Details

sample139.0ms

Algorithm

intervals

Results

50.0ms	115×	body	320	valid
29.0ms	138×	body	160	valid
24.0ms	245×	body	80	nan
0.0ms	3×	body	80	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize29.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite149.0ms

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:

56.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
67.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
9.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series889.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
391.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
73.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify717.0ms

Counts

72 → 72

Iterations

Useful iterations: done (715.0ms)

Iter	Nodes	Cost
0	177	1390
1	397	1227
2	1444	1129
done	5001	1096

prune590.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.1b

localize53.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite128.0ms

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:

17.0ms	(- (* g g) (* h h))
72.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
17.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
441.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
65.0ms	(sqrt (- (* g g) (* h h)))
85.0ms	(sqrt (- (* g g) (* h h)))

simplify785.0ms

Counts

71 → 71

Iterations

Useful iterations: done (783.0ms)

Iter	Nodes	Cost
0	135	1086
1	310	968
2	1342	870
done	5001	863

prune574.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.5b

localize41.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
2.2b	(- (* g g) (* h h))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite47.0ms

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:

13.0ms	(- (* g g) (* h h))
12.0ms	(- (* g g) (* h h))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
43.0ms	(- (* g g) (* h h))
55.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(sqrt (- (* g g) (* h h)))

simplify510.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (80.0ms)

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

prune709.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.5b

localize28.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite120.0ms

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:

18.0ms	(- (* g g) (* h h))
69.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
10.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* g g) (* h h))
464.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
63.0ms	(sqrt (- (* g g) (* h h)))
57.0ms	(sqrt (- (* g g) (* h h)))

simplify873.0ms

Counts

71 → 71

Iterations

Useful iterations: done (869.0ms)

Iter	Nodes	Cost
0	135	1086
1	310	968
2	1342	870
done	5001	863

prune529.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.5b

regimes1.2s

Accuracy

72.5% (0.9b remaining)

Error of 31.7b against oracle of 30.8b and baseline of 34.0b

bsearch197.0ms

Steps

Iters	Range		Point
8	-8.655542616090105e-164	-1.300757130669729e-167	-8.483083017653632e-164

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	71
1	38	71
done	38	71

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.9s	3770×	body	320	valid
1.5s	8040×	body	80	nan
1.2s	4069×	body	160	valid
18.0ms	161×	body	80	valid