Details

sample72.0ms

Algorithm

intervals

Results

20.0ms	107×	body	320	valid
16.0ms	302×	body	80	nan
16.0ms	141×	body	160	valid
0.0ms	8×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize17.0ms

Local error

Found 4 expressions with local error:

9.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.2b	(sqrt (- (* g g) (* h h)))
31.2b	(sqrt (- (* g g) (* h h)))

rewrite33.0ms

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))))))
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)))

series710.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
315.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(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

prune402.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 33.5b

localize19.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
9.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.2b	(sqrt (- (* g g) (* h h)))
31.2b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

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))
14.0ms	(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)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
298.0ms	(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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	297	571
1	1186	537
2	5001	533

prune407.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 33.0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
3.0b	(- (* g g) (* h h))
31.2b	(sqrt (- (* g g) (* h h)))
31.2b	(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` `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:

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

series157.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
31.0ms	(- (* g g) (* h h))
48.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify46.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	122	378
1	432	350
2	1459	350
3	5001	348

prune415.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 33.0b

localize19.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
9.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.2b	(sqrt (- (* g g) (* h h)))
31.2b	(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` `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))
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)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
303.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune330.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 33.0b

regimes793.0ms

Accuracy

0% (1.3b remaining)

Error of 32.0b against oracle of 30.7b and baseline of 32.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	23
1	27	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

628.0ms	3770×	body	320	valid
461.0ms	4080×	body	160	valid
447.0ms	8049×	body	80	nan
10.0ms	150×	body	80	valid