Details

sample145.0ms

Algorithm

intervals

Results

41.0ms	132×	body	160	valid
36.0ms	118×	body	320	valid
25.0ms	265×	body	80	nan
1.0ms	6×	body	80	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4870
7	2196
6	1617
5	1088
4	640
3	315
2	125
1	44
0	19

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.1b

localize59.0ms

Local error

Found 4 expressions with local error:

8.1b	(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))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (- (* g g) (* h h)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `frac-times` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*r/` `add-exp-log` `log1p-expm1-u` `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 → 68

Calls

4 calls:

44.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(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)))

series979.0ms

Counts

4 → 12

Calls

4 calls:

420.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
419.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
69.0ms	(sqrt (- (* g g) (* h h)))
71.0ms	(sqrt (- (* g g) (* h h)))

simplify1.0s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1507
1	415
0	172

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 30.5b

localize60.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (* (- g h) (+ g h)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

13.0ms	(- (* g g) (* h h))
42.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (* (- g h) (+ g h)))

series713.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
481.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
79.0ms	(sqrt (- (* g g) (* h h)))
110.0ms	(sqrt (* (- g h) (+ g h)))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	2680
1	470
0	189

prune981.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 30.0b

localize90.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
8.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (* (- g h) (+ g h)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

12.0ms	(- (* g g) (* h h))
43.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (* (- g h) (+ g h)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* g g) (* h h))
433.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
67.0ms	(sqrt (- (* g g) (* h h)))
100.0ms	(sqrt (* (- g h) (+ g h)))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	2680
1	470
0	189

prune998.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 30.0b

localize76.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (* (- g h) (+ g h)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

7.0ms	(- (* g g) (* h h))
44.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (* (- g h) (+ g h)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* g g) (* h h))
403.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
78.0ms	(sqrt (- (* g g) (* h h)))
73.0ms	(sqrt (* (- g h) (+ g h)))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	2780
1	492
0	191

prune938.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 30.0b

regimes1.2s

Accuracy

66.1% (1.2b remaining)

Error of 31.0b against oracle of 29.8b and baseline of 33.3b

bsearch414.0ms

Steps

Iters	Range		Point
11	9.11596973352329e-156	1.050264105176939e-135	9.191731187329127e-156

simplify17.0ms

Iterations

Iter	Nodes
done	62
2	62
1	57
0	43

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.9s	3719×	body	320	valid
1.6s	8101×	body	80	nan
1.0s	4125×	body	160	valid
16.0ms	156×	body	80	valid