Details

sample18.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
3.0ms	281×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	5	2
1	5	2

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(sqrt (+ x y))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity` `sqrt-prod`
3×	`add-sqr-sqrt`
2×	`pow1` `add-cube-cbrt` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

1 → 16

Calls

1 calls:

5.0ms

(sqrt (+ x y))

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(sqrt (+ x y))

simplify69.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	111	89
1	273	81
2	832	78
3	2351	73
4	5001	73

prune31.0ms

Filtered

19 candidates to 14 candidates (26.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	3	20

Merged error: 0b

Counts

20 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ x y)))
0.4b	(* (fabs (cbrt (+ x y))) (sqrt (cbrt (+ x y))))
0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`cbrt-prod`
16×	`sqrt-prod`
12×	`add-cube-cbrt`
10×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `distribute-lft-out` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 78

Calls

4 calls:

3.0ms	(sqrt (cbrt (+ x y)))
8.0ms	(* (fabs (cbrt (+ x y))) (sqrt (cbrt (+ x y))))
3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))

series623.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (cbrt (+ x y)))
197.0ms	(* (fabs (cbrt (+ x y))) (sqrt (cbrt (+ x y))))
132.0ms	(cbrt (+ x y))
140.0ms	(cbrt (+ x y))

simplify106.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	312	623
1	1013	590
2	4055	582
3	5002	568

prune181.0ms

Filtered

90 candidates to 71 candidates (21.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	90	3	93

Merged error: 0b

Counts

93 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* y y) (* x y))
18.3b	(/ (sqrt (+ (pow x 3) (pow y 3))) (sqrt (+ (* x x) (- (* y y) (* x y)))))
20.8b	(sqrt (+ (pow x 3) (pow y 3)))
27.6b	(sqrt (+ (* x x) (- (* y y) (* x y))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

615×	`*-un-lft-identity`
344×	`sqrt-prod`
192×	`times-frac`
186×	`associate-l`
176×	`distribute-lft-out`
118×	`distribute-lft-out--`
95×	`add-sqr-sqrt`
72×	`pow-unpow` `sum-cubes`
68×	`add-cube-cbrt`
36×	`unpow-prod-down`
16×	`associate-/r*`
12×	`associate-/l*`
10×	`difference-of-squares`
9×	`associate-r`
8×	`distribute-rgt-out--` `sqrt-div`
7×	`*-commutative` `unswap-sqr`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `swap-sqr` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `sqrt-undiv` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 319

Calls

4 calls:

17.0ms	(- (* y y) (* x y))
45.0ms	(/ (sqrt (+ (pow x 3) (pow y 3))) (sqrt (+ (* x x) (- (* y y) (* x y)))))
10.0ms	(sqrt (+ (pow x 3) (pow y 3)))
31.0ms	(sqrt (+ (* x x) (- (* y y) (* x y))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* y y) (* x y))
93.0ms	(/ (sqrt (+ (pow x 3) (pow y 3))) (sqrt (+ (* x x) (- (* y y) (* x y)))))
87.0ms	(sqrt (+ (pow x 3) (pow y 3)))
87.0ms	(sqrt (+ (* x x) (- (* y y) (* x y))))

simplify106.0ms

Algorithm

egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	610	4833
1	2274	4382
2	5002	4371

prune307.0ms

Filtered

331 candidates to 96 candidates (71.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	331	0	331
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	331	3	334

Merged error: 0b

Counts

334 → 3

regimes66.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	2
1	5	2

end0.0ms

sample466.0ms

Algorithm

intervals

Results

122.0ms	8000×	body	80	valid
102.0ms	7997×	body	80	nan