Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	9	12
1	14	11
2	24	10
3	30	10
done	30	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize20.0ms

Local error

Found 1 expressions with local error:

35.4b

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

rewrite89.0ms

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:

88.0ms

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

series165.0ms

Counts

1 → 3

Calls

1 calls:

165.0ms

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

simplify3.2s

Counts

21 → 21

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	43	331
1	98	272
2	300	243
3	1040	235
4	4140	234
done	5000	234

prune96.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
29.2b	(sqrt (+ (* x x) (* y y)))

rewrite10.0ms

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)
9.0ms	(sqrt (+ (* x x) (* y y)))

series340.0ms

Counts

2 → 6

Calls

2 calls:

271.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
69.0ms	(sqrt (+ (* x x) (* y y)))

simplify4.6s

Counts

34 → 34

Iterations

Useful iterations: 3 (193.0ms)

Iter	Nodes	Cost
0	53	389
1	115	220
2	268	194
3	586	188
4	1444	188
5	4140	188
done	5000	188

prune144.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

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

series338.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(hypot x y)
271.0ms	(hypot (hypot x y) z)

simplify3.8s

Counts

26 → 26

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	30	148
1	38	144
2	43	128
3	50	128
4	59	128
5	76	128
6	115	128
7	252	128
8	816	128
9	3627	128
done	5000	128

prune101.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
done	5	5

end0.0ms

sample891.0ms

Algorithm

intervals

Results

618.0ms

8000×

body

valid