Details

sample33.0ms

Algorithm

intervals

Results

23.0ms

449×

body

valid

simplify281.0ms

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 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))

rewrite63.0ms

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:

2.0ms	(+ (* x x) (* y y))
14.0ms	(+ (+ (* x x) (* y y)) (* y y))
46.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series98.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
33.0ms	(+ (+ (* x x) (* y y)) (* y y))
34.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify126.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (122.0ms)

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

prune99.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
0.2b	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
5.8b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.8b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite110.0ms

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:

21.0ms	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
60.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))) (* y y))
41.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
49.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
54.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	244	1209
1	1203	1041
2	5001	979

prune221.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* y y) (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))))
0.2b	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
5.8b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.8b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite91.0ms

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:

2.0ms	(+ (* y y) (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))))
60.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* y y) (* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y)))))
36.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))))
56.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
50.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	246	1191
1	1187	1037
2	5002	987

prune219.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
0.2b	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
5.8b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
5.8b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite367.0ms

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:

47.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
213.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
50.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
54.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
35.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
54.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
48.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

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

prune197.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes175.0ms

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

sample887.0ms

Algorithm

intervals

Results

660.0ms

14356×

body

valid