Details

sample67.0ms

Algorithm

intervals

Results

18.0ms	118×	body	320	valid
14.0ms	136×	body	160	valid
11.0ms	229×	body	80	nan
0.0ms	2×	body	80	valid

simplify7.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	19	37
1	43	37
2	122	36
3	297	36
4	583	36
5	891	36
6	1079	36
7	1300	36
8	2491	36
done	5000	36

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize18.0ms

Local error

Found 4 expressions with local error:

8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.2b	(sqrt (- (* g g) (* h h)))
28.2b	(sqrt (- (* g g) (* h h)))

rewrite88.0ms

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` `frac-times` `flip3--` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

33.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
34.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series756.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
335.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
54.0ms	(sqrt (- (* g g) (* h h)))

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	166	1416
1	385	1249
2	1268	1135
3	4957	1078
done	5000	1076

prune417.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 30.2b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
8.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.2b	(sqrt (- (* g g) (* h h)))
28.2b	(sqrt (- (* g g) (* h h)))

rewrite60.0ms

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` `sqrt-div` `add-cbrt-cube`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
34.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
327.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify2.1s

Counts

71 → 71

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	137	1112
1	317	990
2	1031	876
3	4329	853
done	5001	842

prune409.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.4b

localize23.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.2b	(sqrt (- (* g g) (* h h)))
28.2b	(sqrt (- (* g g) (* h h)))

rewrite62.0ms

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

Counts

4 → 59

Calls

4 calls:

10.0ms	(- (* g g) (* h h))
32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
310.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

71 → 71

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	135	1112
1	294	991
2	968	887
3	3952	865
done	5000	855

prune421.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.4b

localize21.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.2b	(sqrt (- (* g g) (* h h)))
28.2b	(sqrt (- (* g g) (* h h)))

rewrite63.0ms

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

Counts

4 → 59

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
318.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
52.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

71 → 71

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	135	1112
1	294	991
2	968	887
3	3952	865
done	5000	855

prune345.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.3b

regimes718.0ms

Accuracy

75% (1.4b remaining)

Error of 32.0b against oracle of 30.6b and baseline of 36.4b

bsearch175.0ms

Steps

Iters	Range		Point
11	4.433686711295453e-204	1.0858178099828958e-181	1.0748725376260726e-181

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	33	80
1	42	78
done	42	78

end0.0ms

sample2.0s

Algorithm

intervals

Results

594.0ms	3687×	body	320	valid
452.0ms	4170×	body	160	valid
389.0ms	7970×	body	80	nan
8.0ms	143×	body	80	valid