Details

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 27.253101%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

20.0ms	40×	body	1280	valid
14.0ms	47×	body	640	valid
7.0ms	134×	body	80	valid
5.0ms	16×	body	640	invalid
3.0ms	16×	body	320	valid
2.0ms	19×	body	160	valid
1.0ms	6×	body	320	invalid
1.0ms	2×	body	1280	invalid
1.0ms	6×	body	160	invalid
0.0ms	4×	body	80	nan
0.0ms	2×	body	80	invalid

simplify118.0ms

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

prune6.0ms

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: 13.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
8.3b	(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)

simplify54.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (46.0ms)

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

prune110.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 0.6b

Counts

73 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
3.2b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite32.0ms

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)
14.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series106.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
21.0ms	(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)

simplify92.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (74.0ms)

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

prune175.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	129	5	134

Merged error: 0.3b

Counts

134 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.6b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite26.0ms

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)
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
21.0ms	(cbrt x)
25.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
26.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify80.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (60.0ms)

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

prune196.0ms

Filtered

103 candidates to 156 candidates (-51.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	156	5	161

Merged error: 0.3b

Counts

161 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
1.2b	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
3.2b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
15.1b	(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

199×	`cbrt-prod`
125×	`unpow-prod-down`
95×	`times-frac`
88×	`*-un-lft-identity`
70×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`cbrt-div`
26×	`add-exp-log`
18×	`associate-/r/`
13×	`flip3-+` `flip-+`
10×	`pow-exp`
9×	`pow-unpow` `distribute-lft-out`
8×	`frac-times`
7×	`pow1` `div-exp`
5×	`prod-exp`
4×	`associate-r/` `associate-l/` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-inv` `sqr-pow`
1×	`pow1/3`

Counts

4 → 188

Calls

4 calls:

2.0ms	(cbrt (cbrt x))
16.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
14.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
13.0ms	(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) x)

series129.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (cbrt x))
26.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
34.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
39.0ms	(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1540	3431
1	5001	3352

prune291.0ms

Filtered

159 candidates to 200 candidates (-25.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	200	5	205

Merged error: 0.3b

Counts

205 → 5

regimes94.0ms

Accuracy

25.9% (3.3b remaining)

Error of 4.4b against oracle of 1.2b and baseline of 5.5b

bsearch78.0ms

Steps

Iters	Range		Point
10	8.963403361582824e-15	0.06426469400584847	0.06295955642565228

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	48
1	38	48

end0.0ms

sample3.8s

Algorithm

intervals

sampling

Space saved by range analysis: 27.253101%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

897.0ms	1396×	body	1280	valid
378.0ms	1268×	body	640	valid
237.0ms	4308×	body	80	valid
129.0ms	657×	body	320	valid
69.0ms	245×	body	640	invalid
46.0ms	371×	body	160	valid
45.0ms	103×	body	1280	invalid
32.0ms	162×	body	320	invalid
12.0ms	99×	body	160	invalid
7.0ms	123×	body	80	invalid
4.0ms	91×	body	80	nan

Details

sample1.8s

simplify118.0ms

prune6.0ms

localize6.0ms

rewrite13.0ms

series22.0ms

simplify54.0ms

prune110.0ms

localize19.0ms

rewrite32.0ms

series106.0ms

simplify92.0ms

prune175.0ms

localize16.0ms

rewrite26.0ms

series94.0ms

simplify80.0ms

prune196.0ms

localize30.0ms

rewrite55.0ms

series129.0ms

simplify63.0ms

prune291.0ms

regimes94.0ms

bsearch78.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling