Details

sample18.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify9.0ms

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: 36.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series186.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* x x) (* y y))
41.0ms	(+ (+ (* x x) (* y y)) (* z z))
112.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify102.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (97.0ms)

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

prune177.0ms

Filtered

59 candidates to 49 candidates (83.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	4	60

Merged error: 12.5b

Counts

60 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
27.8b	(sqrt (+ (* x x) (* y y)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `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))
4.0ms	(sqrt (+ (* x x) (* y y)))

series81.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* x x) (* y y))
47.0ms	(sqrt (+ (* x x) (* y y)))

simplify67.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	136	177
1	589	162
2	1761	158
3	5002	156

prune107.0ms

Filtered

38 candidates to 32 candidates (84.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	41	1	42

Merged error: 0b

Counts

42 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(hypot x y)

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 x y)

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

(hypot x y)

simplify107.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	22	27
1	25	24
2	29	24
3	34	24
4	53	24
5	107	24
6	513	24
7	1687	24
8	5001	24

prune42.0ms

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: 0b

Counts

14 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	2

end0.0ms

sample403.0ms

Algorithm

intervals

Results

236.0ms

8000×

body

valid