Details

sample32.0ms

Algorithm

intervals

Results

22.0ms

471×

body

valid

simplify288.0ms

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

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.0b	(+ (* x x) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite73.0ms

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:

15.0ms	(+ (+ (* x x) (* y y)) (* y y))
3.0ms	(+ (* x x) (* y y))
54.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series102.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* y y))
27.0ms	(+ (* x x) (* y y))
37.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify138.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (133.0ms)

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

prune131.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (hypot x y) (hypot x y)) (* y y))
0.0b	(* (hypot x y) (hypot x y))
0.1b	(+ (+ (* (hypot x y) (hypot x y)) (* y y)) (* y y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-sqr-sqrt` `add-log-exp`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-exp-log` `add-cbrt-cube`
4×	`hypot-udef` `fma-def` `sum-log`
3×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `log1p-expm1-u`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `pow-prod-down` `prod-exp` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

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

series219.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(+ (* (hypot x y) (hypot x y)) (* y y))
61.0ms	(* (hypot x y) (hypot x y))
81.0ms	(+ (+ (* (hypot x y) (hypot x y)) (* y y)) (* y y))

simplify168.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (162.0ms)

Iter	Nodes	Cost
0	232	387
1	1045	340
2	4632	315
3	5001	314

prune146.0ms

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	(* (hypot x y) (hypot x y))
0.2b	(fma (sqrt (+ (* (hypot x y) (hypot x y)) (* y y))) (sqrt (+ (* (hypot x y) (hypot x y)) (* y y))) (* y y))
6.7b	(sqrt (+ (* (hypot x y) (hypot x y)) (* y y)))
6.7b	(sqrt (+ (* (hypot x y) (hypot x y)) (* y y)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `hypot-udef` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`pow2` `pow-plus` `sqrt-unprod` `pow-prod-down` `prod-exp` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

3.0ms	(* (hypot x y) (hypot x y))
0.0ms	(fma (sqrt (+ (* (hypot x y) (hypot x y)) (* y y))) (sqrt (+ (* (hypot x y) (hypot x y)) (* y y))) (* y y))
3.0ms	(sqrt (+ (* (hypot x y) (hypot x y)) (* y y)))
4.0ms	(sqrt (+ (* (hypot x y) (hypot x y)) (* y y)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (hypot x y) (hypot x y))
205.0ms	(fma (sqrt (+ (* (hypot x y) (hypot x y)) (* y y))) (sqrt (+ (* (hypot x y) (hypot x y)) (* y y))) (* y y))
84.0ms	(sqrt (+ (* (hypot x y) (hypot x y)) (* y y)))
84.0ms	(sqrt (+ (* (hypot x y) (hypot x y)) (* y y)))

simplify118.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	195	604
1	762	499
2	3052	493
3	5002	490

prune241.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (hypot x y) y)
0.1b	(hypot (hypot (hypot x y) y) y)
0.1b	(hypot (hypot (hypot x y) y) y)
0.2b	(* (hypot (hypot (hypot x y) y) y) (hypot (hypot (hypot x y) y) y))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

0.0ms	(hypot (hypot x y) y)
0.0ms	(hypot (hypot (hypot x y) y) y)
0.0ms	(hypot (hypot (hypot x y) y) y)
3.0ms	(* (hypot (hypot (hypot x y) y) y) (hypot (hypot (hypot x y) y) y))

series1.1s

Counts

4 → 12

Calls

4 calls:

127.0ms	(hypot (hypot x y) y)
309.0ms	(hypot (hypot (hypot x y) y) y)
303.0ms	(hypot (hypot (hypot x y) y) y)
362.0ms	(* (hypot (hypot (hypot x y) y) y) (hypot (hypot (hypot x y) y) y))

simplify70.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	124	407
1	405	339
2	1610	307
3	5001	302

prune188.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes52.0ms

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	9	7
1	9	7

end0.0ms

sample826.0ms

Algorithm

intervals

Results

592.0ms

14319×

body

valid