Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

443×

body

valid

simplify274.0ms

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))

rewrite124.0ms

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))
115.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series60.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(+ (* x x) (* y y))
36.0ms	(+ (+ (+ (* 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

prune72.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

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)))

rewrite865.0ms

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:

133.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
494.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
116.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
118.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (+ (+ (* 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))))
46.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
50.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (29.0ms)

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

prune227.0ms

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)))

rewrite728.0ms

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:

470.0ms	(* (* (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)))))
118.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
62.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
75.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (* (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)))))
52.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
98.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
98.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify52.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

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

prune342.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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)))

rewrite740.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

497.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
117.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
60.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
63.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
53.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
102.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
103.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify104.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	293	1783
1	902	1707
2	3854	1691
3	5001	1671

prune345.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes226.0ms

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

sample600.0ms

Algorithm

intervals

Results

297.0ms

14173×

body

valid