Details

sample17.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify9.0ms

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
done	32	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize12.0ms

Local error

Found 1 expressions with local error:

35.9b

(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 18

Calls

1 calls:

32.0ms

(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series108.0ms

Counts

1 → 3

Calls

1 calls:

108.0ms

(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify116.0ms

Counts

21 → 21

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	96	156
1	305	148
2	1103	148
3	4548	148
4	5001	148
done	5001	148

prune63.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
31.5b	(sqrt (+ (* x x) (* y y)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `hypot-udef` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`

Counts

2 → 28

Calls

2 calls:

0.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
11.0ms	(sqrt (+ (* x x) (* y y)))

series213.0ms

Counts

2 → 6

Calls

2 calls:

175.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
38.0ms	(sqrt (+ (* x x) (* y y)))

simplify60.0ms

Counts

34 → 34

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	114	180
1	282	163
2	660	163
3	1620	163
4	5001	163
done	5001	163

prune88.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

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:

0.0ms

(hypot (hypot x y) z)

series200.0ms

Counts

1 → 3

Calls

1 calls:

200.0ms

(hypot (hypot x y) z)

simplify103.0ms

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

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
done	5001	36

prune35.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	2
1	5	2
done	5	2

end0.0ms

sample432.0ms

Algorithm

intervals

Results

215.0ms

8000×

body

valid