Details

sample50.0ms

Algorithm

intervals

Results

26.0ms

443×

body

valid

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (34.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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))

rewrite226.0ms

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:

10.0ms	(+ (* x x) (* y y))
31.0ms	(+ (+ (* x x) (* y y)) (* y y))
184.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series121.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* x x) (* y y))
41.0ms	(+ (+ (* x x) (* y y)) (* y y))
45.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify2.5s

Counts

47 → 47

Iterations

Useful iterations: 3 (915.0ms)

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

prune505.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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 y)) (* y y))
6.1b	(sqrt (+ (* x x) (* y y)))
6.1b	(sqrt (+ (* x x) (* y y)))

rewrite270.0ms

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-+` `add-log-exp`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `sum-log` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

88.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
147.0ms	(+ (+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* y y)) (* y y))
11.0ms	(sqrt (+ (* x x) (* y y)))
18.0ms	(sqrt (+ (* x x) (* y y)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
56.0ms	(+ (+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* y y)) (* y y))
59.0ms	(sqrt (+ (* x x) (* y y)))
53.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.3s

Counts

112 → 112

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	111	2347
1	249	1542
2	778	1300
3	2800	1201
done	5000	1179

prune297.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
0.2b	(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
6.1b	(sqrt (+ (pow x 2) (* 2 (pow y 2))))
6.1b	(sqrt (+ (pow x 2) (* 2 (pow y 2))))

rewrite198.0ms

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:

47.0ms	(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
98.0ms	(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
30.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))
20.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
63.0ms	(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
83.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))
92.0ms	(sqrt (+ (pow x 2) (* 2 (pow y 2))))

simplify3.1s

Counts

110 → 110

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	108	2708
1	247	1699
2	822	1551
3	3241	1429
done	5001	1401

prune356.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow x 2) (* y (* 3 y)))
0.2b	(* y (* 3 y))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

2 → 29

Calls

2 calls:

27.0ms	(+ (pow x 2) (* y (* 3 y)))
38.0ms	(* y (* 3 y))

series88.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ (pow x 2) (* y (* 3 y)))
43.0ms	(* y (* 3 y))

simplify4.7s

Counts

35 → 35

Iterations

Useful iterations: 4 (2.5s)

Iter	Nodes	Cost
0	56	362
1	155	326
2	477	294
3	1323	282
4	3717	280
done	5002	280

prune82.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes177.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	25
1	12	25
done	12	25

end0.0ms

sample1.3s

Algorithm

intervals

Results

794.0ms

14232×

body

valid