Details

sample68.0ms

Algorithm

intervals

Results

38.0ms

441×

body

valid

simplify33.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	47
3	47
2	37
1	17
0	9

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ (* x x) (* (* x 2.0) y)) (* y y))
0.0b	(+ (* x x) (* (* x 2.0) y))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`sum-log`
2×	`add-sqr-sqrt` `pow1` `+-commutative` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `flip-+`
1×	`associate-+l+`

Counts

2 → 24

Calls

2 calls:

47.0ms	(+ (+ (* x x) (* (* x 2.0) y)) (* y y))
7.0ms	(+ (* x x) (* (* x 2.0) y))

series105.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (+ (* x x) (* (* x 2.0) y)) (* y y))
58.0ms	(+ (* x x) (* (* x 2.0) y))

simplify858.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
2	1461
1	210
0	57

prune112.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y (+ (* 2.0 x) y)) (pow x 2))
0.0b	(* (sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2))) (sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2))))
6.5b	(sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2)))
6.5b	(sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2)))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-+l+` `associate-l/` `associate-r/`
1×	`pow2` `distribute-rgt-in` `+-commutative` `sum-log` `rem-square-sqrt` `distribute-lft-in` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

27.0ms	(+ (* y (+ (* 2.0 x) y)) (pow x 2))
156.0ms	(* (sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2))) (sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2))))
26.0ms	(sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2)))
31.0ms	(sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* y (+ (* 2.0 x) y)) (pow x 2))
32.0ms	(* (sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2))) (sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2))))
74.0ms	(sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2)))
74.0ms	(sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2)))

simplify847.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	5002
2	1249
1	247
0	103

prune623.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))) (sqrt (sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))))
6.5b	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
6.5b	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
6.5b	(sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
52×	`add-sqr-sqrt`
35×	`sqrt-pow1`
30×	`pow1` `sqrt-div`
19×	`*-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`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-l/` `associate-r/`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

149.0ms	(* (sqrt (sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))) (sqrt (sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))))
15.0ms	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
22.0ms	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
20.0ms	(sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sqrt (sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))) (sqrt (sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))))
78.0ms	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
96.0ms	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
95.0ms	(sqrt (+ (* y (+ (* 2.0 x) y)) (pow x 2)))

simplify1.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
2	1535
1	342
0	151

prune816.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
6.5b	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
7.1b	(cbrt (+ (* (+ (* x 2.0) y) y) (* x x)))
7.1b	(cbrt (+ (* (+ (* x 2.0) y) y) (* x x)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`cbrt-div` `flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

20.0ms	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
24.0ms	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
16.0ms	(cbrt (+ (* (+ (* x 2.0) y) y) (* x x)))
17.0ms	(cbrt (+ (* (+ (* x 2.0) y) y) (* x x)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
79.0ms	(sqrt (+ (* (+ (* x 2.0) y) y) (* x x)))
211.0ms	(cbrt (+ (* (+ (* x 2.0) y) y) (* x x)))
200.0ms	(cbrt (+ (* (+ (* x 2.0) y) y) (* x x)))

simplify2.0s

Counts

68 → 68

Iterations

Iter	Nodes
done	5002
3	3888
2	603
1	183
0	80

prune619.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.4s

14079×

body

valid