Details

sample17.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify8.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
33.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(+ (* x x) (* y y))
34.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series176.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (+ (* x x) (* y y)) (* z z))
39.0ms	(+ (* x x) (* y y))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify92.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	225	355
1	1043	323
2	3749	312
3	5001	309

prune160.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
0.0b	(+ (* x x) (* y y))
27.1b	(sqrt (+ (* x x) (* y y)))

rewrite17.0ms

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)
8.0ms	(+ (* x x) (* y y))
8.0ms	(sqrt (+ (* x x) (* y y)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
27.0ms	(+ (* x x) (* y y))
32.0ms	(sqrt (+ (* x x) (* y y)))

simplify52.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (48.0ms)

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

prune121.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(hypot (hypot x y) z)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`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

1 → 10

Calls

1 calls:

0.0ms

(hypot (hypot x y) z)

series167.0ms

Counts

1 → 3

Calls

1 calls:

167.0ms

(hypot (hypot x y) z)

simplify90.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	41
1	27	36
2	31	36
3	36	36
4	55	36
5	109	36
6	515	36
7	1689	36
8	5001	36

prune30.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (hypot (hypot x y) z)) (cbrt (hypot (hypot x y) z)))
0.6b	(cbrt (hypot (hypot x y) z))
0.6b	(cbrt (hypot (hypot x y) z))
0.6b	(cbrt (hypot (hypot x y) z))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

14.0ms	(* (cbrt (hypot (hypot x y) z)) (cbrt (hypot (hypot x y) z)))
1.0ms	(cbrt (hypot (hypot x y) z))
1.0ms	(cbrt (hypot (hypot x y) z))
1.0ms	(cbrt (hypot (hypot x y) z))

series718.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (cbrt (hypot (hypot x y) z)) (cbrt (hypot (hypot x y) z)))
174.0ms	(cbrt (hypot (hypot x y) z))
166.0ms	(cbrt (hypot (hypot x y) z))
186.0ms	(cbrt (hypot (hypot x y) z))

simplify126.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	176	642
1	718	590
2	3519	542
3	5001	524

prune244.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes146.0ms

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

sample459.0ms

Algorithm

intervals

Results

225.0ms

8000×

body

valid