Details

sample83.0ms

Algorithm

intervals

Results

24.0ms	124×	body	320	valid
20.0ms	132×	body	160	valid
18.0ms	286×	body	80	nan

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	19	37
1	43	37
2	119	36
3	283	36
4	528	36
5	771	36
6	932	36
7	1131	36
8	2408	36
done	5000	36

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize18.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(sqrt (- (* g g) (* h h)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `flip--`
4×	`add-exp-log` `frac-times` `sqrt-div` `associate-*r/` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-*l/` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

18.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
24.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series708.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
311.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
49.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	177	1390
1	385	1217
2	1258	1121
3	4825	1072
done	5000	1072

prune395.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 31.4b

localize25.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
8.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(sqrt (- (* g g) (* h h)))

rewrite33.0ms

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:

3.0ms	(- (* g g) (* h h))
21.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
326.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
45.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: 3 (479.0ms)

Iter	Nodes	Cost
0	135	1086
1	288	956
2	920	870
3	3540	859
done	5000	859

prune424.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.1b

localize22.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(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` `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:

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)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
36.0ms	(- (* g g) (* h h))
45.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify804.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	55	808
1	122	744
2	380	640
3	1502	640
done	5000	640

prune423.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 31.1b

localize21.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(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` `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:

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)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
31.0ms	(- (* g g) (* h h))
46.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify779.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	55	808
1	122	744
2	380	640
3	1502	640
done	5000	640

prune332.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 31.1b

regimes674.0ms

Accuracy

0% (1.5b remaining)

Error of 32.2b against oracle of 30.7b and baseline of 32.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	38
1	26	38
done	26	38

end0.0ms

sample2.2s

Algorithm

intervals

Results

740.0ms	3693×	body	320	valid
556.0ms	4152×	body	160	valid
486.0ms	7920×	body	80	nan
10.0ms	155×	body	80	valid