Details

sample36.0ms

Algorithm

intervals

Results

23.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

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:

7.0ms	(+ (* x x) (* y y))
11.0ms	(sqrt (+ (* x x) (* y y)))

series70.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* x x) (* y y))
40.0ms	(sqrt (+ (* x x) (* y y)))

simplify632.0ms

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
2	787
1	144
0	50

prune163.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.6b

localize26.0ms

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)))

rewrite80.0ms

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:

7.0ms	(+ (* x x) (* y y))
51.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
10.0ms	(sqrt (+ (* x x) (* y y)))
10.0ms	(sqrt (+ (* x x) (* y y)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* x x) (* y y))
43.0ms	(* (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))))
37.0ms	(sqrt (+ (* x x) (* y y)))
56.0ms	(sqrt (+ (* x x) (* y y)))

simplify1.4s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	1525
1	294
0	124

prune378.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.6b

localize44.0ms

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)))

rewrite91.0ms

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:

71.0ms	(sqrt (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))))
6.0ms	(cbrt (+ (* x x) (* y y)))
6.0ms	(cbrt (+ (* x x) (* y y)))
6.0ms	(cbrt (+ (* x x) (* y y)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))))
101.0ms	(cbrt (+ (* x x) (* y y)))
125.0ms	(cbrt (+ (* x x) (* y y)))
116.0ms	(cbrt (+ (* x x) (* y y)))

simplify1.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5002
3	3008
2	707
1	306
0	166

prune582.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 7.6b

localize1.0ms

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

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 7.6b

regimes419.0ms

Accuracy

57.8% (9.2b remaining)

Error of 16.8b against oracle of 7.7b and baseline of 29.4b

bsearch68.0ms

Steps

Iters	Range		Point
8	1.0202913897586463e+104	3.251572119276446e+106	3.221654116729901e+106
9	-2.3877474970773425e+156	-2.0044150779320932e+149	-2.6806112513558803e+152

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample739.0ms

Algorithm

intervals

Results

588.0ms

8000×

body

valid