Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.1b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
33.4b	(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)))

series133.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(+ (* x x) (* y y))
103.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify81.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (76.0ms)

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

prune95.0ms

Filtered

38 candidates to 31 candidates (81.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	34	4	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	4	39

Merged error: 13.5b

Counts

39 → 4

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)
27.8b	(sqrt (+ (* x x) (* y y)))

rewrite10.0ms

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)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* x x) (* y y))
170.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
38.0ms	(sqrt (+ (* x x) (* y y)))

simplify72.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (67.0ms)

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

prune119.0ms

Filtered

51 candidates to 42 candidates (82.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	54	1	55

Merged error: 0.0b

Counts

55 → 1

localize5.0ms

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:

1.0ms

(hypot (hypot x y) z)

series194.0ms

Counts

1 → 3

Calls

1 calls:

193.0ms

(hypot (hypot x y) z)

simplify117.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (5.0ms)

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

prune32.0ms

Filtered

13 candidates to 13 candidates (100.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	1	14

Merged error: 0.0b

Counts

14 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	2

end0.0ms

sample516.0ms

Algorithm

intervals

Results

334.0ms

8000×

body

valid