Details

sample67.0ms

Algorithm

intervals

Results

19.0ms	115×	body	320	valid
17.0ms	133×	body	160	valid
13.0ms	249×	body	80	nan
0.0ms	8×	body	80	valid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	21
1	122	21
2	299	21
3	591	21
4	931	21
5	1162	21
6	1388	21
7	2798	21
8	5002	21

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 36.6b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

8.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.4b	(sqrt (- (* g g) (* h h)))
29.4b	(sqrt (- (* g g) (* h h)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series714.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
314.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	385	766
1	1380	724
2	5002	718

prune398.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	53	19	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	19	73

Merged error: 31.5b

Counts

73 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
9.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.4b	(sqrt (- (* g g) (* h h)))
29.4b	(sqrt (- (* g g) (* h h)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
12.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
308.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	319	569
1	1259	537
2	5001	533

prune376.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	69	21	90

Merged error: 31.3b

Counts

90 → 21

localize22.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
4.0b	(- (* g g) (* h h))
29.4b	(sqrt (- (* g g) (* h h)))
29.4b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
4.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
35.0ms	(- (* g g) (* h h))
46.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify49.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	122	378
1	432	350
2	1459	350
3	5001	348

prune375.0ms

Filtered

70 candidates to 54 candidates (77.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	20	20
Picked	1	0	1
Done	0	0	0
Total	69	22	91

Merged error: 31.3b

Counts

91 → 22

localize18.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
4.0b	(- (* g g) (* h h))
29.4b	(sqrt (- (* g g) (* h h)))
29.4b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
4.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
35.0ms	(- (* g g) (* h h))
44.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify46.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	122	380
1	432	350
2	1459	350
3	5001	348

prune249.0ms

Filtered

70 candidates to 54 candidates (77.1%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	20	21
Picked	0	1	1
Done	0	0	0
Total	70	22	92

Merged error: 31.3b

Counts

92 → 22

regimes703.0ms

Accuracy

0% (1.3b remaining)

Error of 31.8b against oracle of 30.5b and baseline of 31.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	23
1	25	23

end0.0ms

sample1.8s

Algorithm

intervals

Results

595.0ms	3701×	body	320	valid
450.0ms	4149×	body	160	valid
420.0ms	7973×	body	80	nan
10.0ms	150×	body	80	valid