Details

sample58.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
13.0ms	53×	body	640	valid
7.0ms	157×	body	80	valid
3.0ms	17×	body	320	valid
3.0ms	85×	body	80	nan
1.0ms	12×	body	160	valid

simplify119.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
6.5b	(pow (/ x (+ x y)) x)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
100×	`*-un-lft-identity`
90×	`unpow-prod-down`
70×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/l*`
15×	`distribute-lft-out`
13×	`add-exp-log`
10×	`associate-/r/`
6×	`div-exp` `div-inv`
5×	`flip3-+` `flip-+` `sqr-pow`
4×	`pow-exp` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/r*`
2×	`expm1-log1p-u` `pow-to-exp` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `clear-num`

Counts

2 → 143

Calls

2 calls:

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

series360.0ms

Counts

2 → 6

Calls

2 calls:

135.0ms	(/ (pow (/ x (+ x y)) x) x)
225.0ms	(pow (/ x (+ x y)) x)

simplify68.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	512	1297
1	2369	1276
2	5001	1276

prune332.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.9b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.4b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite38.0ms

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)
19.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series895.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt x)
179.0ms	(cbrt x)
261.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
277.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (54.0ms)

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

prune423.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.9b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
3.7b	(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×	`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)
11.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt x)
189.0ms	(cbrt x)
264.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify59.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (44.0ms)

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

prune539.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.9b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.4b	(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)
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series904.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
180.0ms	(cbrt x)
269.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
273.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (51.0ms)

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

prune417.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

89.4% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 5.9b

bsearch108.0ms

Steps

Iters	Range		Point
9	2.2414413436101348e-30	2.5947478503916157e-23	2.5643233024290284e-23
7	-5.356651369818307e+88	-2.3687169017960367e+86	-2.930752839587006e+86

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

674.0ms	1528×	body	1280	valid
364.0ms	1433×	body	640	valid
220.0ms	4834×	body	80	valid
136.0ms	813×	body	320	valid
93.0ms	3038×	body	80	nan
54.0ms	500×	body	160	valid