms

simplify112.0ms

prune257.0ms

regimes127.0ms

bsearch72.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling