Details

sample72.0ms

Algorithm

intervals

Results

23.0ms	119×	body	320	valid
15.0ms	131×	body	160	valid
14.0ms	282×	body	80	nan
0.0ms	6×	body	80	valid

simplify127.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	21
1	125	21
2	317	21
3	648	21
4	1073	21
5	1417	21
6	1725	21
7	3333	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: 39.2b

localize18.0ms

Local error

Found 4 expressions with local error:

7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
8.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
33.1b	(sqrt (- (* g g) (* h h)))
33.1b	(sqrt (- (* g g) (* h h)))

rewrite46.0ms

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` `expm1-log1p-u` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

19.0ms	(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)))

series726.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
311.0ms	(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)))

simplify52.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	403	824
1	1484	782
2	5001	775

prune654.0ms

Filtered

80 candidates to 73 candidates (91.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 36.0b

localize20.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
33.1b	(sqrt (- (* g g) (* h h)))
33.1b	(sqrt (- (* g g) (* h h)))

rewrite32.0ms

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` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
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` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
18.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
4.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
306.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	337	621
1	1359	588
2	5001	580

prune482.0ms

Filtered

81 candidates to 70 candidates (86.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 35.6b

localize20.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
4.8b	(- (* g g) (* h h))
33.1b	(sqrt (- (* g g) (* h h)))
33.1b	(sqrt (- (* g g) (* h h)))

rewrite15.0ms

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` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

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)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
34.0ms	(- (* g g) (* h h))
44.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify54.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	135	420
1	482	394
2	1632	388
3	5001	378

prune472.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 35.6b

localize22.0ms

Local error

Found 4 expressions with local error:

4.8b	(- (* g g) (* h h))
4.8b	(- (* g g) (* h h))
33.1b	(sqrt (- (* g g) (* h h)))
33.1b	(sqrt (- (* g g) (* h h)))

rewrite15.0ms

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` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

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)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
32.0ms	(- (* g g) (* h h))
43.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify51.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	135	422
1	482	394
2	1632	388
3	5001	378

prune401.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 35.6b

regimes849.0ms

Accuracy

77.3% (0.7b remaining)

Error of 31.6b against oracle of 31.0b and baseline of 33.8b

bsearch140.0ms

Steps

Iters	Range		Point
9	-7.812206201917273e-155	-8.851182119783336e-163	-8.030232010219059e-161

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	48
1	44	48

end0.0ms

sample1.9s

Algorithm

intervals

Results

633.0ms	3752×	body	320	valid
463.0ms	4100×	body	160	valid
408.0ms	7876×	body	80	nan
8.0ms	148×	body	80	valid