Details

sample245.0ms

Algorithm

intervals

Results

96.0ms	146×	body	160	valid
67.0ms	104×	body	320	valid
53.0ms	285×	body	80	nan
1.0ms	6×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
5	2000
4	1243
3	370
2	119
1	47
0	19

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.3b

localize51.0ms

Local error

Found 4 expressions with local error:

7.6b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
9.1b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
116×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
84×	`cbrt-prod`
62×	`add-cube-cbrt`
28×	`difference-of-squares`
21×	`sqrt-prod`
13×	`distribute-lft-out--`
7×	`div-inv`
6×	`pow1` `cbrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `pow1/3` `associate-*r/` `flip-+` `flip--`
1×	`associate-*l/` `associate-/r/`

Counts

4 → 150

Calls

4 calls:

26.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
28.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
19.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series890.0ms

Counts

4 → 12

Calls

4 calls:

431.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
318.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
83.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

162 → 162

Iterations

Iter	Nodes
done	2001
2	2001
1	890
0	409

prune2.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 33.1b

localize48.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
9.1b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
116×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
83×	`cbrt-prod`
62×	`add-cube-cbrt`
29×	`difference-of-squares`
21×	`sqrt-prod`
13×	`distribute-lft-out--`
7×	`div-inv`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 151

Calls

4 calls:

12.0ms	(- (* g g) (* h h))
13.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
13.0ms	(sqrt (- (* g g) (* h h)))
25.0ms	(sqrt (- (* g g) (* h h)))

series584.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* g g) (* h h))
390.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
61.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(sqrt (- (* g g) (* h h)))

simplify1.8s

Counts

163 → 163

Iterations

Iter	Nodes
done	2000
3	2000
2	1879
1	776
0	370

prune3.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.6b

localize83.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
10×	`add-sqr-sqrt`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 75

Calls

4 calls:

15.0ms	(- (* g g) (* h h))
18.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* g g) (* h h))
60.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
done	2011
4	2011
3	1666
2	377
1	138
0	64

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.6b

localize77.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
9.1b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
116×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
83×	`cbrt-prod`
62×	`add-cube-cbrt`
29×	`difference-of-squares`
21×	`sqrt-prod`
13×	`distribute-lft-out--`
7×	`div-inv`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 151

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
18.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* g g) (* h h))
303.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
70.0ms	(sqrt (- (* g g) (* h h)))
52.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

163 → 163

Iterations

Iter	Nodes
done	2000
3	2000
2	1879
1	776
0	370

prune2.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.6b

regimes789.0ms

Accuracy

61.7% (1.5b remaining)

Error of 31.6b against oracle of 30.1b and baseline of 34.0b

bsearch405.0ms

Steps

Iters	Range		Point
11	-4.5596823755857694e-157	-7.384045806005983e-186	-1.5974918824598454e-162

simplify16.0ms

Iterations

Iter	Nodes
done	41
1	41
0	35

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.5s	3746×	body	320	valid
2.1s	8203×	body	80	nan
2.1s	4124×	body	160	valid
22.0ms	130×	body	80	valid