Details

sample68.0ms

Algorithm

intervals

Results

19.0ms	116×	body	320	valid
15.0ms	236×	body	80	nan
15.0ms	136×	body	160	valid
0.0ms	4×	body	80	valid

simplify115.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize17.0ms

Local error

Found 4 expressions with local error:

7.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.1b	(sqrt (- (* g g) (* h h)))
30.1b	(sqrt (- (* g g) (* h h)))

rewrite45.0ms

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:

20.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* 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)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
313.0ms	(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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (35.0ms)

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

prune395.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.7b

localize26.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
7.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.1b	(sqrt (- (* g g) (* h h)))
30.1b	(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:

2.0ms	(- (* 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)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
506.0ms	(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)))

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

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

prune411.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.3b

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
3.2b	(- (* g g) (* h h))
30.1b	(sqrt (- (* g g) (* h h)))
30.1b	(sqrt (- (* g g) (* h h)))

rewrite14.0ms

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:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
31.0ms	(- (* g g) (* h h))
44.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(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

prune394.0ms

Filtered

70 candidates to 54 candidates (77.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.3b

localize24.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
3.2b	(- (* g g) (* h h))
30.1b	(sqrt (- (* g g) (* h h)))
30.1b	(sqrt (- (* g g) (* h h)))

rewrite14.0ms

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:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
50.0ms	(sqrt (- (* g g) (* h h)))
44.0ms	(sqrt (- (* g g) (* h h)))

simplify48.0ms

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

prune300.0ms

Filtered

70 candidates to 54 candidates (77.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.3b

regimes600.0ms

Accuracy

68.1% (0.9b remaining)

Error of 31.7b against oracle of 30.8b and baseline of 33.7b

bsearch215.0ms

Steps

Iters	Range		Point
11	1.8561269738033104e-245	1.7673904685269123e-220	1.7494555242604437e-220

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	38
1	49	38
2	53	38
3	56	38
4	56	38

end0.0ms

sample1.8s

Algorithm

intervals

Results

610.0ms	3701×	body	320	valid
455.0ms	4140×	body	160	valid
400.0ms	7976×	body	80	nan
9.0ms	159×	body	80	valid