Details

sample155.0ms

Algorithm

intervals

Results

49.0ms	140×	body	160	valid
38.0ms	109×	body	320	valid
26.0ms	231×	body	80	nan
1.0ms	7×	body	80	valid

simplify5.2s

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize23.0ms

Local error

Found 4 expressions with local error:

8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))

rewrite155.0ms

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:

50.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
71.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
18.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

481.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
449.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
65.0ms	(sqrt (- (* g g) (* h h)))
61.0ms	(sqrt (- (* g g) (* h h)))

simplify829.0ms

Counts

72 → 72

Iterations

Useful iterations: done (826.0ms)

Iter	Nodes	Cost
0	177	1390
1	397	1227
2	1442	1129
done	5000	1096

prune664.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 32.7b

localize33.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(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:

8.0ms	(- (* g g) (* h h))
76.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
14.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* g g) (* h h))
444.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
59.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify881.0ms

Counts

71 → 71

Iterations

Useful iterations: done (878.0ms)

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

prune620.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 32.4b

localize33.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
4.4b	(- (* g g) (* h h))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))

rewrite51.0ms

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:

8.0ms	(- (* g g) (* h h))
8.0ms	(- (* g g) (* h h))
16.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* g g) (* h h))
52.0ms	(- (* g g) (* h h))
89.0ms	(sqrt (- (* g g) (* h h)))
83.0ms	(sqrt (- (* g g) (* h h)))

simplify556.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (113.0ms)

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

prune491.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 32.4b

localize37.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
30.4b	(sqrt (- (* g g) (* h h)))
30.4b	(sqrt (- (* g g) (* h h)))

rewrite134.0ms

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:

10.0ms	(- (* g g) (* h h))
93.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
20.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* g g) (* h h))
466.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
89.0ms	(sqrt (- (* g g) (* h h)))
73.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: done (1.0s)

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

prune445.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.4b

regimes803.0ms

Accuracy

0% (1.5b remaining)

Error of 31.9b against oracle of 30.4b and baseline of 31.9b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.1s	3697×	body	320	valid
1.8s	4159×	body	160	valid
1.1s	7982×	body	80	nan
17.0ms	144×	body	80	valid