Details

sample70.0ms

Algorithm

intervals

Results

28.0ms	57×	body	1280	valid
12.0ms	40×	body	640	valid
9.0ms	163×	body	80	valid
5.0ms	23×	body	320	valid
3.0ms	83×	body	80	nan
2.0ms	15×	body	160	valid

simplify117.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (9.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4192	4
7	5002	4

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 11.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.0b	(/ (pow (/ x (+ x y)) x) x)
7.1b	(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×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 178

Calls

3 calls:

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

series408.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ x (+ x y))
133.0ms	(/ (pow (/ x (+ x y)) x) x)
230.0ms	(pow (/ x (+ x y)) x)

simplify80.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	554	1456
1	2726	1426
2	5003	1426

prune358.0ms

Filtered

187 candidates to 137 candidates (73.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	182	5	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	5	188

Merged error: 0.8b

Counts

188 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.7b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite34.0ms

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×	`expm1-log1p-u` `frac-times` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 124

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)

series913.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
186.0ms	(cbrt x)
267.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
277.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify73.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	708	1370
1	2244	1300
2	5002	1271

prune372.0ms

Filtered

136 candidates to 98 candidates (72.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	137	4	141

Merged error: 0.0b

Counts

141 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.5b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite33.0ms

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×	`expm1-log1p-u` `cbrt-div` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `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 → 152

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
15.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt x)
174.0ms	(cbrt x)
258.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
75.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify60.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	612	1563
1	1928	1530
2	5002	1462

prune481.0ms

Filtered

164 candidates to 112 candidates (68.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	164	4	168

Merged error: 0.0b

Counts

168 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

1.7b	(pow (* (cbrt (/ x (+ x y))) (cbrt (/ x (+ x y)))) x)
6.5b	(cbrt (/ x (+ x y)))
6.5b	(cbrt (/ x (+ x y)))
6.5b	(cbrt (/ x (+ x y)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
47×	`*-un-lft-identity`
36×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`pow1`
9×	`pow-pow` `pow1/3` `distribute-lft-out`
7×	`add-exp-log`
6×	`associate-/r/`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `flip3-+` `flip-+` `div-inv`
2×	`pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-to-exp` `unpow-prod-down` `pow-plus` `prod-exp` `sqr-pow`

Counts

4 → 113

Calls

4 calls:

13.0ms	(pow (* (cbrt (/ x (+ x y))) (cbrt (/ x (+ x y)))) x)
5.0ms	(cbrt (/ x (+ x y)))
5.0ms	(cbrt (/ x (+ x y)))
5.0ms	(cbrt (/ x (+ x y)))

series667.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(pow (* (cbrt (/ x (+ x y))) (cbrt (/ x (+ x y)))) x)
129.0ms	(cbrt (/ x (+ x y)))
128.0ms	(cbrt (/ x (+ x y)))
130.0ms	(cbrt (/ x (+ x y)))

simplify178.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	284	837
1	1000	806
2	4439	791
3	5001	791

prune303.0ms

Filtered

125 candidates to 94 candidates (75.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	125	4	129

Merged error: 0.0b

Counts

129 → 4

regimes66.0ms

Accuracy

94.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 5.5b

bsearch120.0ms

Steps

Iters	Range		Point
11	3.029362037509861e-19	14.716166499582775	6.4371159547725245
6	-5.5420202094963326e+107	-3.545331371370155e+106	-3.602031580985259e+106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample2.1s

Algorithm

intervals

Results

767.0ms	1537×	body	1280	valid
428.0ms	1445×	body	640	valid
274.0ms	4887×	body	80	valid
165.0ms	840×	body	320	valid
123.0ms	3020×	body	80	nan
55.0ms	442×	body	160	valid