Details

sample229.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.83728%

Guaranteed chance to sample good point: 97.451617%

Results

28.0ms	42×	body	1280	valid
13.0ms	44×	body	640	valid
9.0ms	162×	body	80	valid
7.0ms	32×	body	320	valid
2.0ms	14×	body	160	valid
0.0ms	3×	body	80	nan

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (8.0ms)

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

localize7.0ms

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)

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:

11.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) x)

series49.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
23.0ms	(pow (/ x (+ x y)) x)

simplify102.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (23.0ms)

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

prune225.0ms

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

localize16.0ms

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)

rewrite36.0ms

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)
17.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series111.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
23.0ms	(cbrt x)
30.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
35.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify92.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (76.0ms)

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

prune184.0ms

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

localize20.0ms

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))))

rewrite29.0ms

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

series99.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt x)
22.0ms	(cbrt x)
30.0ms	(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

prune216.0ms

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)

rewrite40.0ms

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:

11.0ms	(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:

41.0ms	(cbrt (/ (pow (/ x (+ x y)) x) x))
17.0ms	(pow (/ x (+ x y)) x)
17.0ms	(pow (/ x (+ x y)) x)
21.0ms	(pow (/ x (+ x y)) x)

simplify106.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (81.0ms)

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

prune271.0ms

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

regimes126.0ms

Accuracy

1.5% (5.1b remaining)

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

bsearch71.0ms

Steps

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

simplify1.0ms

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

774.0ms	1531×	body	1280	valid
456.0ms	1493×	body	640	valid
275.0ms	4828×	body	80	valid
177.0ms	842×	body	320	valid
63.0ms	448×	body	160	valid
6.0ms	144×	body	80	nan

Details

sample229.0ms

simplify124.0ms

prune7.0ms

localize7.0ms

rewrite32.0ms

series49.0ms

simplify102.0ms

prune225.0ms

localize16.0ms

rewrite36.0ms

series111.0ms

simplify92.0ms

prune184.0ms

localize20.0ms

rewrite29.0ms

series99.0ms

simplify79.0ms

prune216.0ms

localize11.0ms

rewrite40.0ms

series97.0ms

simplify106.0ms

prune271.0ms

regimes126.0ms

bsearch71.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling