Details

sample44.0ms

Algorithm

intervals

Results

23.0ms

443×

body

valid

simplify60.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (20.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	23	13
3	35	9
4	43	9
5	46	9
done	46	9

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
3×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`associate-+l+`

Counts

3 → 38

Calls

3 calls:

14.0ms	(+ (* x x) (* y y))
44.0ms	(+ (+ (* x x) (* y y)) (* y y))
168.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series154.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* x x) (* y y))
66.0ms	(+ (+ (* x x) (* y y)) (* y y))
53.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify2.3s

Counts

47 → 47

Iterations

Useful iterations: 3 (973.0ms)

Iter	Nodes	Cost
0	70	791
1	211	667
2	725	591
3	2852	513
done	5000	513

prune177.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* 2 (pow y 2))
0.1b	(+ (+ (* x x) (* y y)) (* 2 (pow y 2)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-log-exp`
8×	`add-exp-log` `associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `sum-log` `unswap-sqr`
3×	`pow1` `associate-l` `prod-exp`
2×	`+-commutative` `flip3-+` `flip-+` `unpow2` `sqr-pow`
1×	`pow-to-exp` `associate-+l+` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 51

Calls

3 calls:

12.0ms	(+ (* x x) (* y y))
14.0ms	(* 2 (pow y 2))
38.0ms	(+ (+ (* x x) (* y y)) (* 2 (pow y 2)))

series137.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* x x) (* y y))
50.0ms	(* 2 (pow y 2))
49.0ms	(+ (+ (* x x) (* y y)) (* 2 (pow y 2)))

simplify2.8s

Counts

60 → 60

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	98	703
1	262	630
2	775	521
3	3061	503
done	5000	486

prune219.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(+ (+ (* x x) (* y y)) (* (* y 2) y))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

13.0ms	(+ (* x x) (* y y))
59.0ms	(+ (+ (* x x) (* y y)) (* (* y 2) y))

series108.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(+ (* x x) (* y y))
59.0ms	(+ (+ (* x x) (* y y)) (* (* y 2) y))

simplify1.9s

Counts

30 → 30

Iterations

Useful iterations: 3 (854.0ms)

Iter	Nodes	Cost
0	55	471
1	184	415
2	659	349
3	2528	337
done	5001	337

prune107.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
0.1b	(+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* (* y 2) y))
6.1b	(sqrt (+ (* x x) (* y y)))
6.1b	(sqrt (+ (* x x) (* y y)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

76.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
52.0ms	(+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* (* y 2) y))
12.0ms	(sqrt (+ (* x x) (* y y)))
8.0ms	(sqrt (+ (* x x) (* y y)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
57.0ms	(+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* (* y 2) y))
54.0ms	(sqrt (+ (* x x) (* y y)))
54.0ms	(sqrt (+ (* x x) (* y y)))

simplify3.3s

Counts

110 → 110

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	109	2276
1	253	1481
2	847	1291
3	3301	1193
done	5000	1171

prune325.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	14	21
done	14	21

end0.0ms

sample1.4s

Algorithm

intervals

Results

863.0ms

14232×

body

valid