Details

sample201.0ms

Algorithm

intervals

Results

77.0ms	133×	body	320	valid
38.0ms	294×	body	80	nan
33.0ms	118×	body	160	valid
1.0ms	5×	body	80	valid

simplify13.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	125	36
3	314	36
4	633	36
5	1023	36
6	1325	36
7	1628	36
8	2988	36
done	5001	36

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize41.0ms

Local error

Found 4 expressions with local error:

6.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

41.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
20.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

440.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
431.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
64.0ms	(sqrt (- (* g g) (* h h)))
68.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	172	1528
1	402	1345
2	1359	1225
done	5000	1180

prune710.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 28.4b

localize27.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(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`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
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))
81.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
23.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series655.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
468.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
65.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify3.5s

Counts

81 → 81

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	146	1220
1	334	1078
2	1124	960
3	4776	938
done	5000	938

prune612.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 27.9b

localize29.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* g g) (* h h))
7.4b	(cbrt (/ 1.0 (/ (* 2.0 a) (- (sqrt (- (* g g) (* h h))) g))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
41×	`cbrt-prod`
39×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
25×	`add-cube-cbrt`
11×	`sqrt-prod`
9×	`difference-of-squares`
7×	`associate-/r/`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`distribute-lft-out--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `cbrt-div` `fma-neg` `pow1/3` `diff-log` `prod-diff`

Counts

4 → 105

Calls

4 calls:

9.0ms	(- (* g g) (* h h))
31.0ms	(cbrt (/ 1.0 (/ (* 2.0 a) (- (sqrt (- (* g g) (* h h))) g))))
12.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* g g) (* h h))
377.0ms	(cbrt (/ 1.0 (/ (* 2.0 a) (- (sqrt (- (* g g) (* h h))) g))))
51.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (- (* g g) (* h h)))

simplify2.5s

Counts

117 → 117

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	272	2457
1	489	2269
2	1372	2169
3	4860	2144
done	5000	2144

prune836.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 27.9b

localize28.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* g g) (* h h))
1.6b	(- (* g g) (* h h))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(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` `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:

9.0ms	(- (* g g) (* h h))
9.0ms	(- (* g g) (* h h))
12.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series173.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* g g) (* h h))
34.0ms	(- (* g g) (* h h))
48.0ms	(sqrt (- (* g g) (* h h)))
52.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

82 → 82

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	62	912
1	132	824
2	347	722
3	1112	722
done	5001	712

prune468.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 27.9b

regimes979.0ms

Accuracy

0% (3.7b remaining)

Error of 33.7b against oracle of 30.0b and baseline of 33.7b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	75
1	31	75
done	31	75

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.7s	3719×	body	320	valid
1.4s	8064×	body	80	nan
993.0ms	4126×	body	160	valid
15.0ms	155×	body	80	valid