Details

sample68.0ms

Algorithm

intervals

Results

18.0ms	114×	body	320	valid
15.0ms	139×	body	160	valid
15.0ms	301×	body	80	nan
0.0ms	3×	body	80	valid

simplify126.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize21.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
8.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
33.5b	(sqrt (- (* g g) (* h h)))
33.5b	(sqrt (- (* g g) (* h h)))

rewrite41.0ms

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:

16.0ms	(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)))

series896.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
492.0ms	(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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (38.0ms)

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

prune457.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 34.8b

localize19.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
33.5b	(sqrt (- (* g g) (* h h)))
33.5b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

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:

6.0ms	(- (* 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)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
310.0ms	(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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	337	619
1	1359	588
2	5001	580

prune472.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 34.3b

localize26.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
33.5b	(sqrt (- (* g g) (* h h)))
33.5b	(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)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
31.0ms	(- (* g g) (* h h))
50.0ms	(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	420
1	482	394
2	1632	388
3	5001	378

prune489.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 34.3b

localize18.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
33.5b	(sqrt (- (* g g) (* h h)))
33.5b	(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)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
35.0ms	(- (* g g) (* h h))
44.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (44.0ms)

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

prune360.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 34.3b

regimes750.0ms

Accuracy

32.4% (0.8b remaining)

Error of 31.8b against oracle of 31.0b and baseline of 32.2b

bsearch132.0ms

Steps

Iters	Range		Point
8	-2.6274238018146333e-186	-4.889467702331972e-190	-2.5831109636145956e-186

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	38
1	44	38
2	44	38

end0.0ms

sample1.9s

Algorithm

intervals

Results

624.0ms	3771×	body	320	valid
453.0ms	4061×	body	160	valid
403.0ms	8066×	body	80	nan
11.0ms	168×	body	80	valid