Details

sample59.0ms

Algorithm

intervals

Results

16.0ms	39×	body	1280	valid
11.0ms	43×	body	640	valid
10.0ms	172×	body	80	valid
4.0ms	22×	body	320	valid
2.0ms	71×	body	80	nan
2.0ms	17×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
6.9b	(pow (/ x (+ x y)) x)

rewrite26.0ms

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×	`expm1-log1p-u` `flip3-+` `div-exp` `pow-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 70

Calls

2 calls:

11.0ms	(/ x (+ x y))
13.0ms	(pow (/ x (+ x y)) x)

series244.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ x (+ x y))
209.0ms	(pow (/ x (+ x y)) x)

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	320	413
1	1304	399
2	5002	398

prune159.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.8b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite54.0ms

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)
19.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
27.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series837.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt x)
172.0ms	(cbrt x)
240.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
254.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (48.0ms)

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

prune439.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
3.6b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite37.0ms

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)
18.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series666.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt x)
173.0ms	(cbrt x)
250.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
70.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify64.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (42.0ms)

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

prune557.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
3.6b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

180×	`cbrt-prod`
168×	`times-frac`
163×	`*-un-lft-identity`
144×	`unpow-prod-down`
115×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`log-prod`
24×	`distribute-lft-out`
16×	`add-exp-log`
9×	`pow-unpow`
8×	`pow1` `cbrt-div` `associate-/r/`
6×	`pow-exp`
4×	`expm1-log1p-u` `flip3-+` `div-exp` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `sqr-pow`
2×	`rem-log-exp`
1×	`log-div` `log-pow`

Counts

4 → 256

Calls

4 calls:

18.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
18.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
22.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series823.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
251.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
256.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
66.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify73.0ms

Algorithm

egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	587	3015
1	1817	2974
2	5001	2871

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

89.9% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 5.4b

bsearch122.0ms

Steps

Iters	Range		Point
10	3.01453247982213e-27	3.2716599026957865e-16	3.231969950629079e-16
9	-5.519096697972622e+107	-1.6617757044371328e+100	-1.533037271626305e+101

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample1.9s

Algorithm

intervals

Results

649.0ms	1486×	body	1280	valid
374.0ms	1497×	body	640	valid
226.0ms	4951×	body	80	valid
133.0ms	818×	body	320	valid
94.0ms	3017×	body	80	nan
42.0ms	407×	body	160	valid