Details

sample70.0ms

Algorithm

intervals

Results

20.0ms	122×	body	320	valid
16.0ms	243×	body	80	nan
15.0ms	131×	body	160	valid
0.0ms	3×	body	80	valid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 36.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.8b	(sqrt (- (* g g) (* h h)))
31.8b	(sqrt (- (* g g) (* h h)))

rewrite32.0ms

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))))))
11.0ms	(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)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
318.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

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

prune369.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	60	12	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	12	73

Merged error: 33.9b

Counts

73 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.8b	(sqrt (- (* g g) (* h h)))
31.8b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

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

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
11.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
312.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	297	571
1	1186	537
2	5001	533

prune365.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	68	15	83

Merged error: 33.1b

Counts

83 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
31.8b	(sqrt (- (* g g) (* h h)))
31.8b	(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:

30.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
51.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify48.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (42.0ms)

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

prune330.0ms

Filtered

70 candidates to 54 candidates (77.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	70	15	85

Merged error: 33.1b

Counts

85 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.8b	(sqrt (- (* g g) (* h h)))
31.8b	(sqrt (- (* g g) (* h h)))

rewrite29.0ms

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

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
16.0ms	(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)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
309.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	297	569
1	1188	537
2	5001	533

prune287.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	70	16	86

Merged error: 33.1b

Counts

86 → 16

regimes562.0ms

Accuracy

0% (1.2b remaining)

Error of 32.3b against oracle of 31.1b and baseline of 32.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	23
1	25	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

634.0ms	3721×	body	320	valid
467.0ms	4120×	body	160	valid
425.0ms	7892×	body	80	nan
9.0ms	159×	body	80	valid