Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

453×

body

valid

simplify284.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	13	7
1	23	6
2	35	4
3	45	4
4	54	4
5	87	4
6	156	4
7	206	4
8	219	4
9	314	4
10	644	4
11	3197	4
12	5001	4

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.0b	(+ (* x x) (* y y))
0.2b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite19.0ms

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:

6.0ms	(+ (+ (* x x) (* y y)) (* y y))
4.0ms	(+ (* x x) (* y y))
8.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series100.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* y y))
26.0ms	(+ (* x x) (* y y))
35.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify135.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	218	352
1	1048	312
2	4094	291
3	5002	280

prune110.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
5.1b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.1b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite43.0ms

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:

15.0ms	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
14.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
35.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
52.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
53.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	244	1203
1	1165	1041
2	5001	979

prune230.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 13

Calls

1 calls:

10.0ms

(+ (+ (* y (+ y y)) (pow x 2)) (* y y))

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(+ (+ (* y (+ y y)) (pow x 2)) (* y y))

simplify76.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	114	144
1	525	131
2	2265	122
3	5001	122

prune54.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

5.1b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.1b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.2b	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))
5.2b	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
14.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))
18.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
53.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
55.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))
51.0ms	(sqrt (+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y)))

simplify70.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	149	996
1	437	956
2	1864	956
3	5001	938

prune231.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes182.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

end0.0ms

sample540.0ms

Algorithm

intervals

Results

327.0ms

14258×

body

valid