Details

sample71.0ms

Algorithm

intervals

Results

21.0ms	116×	body	320	valid
16.0ms	137×	body	160	valid
15.0ms	268×	body	80	nan
0.0ms	3×	body	80	valid

simplify5.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	19	37
1	43	37
2	119	36
3	283	36
4	528	36
5	773	36
6	934	36
7	1133	36
8	2437	36
done	5000	36

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.1b

localize18.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.3b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
34.1b	(sqrt (- (* g g) (* h h)))
34.1b	(sqrt (- (* g g) (* h h)))

rewrite45.0ms

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))))))
18.0ms	(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)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
308.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
46.0ms	(sqrt (- (* g g) (* h h)))
44.0ms	(sqrt (- (* g g) (* h h)))

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: 3 (893.0ms)

Iter	Nodes	Cost
0	177	1390
1	385	1217
2	1258	1121
3	4828	1072
done	5000	1072

prune397.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 36.0b

localize25.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
34.1b	(sqrt (- (* g g) (* h h)))
34.1b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

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:

2.0ms	(- (* g g) (* h h))
16.0ms	(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)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
305.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify2.2s

Counts

71 → 71

Iterations

Useful iterations: 3 (874.0ms)

Iter	Nodes	Cost
0	135	1112
1	296	991
2	1029	887
3	4867	865
done	5000	865

prune434.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 35.4b

localize26.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (* g g) (* h h))
5.4b	(- (* g g) (* h h))
34.1b	(sqrt (- (* g g) (* h h)))
34.1b	(sqrt (- (* g g) (* h h)))

rewrite14.0ms

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))
2.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
32.0ms	(- (* g g) (* h h))
51.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify921.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (45.0ms)

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

prune435.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 35.4b

localize23.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
34.1b	(sqrt (- (* g g) (* h h)))
34.1b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

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:

2.0ms	(- (* g g) (* h h))
16.0ms	(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)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
322.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify2.4s

Counts

71 → 71

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	135	1112
1	296	991
2	1029	887
3	4867	865
done	5000	865

prune336.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 35.4b

regimes673.0ms

Accuracy

67.1% (1.2b remaining)

Error of 31.7b against oracle of 30.6b and baseline of 34.1b

bsearch147.0ms

Steps

Iters	Range		Point
8	8.449989266088164e-213	2.3113180137991623e-210	2.2872650708578154e-210

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	72
1	38	72
done	38	72

end0.0ms

sample2.0s

Algorithm

intervals

Results

658.0ms	3756×	body	320	valid
480.0ms	4102×	body	160	valid
438.0ms	8037×	body	80	nan
10.0ms	142×	body	80	valid