Details

sample13.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	7	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
32.9b	(sqrt (+ (* x x) (* y y)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

3.0ms	(+ (* x x) (* y y))
3.0ms	(sqrt (+ (* x x) (* y y)))

series66.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* x x) (* y y))
35.0ms	(sqrt (+ (* x x) (* y y)))

simplify50.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	125	177
1	530	163
2	1540	163
3	5001	162

prune76.0ms

Filtered

32 candidates to 25 candidates (78.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* x x) (* y y))))
32.9b	(sqrt (+ (* x x) (* y y)))
32.9b	(sqrt (+ (* x x) (* y y)))
32.9b	(sqrt (+ (* x x) (* y y)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt (sqrt (+ (* x x) (* y y))))
3.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (sqrt (+ (* x x) (* y y))))
38.0ms	(sqrt (+ (* x x) (* y y)))
35.0ms	(sqrt (+ (* x x) (* y y)))
35.0ms	(sqrt (+ (* x x) (* y y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	146	478
1	405	458
2	1153	456
3	5001	452

prune388.0ms

Filtered

73 candidates to 61 candidates (83.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.0b

localize22.0ms

Local error

Found 4 expressions with local error:

32.9b	(sqrt (+ (* x x) (* y y)))
33.9b	(cbrt (+ (* x x) (* y y)))
33.9b	(cbrt (+ (* x x) (* y y)))
33.9b	(cbrt (+ (* x x) (* y y)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

3.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(cbrt (+ (* x x) (* y y)))
3.0ms	(cbrt (+ (* x x) (* y y)))
4.0ms	(cbrt (+ (* x x) (* y y)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* x x) (* y y)))
93.0ms	(cbrt (+ (* x x) (* y y)))
94.0ms	(cbrt (+ (* x x) (* y y)))
96.0ms	(cbrt (+ (* x x) (* y y)))

simplify52.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	141	466
1	440	436
2	1470	430
3	5001	429

prune295.0ms

Filtered

66 candidates to 60 candidates (90.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.0b

localize14.0ms

Local error

Found 4 expressions with local error:

32.9b	(sqrt (+ (* x x) (* y y)))
32.9b	(sqrt (+ (* x x) (* y y)))
32.9b	(sqrt (+ (* x x) (* y y)))
32.9b	(sqrt (+ (* x x) (* y y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

3.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (* x x) (* y y)))
38.0ms	(sqrt (+ (* x x) (* y y)))
36.0ms	(sqrt (+ (* x x) (* y y)))
39.0ms	(sqrt (+ (* x x) (* y y)))

simplify142.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (137.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune236.0ms

Filtered

72 candidates to 60 candidates (83.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.0b

regimes287.0ms

Accuracy

58.7% (10.0b remaining)

Error of 17.7b against oracle of 7.7b and baseline of 31.8b

bsearch43.0ms

Steps

Iters	Range		Point
7	8.038692978176935e+71	1.1196446523800873e+74	1.1038304751290051e+74
9	-5.852158442175802e+75	-5.8276681929279876e+69	-5.781737093335538e+75

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	5
1	17	5

end0.0ms

sample302.0ms

Algorithm

intervals

Results

179.0ms

8000×

body

valid