Details

sample62.0ms

Algorithm

intervals

Results

24.0ms	54×	body	1280	valid
13.0ms	50×	body	640	valid
6.0ms	158×	body	80	valid
4.0ms	23×	body	320	valid
3.0ms	108×	body	80	nan
1.0ms	7×	body	160	valid

simplify114.0ms

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	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: 13.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
6.8b	(pow (/ x (+ x y)) x)

rewrite14.0ms

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:

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

series271.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ x (+ x y))
230.0ms	(pow (/ x (+ x y)) x)

simplify42.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

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

prune157.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

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)
1.9b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite35.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
15.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series898.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt x)
173.0ms	(cbrt x)
256.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
282.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (50.0ms)

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

prune444.0ms

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)
0.7b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
4.9b	(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×	`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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
12.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
186.0ms	(cbrt x)
269.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
74.0ms	(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

prune542.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.7b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
5.0b	(log (cbrt (/ (cbrt x) (cbrt (+ x y)))))
5.0b	(log (cbrt (/ (cbrt x) (cbrt (+ x y)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

234×	`cbrt-prod`
126×	`times-frac`
125×	`*-un-lft-identity`
102×	`log-prod`
89×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`unpow-prod-down`
18×	`distribute-lft-out`
9×	`add-exp-log`
8×	`cbrt-div`
7×	`pow1`
6×	`associate-/r/`
4×	`expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`log-div` `rem-log-exp` `pow-exp`
1×	`pow-to-exp` `pow-pow` `div-exp` `sqr-pow`

Counts

4 → 206

Calls

4 calls:

0.0ms	(cbrt x)
12.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
7.0ms	(log (cbrt (/ (cbrt x) (cbrt (+ x y)))))
7.0ms	(log (cbrt (/ (cbrt x) (cbrt (+ x y)))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt x)
273.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
74.0ms	(log (cbrt (/ (cbrt x) (cbrt (+ x y)))))
77.0ms	(log (cbrt (/ (cbrt x) (cbrt (+ x y)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	606	2554
1	1698	2504
2	5001	2415

prune865.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

97.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 6.0b

bsearch97.0ms

Steps

Iters	Range		Point
9	9.049190128523824e-12	0.0001516457190089863	0.00014878486646836356
7	-4.467281414413093e+46	-1.0453748164938118e+45	-2.7759638164690656e+45

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	27
1	38	27

end0.0ms

sample1.7s

Algorithm

intervals

Results

670.0ms	1540×	body	1280	valid
363.0ms	1450×	body	640	valid
210.0ms	4914×	body	80	valid
131.0ms	822×	body	320	valid
87.0ms	3039×	body	80	nan
43.0ms	439×	body	160	valid