Details

sample68.0ms

Algorithm

intervals

Results

20.0ms	124×	body	320	valid
15.0ms	286×	body	80	nan
14.0ms	132×	body	160	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: 37.2b

localize19.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(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:

17.0ms	(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)))
7.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series731.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
324.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
46.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify906.0ms

Counts

80 → 80

Iterations

Useful iterations: done (903.0ms)

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

prune450.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 31.4b

localize26.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
8.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(sqrt (- (* g g) (* h h)))

rewrite32.0ms

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))
19.0ms	(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)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
314.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
49.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

81 → 81

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	144	1192
1	305	1048
2	986	954
3	3912	944
done	5000	943

prune485.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.1b

localize28.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(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)))
5.0ms	(sqrt (- (* g g) (* h h)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
31.0ms	(- (* g g) (* h h))
51.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify881.0ms

Counts

82 → 82

Iterations

Useful iterations: done (879.0ms)

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

prune696.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 31.1b

localize21.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
29.5b	(sqrt (- (* g g) (* h h)))
29.5b	(sqrt (- (* g g) (* h h)))

rewrite15.0ms

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)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
44.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify885.0ms

Counts

82 → 82

Iterations

Useful iterations: done (883.0ms)

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

prune389.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 31.1b

regimes667.0ms

Accuracy

0% (1.5b remaining)

Error of 32.2b against oracle of 30.7b and baseline of 32.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.8s

Algorithm

intervals

Results

600.0ms	3693×	body	320	valid
463.0ms	4152×	body	160	valid
400.0ms	7920×	body	80	nan
9.0ms	155×	body	80	valid