Details

sample134.0ms

Algorithm

intervals

Results

38.0ms	268×	body	80	nan
32.0ms	113×	body	320	valid
26.0ms	137×	body	160	valid
0.0ms	6×	body	80	valid

simplify10.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (28.0ms)

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize43.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite160.0ms

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:

58.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
62.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
10.0ms	(sqrt (- (* g g) (* h h)))
27.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

505.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
457.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
74.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(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	5001	1072

prune576.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 29.8b

localize25.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite90.0ms

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))
52.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series644.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* g g) (* h h))
480.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
68.0ms	(sqrt (- (* g g) (* h h)))
56.0ms	(sqrt (- (* g g) (* h h)))

simplify2.7s

Counts

71 → 71

Iterations

Useful iterations: done (2.7s)

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

prune701.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.2b

localize46.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite102.0ms

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:

14.0ms	(- (* g g) (* h h))
67.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series722.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* g g) (* h h))
520.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
63.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(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

prune662.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.2b

localize59.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
3.0b	(- (* g g) (* h h))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite71.0ms

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:

17.0ms	(- (* g g) (* h h))
15.0ms	(- (* g g) (* h h))
18.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* g g) (* h h))
61.0ms	(- (* g g) (* h h))
76.0ms	(sqrt (- (* g g) (* h h)))
81.0ms	(sqrt (- (* g g) (* h h)))

simplify3.5s

Counts

70 → 70

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	55	808
1	120	744
2	301	640
3	975	640
4	4860	640
done	5000	640

prune334.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 29.2b

regimes632.0ms

Accuracy

0% (1.8b remaining)

Error of 32.3b against oracle of 30.6b and baseline of 32.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.7s	3770×	body	320	valid
1.3s	7820×	body	80	nan
1.1s	4087×	body	160	valid
14.0ms	143×	body	80	valid