Details

sample95.0ms

Algorithm

intervals

Results

26.0ms	113×	body	320	valid
21.0ms	137×	body	160	valid
20.0ms	268×	body	80	nan
0.0ms	6×	body	80	valid

simplify8.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	19	37
1	60	37
2	256	36
3	828	36
4	3506	36
done	5000	36

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize38.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite131.0ms

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:

48.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
39.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
23.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

447.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
482.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
70.0ms	(sqrt (- (* g g) (* h h)))
67.0ms	(sqrt (- (* g g) (* h h)))

simplify3.3s

Counts

80 → 80

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	172	1528
1	1112	1342
done	5001	1214

prune664.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 29.5b

localize60.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite110.0ms

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:

16.0ms	(- (* g g) (* h h))
52.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
17.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* g g) (* h h))
380.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
74.0ms	(sqrt (- (* g g) (* h h)))
57.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

81 → 81

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	144	1220
1	1093	1062
done	5002	997

prune848.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.2b

localize65.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite112.0ms

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:

19.0ms	(- (* g g) (* h h))
56.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
13.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* g g) (* h h))
502.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
87.0ms	(sqrt (- (* g g) (* h h)))
85.0ms	(sqrt (- (* g g) (* h h)))

simplify1.8s

Counts

81 → 81

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	144	1220
1	1093	1062
done	5002	997

prune702.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.2b

localize42.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
3.0b	(- (* g g) (* h h))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite53.0ms

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))
10.0ms	(- (* g g) (* h h))
19.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
59.0ms	(- (* g g) (* h h))
66.0ms	(sqrt (- (* g g) (* h h)))
84.0ms	(sqrt (- (* g g) (* h h)))

simplify4.1s

Counts

82 → 82

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	62	912
1	360	818
2	3987	726
done	5000	726

prune633.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 29.2b

regimes839.0ms

Accuracy

0% (1.7b remaining)

Error of 32.3b against oracle of 30.6b and baseline of 32.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	39
1	26	39
done	26	39

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.4s	3770×	body	320	valid
1.4s	4087×	body	160	valid
1.1s	7820×	body	80	nan
52.0ms	143×	body	80	valid