Details

sample68.0ms

Algorithm

intervals

Results

20.0ms	116×	body	320	valid
15.0ms	136×	body	160	valid
12.0ms	236×	body	80	nan
4.0ms	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

prune4.0ms

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)))

rewrite38.0ms

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:

16.0ms	(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)))

series918.0ms

Counts

4 → 12

Calls

4 calls:

501.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
319.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify49.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (37.0ms)

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

prune396.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 31.7b

localize25.0ms

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)))

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)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* 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)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune416.0ms

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)))

rewrite17.0ms

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)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
48.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify47.0ms

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

prune397.0ms

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)))

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)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
31.0ms	(- (* g g) (* h h))
51.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify48.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (42.0ms)

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

prune303.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 31.3b

regimes652.0ms

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

sample1.9s

Algorithm

intervals

Results

634.0ms	3701×	body	320	valid
467.0ms	4140×	body	160	valid
421.0ms	7976×	body	80	nan
9.0ms	159×	body	80	valid