Details

sample19.0ms

Algorithm

intervals

Results

10.0ms

469×

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

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(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:

1.0ms

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

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

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

prune30.0ms

Pruning

4 alts after pruning (4 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))

rewrite19.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* y y))
9.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series99.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* x x) (* y y))
33.0ms	(+ (+ (* x x) (* y y)) (* y y))
37.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify134.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (129.0ms)

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

prune133.0ms

Pruning

8 alts after pruning (7 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))
0.2b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
5.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite21.0ms

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:

6.0ms	(+ (+ (* x x) (* y y)) (* y y))
1.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
8.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (+ (* x x) (* y y)) (* y y))
123.0ms	(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)))
50.0ms	(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

prune216.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.2b	(fma (* (sqrt 1) (hypot x (* (sqrt 2) y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
0.5b	(* (sqrt 2) y)
5.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* y y))
1.0ms	(fma (* (sqrt 1) (hypot x (* (sqrt 2) y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
5.0ms	(* (sqrt 2) y)
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (+ (* x x) (* y y)) (* y y))
271.0ms	(fma (* (sqrt 1) (hypot x (* (sqrt 2) y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
37.0ms	(* (sqrt 2) y)
51.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify40.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	244	579
1	1076	487
2	5001	463

prune262.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes146.0ms

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

sample511.0ms

Algorithm

intervals

Results

304.0ms

14239×

body

valid