Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

476×

body

valid

simplify285.0ms

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))

rewrite74.0ms

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:

3.0ms	(+ (* x x) (* y y))
13.0ms	(+ (+ (* x x) (* y y)) (* y y))
57.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series102.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify137.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (132.0ms)

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

prune127.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b	(fma (pow y 2) 3 (pow x 2))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (pow y 2) 3 (pow x 2))

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

(fma (pow y 2) 3 (pow x 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	29	59
1	78	52
2	260	52
3	1095	52
4	5002	52

prune40.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.1b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
5.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite46.0ms

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:

13.0ms	(+ (+ (* 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))
16.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* y y))
128.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
51.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
48.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify92.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (85.0ms)

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

prune211.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot y (hypot x (* (sqrt 2) y)))
0.3b	(* (hypot y (hypot x (* (sqrt 2) y))) (hypot y (hypot x (* (sqrt 2) y))))
0.4b	(* (sqrt 2) y)
0.4b	(* (sqrt 2) y)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
15×	`pow1` `associate-l`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r`
8×	`sqrt-prod`
5×	`hypot-udef` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `pow-sqr` `pow-prod-up`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot y (hypot x (* (sqrt 2) y)))
3.0ms	(* (hypot y (hypot x (* (sqrt 2) y))) (hypot y (hypot x (* (sqrt 2) y))))
4.0ms	(* (sqrt 2) y)
5.0ms	(* (sqrt 2) y)

series887.0ms

Counts

4 → 12

Calls

4 calls:

360.0ms	(hypot y (hypot x (* (sqrt 2) y)))
445.0ms	(* (hypot y (hypot x (* (sqrt 2) y))) (hypot y (hypot x (* (sqrt 2) y))))
39.0ms	(* (sqrt 2) y)
42.0ms	(* (sqrt 2) y)

simplify150.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	164	571
1	661	479
2	3791	442
3	5001	436

prune222.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes136.0ms

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	7	3

end0.0ms

sample540.0ms

Algorithm

intervals

Results

313.0ms

14384×

body

valid