Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 34.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
32.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite20.0ms

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)))

series161.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (* x x) (* y y))
127.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify85.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (80.0ms)

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

prune123.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
0.0b	(+ (* x x) (* y y))
27.6b	(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:

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

series282.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
34.0ms	(+ (* x x) (* y y))
48.0ms	(sqrt (+ (* x x) (* y y)))

simplify74.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	152	255
1	617	227
2	1802	223
3	5002	221

prune154.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot (* 1 (hypot x y)) z)
0.0b	(hypot x y)

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

series284.0ms

Counts

2 → 6

Calls

2 calls:

227.0ms	(hypot (* 1 (hypot x y)) z)
57.0ms	(hypot x y)

simplify81.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	50	82
1	75	70
2	106	70
3	221	70
4	818	70
5	5001	70

prune87.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* 1 (hypot x y)) z)
0.0b	(hypot x y)
0.0b	(hypot x y)
0.5b	(* (sqrt (hypot (* 1 (hypot x y)) z)) (sqrt (hypot (* 1 (hypot x y)) z)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `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×	`hypot-udef` `pow-prod-down` `pow-sqr`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

0.0ms	(hypot (* 1 (hypot x y)) z)
0.0ms	(hypot x y)
0.0ms	(hypot x y)
7.0ms	(* (sqrt (hypot (* 1 (hypot x y)) z)) (sqrt (hypot (* 1 (hypot x y)) z)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(hypot (* 1 (hypot x y)) z)
55.0ms	(hypot x y)
60.0ms	(hypot x y)
233.0ms	(* (sqrt (hypot (* 1 (hypot x y)) z)) (sqrt (hypot (* 1 (hypot x y)) z)))

simplify144.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	126	416
1	432	358
2	2555	338
3	5002	323

prune258.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes135.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	12	3
2	12	3

end0.0ms

sample409.0ms

Algorithm

intervals

Results

243.0ms

8000×

body

valid