Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	6

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize49.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
30.4b	(sqrt (+ (* x x) (* y y)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
2×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+` `insert-posit16`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

2 → 28

Calls

2 calls:

39.0ms	(+ (* x x) (* y y))
34.0ms	(sqrt (+ (* x x) (* y y)))

series125.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(+ (* x x) (* y y))
85.0ms	(sqrt (+ (* x x) (* y y)))

simplify4.8s

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
3	1563
2	372
1	129
0	50

prune404.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.8b

localize158.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.5b	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
30.4b	(sqrt (+ (* x x) (* y y)))
30.4b	(sqrt (+ (* x x) (* y y)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `insert-posit16`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

25.0ms	(+ (* x x) (* y y))
176.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
16.0ms	(sqrt (+ (* x x) (* y y)))
30.0ms	(sqrt (+ (* x x) (* y y)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* x x) (* y y))
77.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
57.0ms	(sqrt (+ (* x x) (* y y)))
55.0ms	(sqrt (+ (* x x) (* y y)))

simplify4.5s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
3	1680
2	571
1	271
0	124

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.8b

localize257.0ms

Local error

Found 4 expressions with local error:

30.4b	(sqrt (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))))
31.3b	(cbrt (+ (* x x) (* y y)))
31.3b	(cbrt (+ (* x x) (* y y)))
31.3b	(cbrt (+ (* x x) (* y y)))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 93

Calls

4 calls:

190.0ms	(sqrt (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))))
11.0ms	(cbrt (+ (* x x) (* y y)))
22.0ms	(cbrt (+ (* x x) (* y y)))
25.0ms	(cbrt (+ (* x x) (* y y)))

series701.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))))
218.0ms	(cbrt (+ (* x x) (* y y)))
201.0ms	(cbrt (+ (* x x) (* y y)))
213.0ms	(cbrt (+ (* x x) (* y y)))

simplify5.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
4	2402
3	941
2	477
1	288
0	166

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 7.8b

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 7.8b

regimes1.7s

Accuracy

55% (10.6b remaining)

Error of 18.5b against oracle of 7.9b and baseline of 31.4b

bsearch154.0ms

Steps

Iters	Range		Point
8	1.0202913897586463e+104	3.251572119276446e+106	3.161818111636812e+106
3	1.3373501688296423e-158	1.7803579200561248e-158	1.6972939667011593e-158
8	-3.147576329037351e-256	-6.1523601201211696e-260	-2.35268515513709e-257
9	-2.3877474970773425e+156	-2.0044150779320932e+149	-2.5847343597756595e+152

simplify8.0ms

Iterations

Iter	Nodes
done	20
1	20
0	19

end0.0ms

sample848.0ms

Algorithm

intervals

Results

567.0ms

8000×

body

valid