Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

481×

body

valid

simplify286.0ms

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 2 expressions with local error:

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

16×	`add-log-exp`
9×	`sum-log`
6×	`fma-def`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `associate-+l+` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

2 → 37

Calls

2 calls:

14.0ms	(+ (+ (* x x) (* y y)) (* y y))
60.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series74.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* y y))
39.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify110.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	178	305
1	842	249
2	4026	226
3	5001	221

prune100.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 3 (* y y) (* x x))

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 3 (* y y) (* x x))

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(fma 3 (* y y) (* x x))

simplify53.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	33	59
1	84	52
2	267	52
3	1089	52
4	5002	52

prune32.0ms

Pruning

6 alts after pruning (5 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))
6.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
6.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite50.0ms

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:

14.0ms	(+ (+ (* 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))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* y y))
136.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
48.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
53.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify90.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (84.0ms)

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

prune229.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x (* (sqrt 2) y))
0.1b	(fma (* (sqrt 1) (hypot x (* (sqrt 2) y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
0.4b	(* (sqrt 2) y)
6.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

0.0ms	(hypot x (* (sqrt 2) y))
0.0ms	(fma (* (sqrt 1) (hypot x (* (sqrt 2) y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
5.0ms	(* (sqrt 2) y)
16.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series506.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(hypot x (* (sqrt 2) y))
292.0ms	(fma (* (sqrt 1) (hypot x (* (sqrt 2) y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
40.0ms	(* (sqrt 2) y)
55.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify34.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	218	503
1	854	445
2	5001	404

prune247.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes98.0ms

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	6	3

end0.0ms

sample535.0ms

Algorithm

intervals

Results

311.0ms

14274×

body

valid