Details

sample77.0ms

Algorithm

intervals

Results

23.0ms	123×	body	320	valid
14.0ms	291×	body	80	nan
14.0ms	127×	body	160	valid
0.0ms	6×	body	80	valid

simplify124.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	21
1	125	21
2	317	21
3	648	21
4	1073	21
5	1417	21
6	1725	21
7	3333	21
8	5002	21
done	5002	21

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize19.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
11.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))

rewrite95.0ms

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:

35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
33.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
13.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series741.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
316.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
54.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify45.0ms

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	403	824
1	1484	782
2	5001	775
done	5001	775

prune448.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 33.6b

localize26.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
6.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))

rewrite68.0ms

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:

9.0ms	(- (* g g) (* h h))
35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
326.0ms	(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)))

simplify40.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	337	619
1	1359	588
2	5001	580
done	5001	580

prune491.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 33.0b

localize25.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
6.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))

rewrite67.0ms

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:

11.0ms	(- (* g g) (* h h))
32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
329.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
53.0ms	(sqrt (- (* g g) (* h h)))
47.0ms	(sqrt (- (* g g) (* h h)))

simplify40.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	337	619
1	1359	588
2	5001	580
done	5001	580

prune471.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 33.0b

localize27.0ms

Local error

Found 4 expressions with local error:

32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))
32.9b	(sqrt (- (* g g) (* h h)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

11.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))
52.0ms	(sqrt (- (* g g) (* h h)))

simplify56.0ms

Counts

84 → 84

Iterations

Useful iterations: 4 (50.0ms)

Iter	Nodes	Cost
0	105	456
1	265	444
2	693	444
3	1746	444
4	5001	440
done	5001	440

prune511.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 32.9b

regimes1.0s

Accuracy

83.7% (0.6b remaining)

Error of 32.1b against oracle of 31.5b and baseline of 35.4b

bsearch133.0ms

Steps

Iters	Range		Point
8	-8.976264522949468e-179	-1.4293628387956914e-182	-8.824957770492126e-179

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	40
1	39	40
done	39	40

end0.0ms

sample2.0s

Algorithm

intervals

Results

619.0ms	3790×	body	320	valid
442.0ms	4058×	body	160	valid
409.0ms	7987×	body	80	nan
8.0ms	152×	body	80	valid