Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

443×

body

valid

simplify271.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-log-exp`
7×	`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 → 25

Calls

2 calls:

8.0ms	(+ (* x x) (* y y))
108.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series70.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ (* x x) (* y y))
42.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify94.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	182	246
1	872	207
2	3289	192
3	5001	192

prune64.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
0.3b	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
6.3b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.3b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite815.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-log-exp`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `sum-log` `add-cbrt-cube`
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` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

120.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
468.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
112.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
112.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
38.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
51.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
54.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	221	1378
1	1003	1237
2	5001	1160

prune217.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (fabs (cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
6.3b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.8b	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.8b	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite673.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

441.0ms	(* (* (fabs (cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
112.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
58.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
60.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (* (fabs (cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
55.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
105.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
107.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify60.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	374	1882
1	1521	1733
2	5002	1701

prune327.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.8b	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.8b	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.8b	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

111.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
58.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
58.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
59.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
107.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
105.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
108.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify64.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	155	853
1	439	794
2	1894	779
3	5003	778

prune247.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes199.0ms

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	10	7
1	10	7

end0.0ms

sample591.0ms

Algorithm

intervals

Results

298.0ms

14173×

body

valid