Details

sample195.0ms

Algorithm

intervals

Results

74.0ms	118×	body	160	valid
47.0ms	133×	body	320	valid
33.0ms	297×	body	80	nan
1.0ms	5×	body	80	valid

simplify10.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	19	37
1	43	37
2	122	36
3	297	36
4	583	36
5	891	36
6	1079	36
7	1300	36
8	2491	36
done	5000	36

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize38.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
9.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite173.0ms

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:

64.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
79.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
17.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

477.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
433.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
86.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

72 → 72

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	177	1390
1	385	1217
2	1281	1121
done	5000	1072

prune661.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 27.9b

localize42.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite109.0ms

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:

9.0ms	(- (* g g) (* h h))
60.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
18.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* g g) (* h h))
489.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
80.0ms	(sqrt (- (* g g) (* h h)))
54.0ms	(sqrt (- (* g g) (* h h)))

simplify1.9s

Counts

71 → 71

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	135	1086
1	286	956
2	846	870
3	3101	859
done	5000	836

prune765.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 26.7b

localize56.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite130.0ms

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:

9.0ms	(- (* g g) (* h h))
97.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
12.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* g g) (* h h))
458.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
65.0ms	(sqrt (- (* g g) (* h h)))
61.0ms	(sqrt (- (* g g) (* h h)))

simplify2.0s

Counts

71 → 71

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	135	1086
1	286	956
2	846	870
3	3101	859
done	5000	836

prune676.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 26.7b

localize65.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
9.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite108.0ms

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:

12.0ms	(- (* g g) (* h h))
57.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series617.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* g g) (* h h))
462.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
56.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify2.8s

Counts

71 → 71

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	135	1112
1	294	991
2	968	887
3	3952	865
done	5000	855

prune481.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 26.7b

regimes905.0ms

Accuracy

64.2% (1.3b remaining)

Error of 30.6b against oracle of 29.3b and baseline of 33.0b

bsearch307.0ms

Steps

Iters	Range		Point
10	-2.6442941124154403e-179	-3.996486807713146e-190	-1.213814236807821e-179

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	71
1	36	71
done	36	71

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.2s	3714×	body	320	valid
1.4s	4134×	body	160	valid
1.2s	8019×	body	80	nan
17.0ms	152×	body	80	valid