Details

sample91.0ms

Algorithm

intervals

Results

25.0ms	114×	body	320	valid
23.0ms	140×	body	160	valid
22.0ms	307×	body	80	nan
0.0ms	2×	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

prune4.0ms

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: 36.8b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

8.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
10.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (- (* g g) (* h h)))

rewrite36.0ms

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))))))
15.0ms	(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)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(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))))))
50.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify45.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	385	766
1	1380	724
2	5001	718

prune419.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	54	18	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	18	73

Merged error: 31.0b

Counts

73 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (* g g) (* h h))
10.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (- (* g g) (* h h)))

rewrite28.0ms

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:

6.0ms	(- (* 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)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
316.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune390.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	1	16	17
Picked	1	0	1
Done	0	0	0
Total	67	22	89

Merged error: 30.4b

Counts

89 → 22

localize22.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (* g g) (* h h))
10.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (- (* g g) (* h h)))

rewrite28.0ms

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))
15.0ms	(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)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
316.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

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

prune401.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	2	19	21
Picked	1	0	1
Done	0	0	0
Total	71	22	93

Merged error: 30.4b

Counts

93 → 22

localize24.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (* g g) (* h h))
8.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(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)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
326.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify40.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (33.0ms)

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

prune297.0ms

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	2	19	21
Picked	1	0	1
Done	0	0	0
Total	72	21	93

Merged error: 30.4b

Counts

93 → 21

regimes916.0ms

Accuracy

78.8% (0.7b remaining)

Error of 31.1b against oracle of 30.4b and baseline of 33.5b

bsearch223.0ms

Steps

Iters	Range		Point
12	3.0576626726219996e-203	1.338347020619449e-155	2.353375866047627e-160

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	48
1	54	48
2	58	48
3	61	48
4	61	48

end0.0ms

sample2.5s

Algorithm

intervals

Results

843.0ms	3714×	body	320	valid
626.0ms	4153×	body	160	valid
610.0ms	8065×	body	80	nan
10.0ms	133×	body	80	valid