Details

sample16.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	6
1	25	6
2	31	6
3	32	6
4	32	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
36.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(+ (* x x) (* y y))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series143.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* x x) (* y y))
110.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify77.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	186	224
1	767	212
2	2319	209
3	5001	207

prune108.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
32.2b	(sqrt (+ (* x x) (* y y)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

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

series244.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
175.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
39.0ms	(sqrt (+ (* x x) (* y y)))

simplify66.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	152	254
1	617	227
2	1802	223
3	5002	221

prune138.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot x y)
0.0b	(hypot (hypot x y) z)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(hypot x y)
0.0ms	(hypot (hypot x y) z)

series251.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(hypot x y)
198.0ms	(hypot (hypot x y) z)

simplify120.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	38	68
1	43	60
2	49	60
3	57	60
4	85	60
5	159	60
6	660	60
7	2200	60
8	5001	60

prune72.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (hypot x y) z)
0.0b	(sqrt (hypot (hypot x y) z))
0.0b	(sqrt (hypot (hypot x y) z))
0.5b	(* (sqrt (hypot (hypot x y) z)) (sqrt (hypot (hypot x y) z)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `hypot-udef` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

0.0ms	(hypot (hypot x y) z)
1.0ms	(sqrt (hypot (hypot x y) z))
1.0ms	(sqrt (hypot (hypot x y) z))
7.0ms	(* (sqrt (hypot (hypot x y) z)) (sqrt (hypot (hypot x y) z)))

series959.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(hypot (hypot x y) z)
279.0ms	(sqrt (hypot (hypot x y) z))
284.0ms	(sqrt (hypot (hypot x y) z))
199.0ms	(* (sqrt (hypot (hypot x y) z)) (sqrt (hypot (hypot x y) z)))

simplify147.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (140.0ms)

Iter	Nodes	Cost
0	154	445
1	576	389
2	3200	367
3	5001	354

prune210.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	2

end0.0ms

sample403.0ms

Algorithm

intervals

Results

235.0ms

8000×

body

valid