Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

481×

body

valid

simplify277.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (6.0ms)

Iter	Nodes	Cost
0	14	6
1	29	4
2	50	4
3	70	3
4	82	3
5	125	3
6	229	3
7	321	3
8	336	3
9	436	3
10	790	3
11	3492	3
12	5001	3

prune5.0ms

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))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
7×	`fma-def`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate-+l+`

Counts

3 → 51

Calls

3 calls:

8.0ms	(+ (* x x) (* y y))
33.0ms	(+ (+ (* x x) (* y y)) (* y y))
124.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series91.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (* x x) (* y y))
34.0ms	(+ (+ (* x x) (* y y)) (* y y))
33.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify137.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	237	373
1	1141	313
2	4748	287
3	5001	286

prune126.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.2b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
6.5b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
6.5b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `sum-log` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`+-commutative` `associate-+l+` `fma-udef`

Counts

4 → 64

Calls

4 calls:

32.0ms	(+ (+ (* x x) (* y y)) (* y y))
0.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
34.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (+ (* x x) (* y y)) (* y y))
118.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
45.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
48.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify90.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	175	645
1	742	534
2	3044	495
3	5001	493

prune219.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) y)
0.4b	(* (sqrt 2) y)
6.5b	(sqrt (* (hypot x (* (sqrt 2) y)) (hypot x (* (sqrt 2) y))))
6.5b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`pow1`
12×	`associate-l` `sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
7×	`sqrt-pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`rem-sqrt-square` `pow1/2` `sqrt-div` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`pow2` `flip3-+` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+` `hypot-def`

Counts

4 → 84

Calls

4 calls:

10.0ms	(* (sqrt 2) y)
10.0ms	(* (sqrt 2) y)
5.0ms	(sqrt (* (hypot x (* (sqrt 2) y)) (hypot x (* (sqrt 2) y))))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sqrt 2) y)
38.0ms	(* (sqrt 2) y)
106.0ms	(sqrt (* (hypot x (* (sqrt 2) y)) (hypot x (* (sqrt 2) y))))
45.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify104.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	174	446
1	572	420
2	3320	376
3	5001	376

prune289.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

localize9.0ms

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))))
6.5b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.5b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite859.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
15×	`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×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `hypot-def`
1×	`+-commutative` `pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 114

Calls

4 calls:

123.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
478.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
127.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
128.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
33.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
48.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
46.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify47.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	232	1434
1	1052	1249
2	5001	1189

prune237.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 0.0b

regimes170.0ms

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

sample565.0ms

Algorithm

intervals

Results

292.0ms

14189×

body

valid