Details

sample67.0ms

Algorithm

intervals

Results

19.0ms	116×	body	320	valid
17.0ms	136×	body	160	valid
12.0ms	236×	body	80	nan
0.0ms	4×	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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize18.0ms

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)))

rewrite47.0ms

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))))))
17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series714.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
314.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify48.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (39.0ms)

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

prune449.0ms

Filtered

80 candidates to 73 candidates (91.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.7b

localize22.0ms

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)))

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` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
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))
17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
47.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	315	619
1	1280	588
2	5002	581

prune489.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 31.3b

localize22.0ms

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)))

rewrite16.0ms

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))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
44.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(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

prune490.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

18 alts after pruning (18 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)))

rewrite16.0ms

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)))
5.0ms	(sqrt (- (* g g) (* h h)))

series160.0ms

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

simplify50.0ms

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

prune377.0ms

Filtered

82 candidates to 66 candidates (80.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 31.3b

regimes660.0ms

Accuracy

0% (1.2b remaining)

Error of 32.0b against oracle of 30.8b and baseline of 32.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	23
1	26	23

end0.0ms

sample1.8s

Algorithm

intervals

Results

598.0ms	3701×	body	320	valid
448.0ms	4140×	body	160	valid
403.0ms	7976×	body	80	nan
9.0ms	159×	body	80	valid