Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify11.0ms

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: 39.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
36.4b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite10.0ms

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:

4.0ms	(+ (* x x) (* y y))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series140.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(+ (* x x) (* y y))
111.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify72.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (68.0ms)

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

prune115.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.2b

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)
31.0b	(sqrt (+ (* x x) (* y y)))

rewrite9.0ms

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:

4.0ms	(+ (* x x) (* y y))
1.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
4.0ms	(sqrt (+ (* x x) (* y y)))

series254.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
181.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
44.0ms	(sqrt (+ (* x x) (* y y)))

simplify63.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (58.0ms)

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

prune143.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

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:

1.0ms	(hypot (hypot x y) z)
1.0ms	(hypot x y)

series255.0ms

Counts

2 → 6

Calls

2 calls:

202.0ms	(hypot (hypot x y) z)
52.0ms	(hypot x y)

simplify116.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (5.0ms)

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

prune81.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

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:

1.0ms	(cbrt (hypot (hypot x y) z))
1.0ms	(cbrt (hypot (hypot x y) z))
1.0ms	(cbrt (hypot (hypot x y) z))
6.0ms	(* (cbrt (hypot (hypot x y) z)) (cbrt (hypot (hypot x y) z)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt (hypot (hypot x y) z))
204.0ms	(cbrt (hypot (hypot x y) z))
209.0ms	(cbrt (hypot (hypot x y) z))
222.0ms	(* (cbrt (hypot (hypot x y) z)) (cbrt (hypot (hypot x y) z)))

simplify139.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	176	642
1	725	590
2	3525	542
3	5001	524

prune250.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes44.0ms

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

sample408.0ms

Algorithm

intervals

Results

243.0ms

8000×

body

valid