Details

sample69.0ms

Algorithm

intervals

Results

20.0ms	121×	body	320	valid
16.0ms	259×	body	80	nan
14.0ms	128×	body	160	valid
0.0ms	7×	body	80	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	122	36
3	298	36
4	575	36
5	886	36
6	1138	36
7	1412	36
8	2896	36
done	5001	36

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize18.0ms

Local error

Found 4 expressions with local error:

6.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite49.0ms

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` `expm1-log1p-u` `frac-times` `sqrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-*l/` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

19.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
317.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
50.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify905.0ms

Counts

80 → 80

Iterations

Useful iterations: done (903.0ms)

Iter	Nodes	Cost
0	183	1500
1	403	1315
2	1335	1211
done	5000	1165

prune445.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 34.3b

localize19.0ms

Local error

Found 4 expressions with local error:

4.2b	(- (* g g) (* h h))
6.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite34.0ms

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` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
20.0ms	(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)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
316.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
52.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify860.0ms

Counts

81 → 81

Iterations

Useful iterations: done (858.0ms)

Iter	Nodes	Cost
0	144	1220
1	313	1079
2	1107	975
done	5000	953

prune490.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 33.7b

localize19.0ms

Local error

Found 4 expressions with local error:

4.2b	(- (* g g) (* h h))
4.2b	(- (* g g) (* h h))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

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` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* 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:

32.0ms	(- (* g g) (* h h))
37.0ms	(- (* g g) (* h h))
46.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	62	912
1	134	824
2	426	722
3	1689	722
done	5001	720

prune462.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 33.7b

localize21.0ms

Local error

Found 4 expressions with local error:

4.2b	(- (* g g) (* h h))
4.2b	(- (* g g) (* h h))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite16.0ms

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` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
33.0ms	(- (* g g) (* h h))
45.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify866.0ms

Counts

82 → 82

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	62	912
1	134	824
2	426	722
3	1689	722
done	5001	720

prune401.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 33.7b

regimes765.0ms

Accuracy

0% (1.8b remaining)

Error of 33.0b against oracle of 31.2b and baseline of 33.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	24	38
done	24	38

end0.0ms

sample1.8s

Algorithm

intervals

Results

616.0ms	3755×	body	320	valid
448.0ms	4089×	body	160	valid
390.0ms	7743×	body	80	nan
9.0ms	156×	body	80	valid