Details

sample44.0ms

Algorithm

intervals

Results

24.0ms

445×

body

valid

simplify23.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite76.0ms

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:

14.0ms	(+ (* x x) (* (* x 2.0) y))
61.0ms	(+ (+ (* x x) (* (* x 2.0) y)) (* y y))

series91.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(+ (* x x) (* (* x 2.0) y))
43.0ms	(+ (+ (* x x) (* (* x 2.0) y)) (* y y))

simplify956.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5002
2	1488
1	210
0	57

prune137.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (+ x (* 2.0 y))) (pow y 2))
0.0b	(* (sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2))) (sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2))))
5.8b	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))
5.8b	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))

rewrite186.0ms

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:

22.0ms	(+ (* x (+ x (* 2.0 y))) (pow y 2))
109.0ms	(* (sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2))) (sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2))))
20.0ms	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))
29.0ms	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* x (+ x (* 2.0 y))) (pow y 2))
49.0ms	(* (sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2))) (sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2))))
86.0ms	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))
79.0ms	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))

simplify687.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1131
1	255
0	105

prune499.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))) (sqrt (sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))))
5.8b	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))
5.8b	(sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))
5.8b	(sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))

rewrite199.0ms

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:

128.0ms	(* (sqrt (sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))) (sqrt (sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))))
32.0ms	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))
18.0ms	(sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))
16.0ms	(sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sqrt (sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))) (sqrt (sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))))
83.0ms	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))
72.0ms	(sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))
75.0ms	(sqrt (+ (* (+ x (* y 2.0)) x) (* y y)))

simplify1.9s

Counts

140 → 140

Iterations

Iter	Nodes
done	5002
2	1770
1	340
0	150

prune911.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))) (sqrt (cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))))
5.8b	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))
6.3b	(cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))
6.3b	(cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
10×	`cbrt-prod`
9×	`associate-r`
7×	`pow1`
6×	`cbrt-div` `add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3` `associate-*r/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

52.0ms	(* (fabs (cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))) (sqrt (cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))))
17.0ms	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))
7.0ms	(cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))
8.0ms	(cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))

series791.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(* (fabs (cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))) (sqrt (cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))))
106.0ms	(sqrt (+ (* x (+ x (* 2.0 y))) (pow y 2)))
209.0ms	(cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))
214.0ms	(cbrt (+ (* (+ x (* y 2.0)) x) (* y y)))

simplify945.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
2	1719
1	409
0	170

prune733.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes176.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.4s

14131×

body

valid