Details

sample126.0ms

Algorithm

intervals

Results

47.0ms	109×	body	320	valid
25.0ms	139×	body	160	valid
21.0ms	251×	body	80	nan
1.0ms	8×	body	80	valid

simplify6.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	125	36
3	315	36
4	640	36
5	1087	36
6	1581	36
7	2180	36
8	4936	36
done	5000	36

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize54.0ms

Local error

Found 4 expressions with local error:

9.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
11.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite157.0ms

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:

50.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
71.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
12.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

386.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
476.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
77.0ms	(sqrt (- (* g g) (* h h)))
84.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	183	1500
1	418	1325
2	1557	1219
done	5001	1192

prune727.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.9b

localize51.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
9.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(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` `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:

17.0ms	(- (* g g) (* h h))
65.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* g g) (* h h))
403.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
62.0ms	(sqrt (- (* g g) (* h h)))
59.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

81 → 81

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	144	1220
1	336	1085
2	1601	975
done	5001	956

prune630.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.6b

localize52.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
3.6b	(- (* g g) (* h h))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite98.0ms

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:

18.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
23.0ms	(sqrt (- (* g g) (* h h)))
24.0ms	(sqrt (- (* g g) (* h h)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
52.0ms	(- (* g g) (* h h))
71.0ms	(sqrt (- (* g g) (* h h)))
79.0ms	(sqrt (- (* g g) (* h h)))

simplify582.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	62	912
1	151	832
2	699	722
done	5001	722

prune719.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.6b

localize32.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
9.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite105.0ms

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:

9.0ms	(- (* g g) (* h h))
62.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series566.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
408.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(sqrt (- (* g g) (* h h)))

simplify1.6s

Counts

81 → 81

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	144	1220
1	336	1085
2	1601	975
done	5001	956

prune759.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 32.6b

regimes1.3s

Accuracy

0% (1.5b remaining)

Error of 32.1b against oracle of 30.7b and baseline of 32.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.9s	3706×	body	320	valid
1.7s	4146×	body	160	valid
1.1s	7861×	body	80	nan
54.0ms	148×	body	80	valid