Details

sample92.0ms

Algorithm

intervals

Results

28.0ms	127×	body	320	valid
22.0ms	128×	body	160	valid
21.0ms	292×	body	80	nan
0.0ms	1×	body	80	valid

simplify114.0ms

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: 34.0b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.2b	(sqrt (- (* g g) (* h h)))
29.2b	(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)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
309.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

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

prune407.0ms

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: 31.4b

Counts

73 → 19

localize20.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.2b	(sqrt (- (* g g) (* h h)))
29.2b	(sqrt (- (* g g) (* h h)))

rewrite24.0ms

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))
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)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
316.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune367.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	69	21	90

Merged error: 31.4b

Counts

90 → 21

localize20.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
6.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.2b	(sqrt (- (* g g) (* h h)))
29.2b	(sqrt (- (* g g) (* h h)))

rewrite24.0ms

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))
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)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
312.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune363.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	71	21	92

Merged error: 31.4b

Counts

92 → 21

localize19.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.2b	(sqrt (- (* g g) (* h h)))
29.2b	(sqrt (- (* g g) (* h h)))

rewrite24.0ms

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))
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)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
316.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify41.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (33.0ms)

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

prune276.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	72	20	92

Merged error: 31.4b

Counts

92 → 20

regimes745.0ms

Accuracy

62% (1.1b remaining)

Error of 31.6b against oracle of 30.5b and baseline of 33.4b

bsearch143.0ms

Steps

Iters	Range		Point
7	5.335926843290002e-199	8.270369477317621e-197	5.454634309178213e-199

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	53
1	43	53

end0.0ms

sample2.5s

Algorithm

intervals

Results

837.0ms	3741×	body	320	valid
620.0ms	4126×	body	160	valid
598.0ms	8093×	body	80	nan
11.0ms	133×	body	80	valid