Details

sample129.0ms

Algorithm

intervals

Results

51.0ms	109×	body	320	valid
24.0ms	139×	body	160	valid
21.0ms	251×	body	80	nan
1.0ms	8×	body	80	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	19	37
1	43	37
2	122	36
3	298	36
4	590	36
5	959	36
6	1294	36
7	1789	36
8	4192	36
done	5001	36

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize48.0ms

Local error

Found 4 expressions with local error:

9.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
11.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite151.0ms

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:

56.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
62.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
15.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series952.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
477.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
53.0ms	(sqrt (- (* g g) (* h h)))
71.0ms	(sqrt (- (* g g) (* h h)))

simplify827.0ms

Counts

72 → 72

Iterations

Useful iterations: done (824.0ms)

Iter	Nodes	Cost
0	166	1416
1	395	1249
2	1397	1135
done	5000	1090

prune628.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.6b

localize26.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
9.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite98.0ms

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:

8.0ms	(- (* g g) (* h h))
55.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
24.0ms	(sqrt (- (* g g) (* h h)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
445.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
63.0ms	(sqrt (- (* g g) (* h h)))
62.0ms	(sqrt (- (* g g) (* h h)))

simplify923.0ms

Counts

71 → 71

Iterations

Useful iterations: done (920.0ms)

Iter	Nodes	Cost
0	135	1112
1	321	991
2	1515	887
done	5000	869

prune575.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 32.4b

localize32.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
3.6b	(- (* g g) (* h h))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite37.0ms

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:

9.0ms	(- (* g g) (* h h))
8.0ms	(- (* g g) (* h h))
9.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* g g) (* h h))
42.0ms	(- (* g g) (* h h))
81.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify593.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	55	808
1	141	744
2	653	640
done	5001	640

prune628.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 32.3b

localize33.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
9.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite86.0ms

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:

8.0ms	(- (* g g) (* h h))
53.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series647.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
448.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
67.0ms	(sqrt (- (* g g) (* h h)))
80.0ms	(sqrt (- (* g g) (* h h)))

simplify1.0s

Counts

71 → 71

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	135	1112
1	321	991
2	1515	887
done	5000	869

prune553.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.3b

regimes1.2s

Accuracy

0% (1.7b remaining)

Error of 32.1b against oracle of 30.4b and baseline of 32.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	38
1	25	38
done	25	38

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.8s	7861×	body	80	nan
1.7s	3706×	body	320	valid
1.1s	4146×	body	160	valid
18.0ms	148×	body	80	valid