Details

sample16.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
35.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite18.0ms

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:

3.0ms	(+ (* x x) (* y y))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series128.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) (* y y))
102.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.1s

Counts

38 → 38

Iterations

Useful iterations: 3 (268.0ms)

Iter	Nodes	Cost
0	67	513
1	186	411
2	644	367
3	2347	359
done	5000	359

prune109.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.8b

localize10.0ms

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)))

rewrite7.0ms

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:

3.0ms	(+ (* x x) (* y y))
0.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
4.0ms	(sqrt (+ (* x x) (* y y)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
157.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
34.0ms	(sqrt (+ (* x x) (* y y)))

simplify881.0ms

Counts

51 → 51

Iterations

Useful iterations: 3 (239.0ms)

Iter	Nodes	Cost
0	65	571
1	151	371
2	514	312
3	1894	308
done	5001	308

prune126.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 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)

series185.0ms

Counts

1 → 3

Calls

1 calls:

185.0ms

(hypot (hypot x y) z)

simplify1.5s

Counts

13 → 13

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	19	88
1	24	86
2	27	76
3	32	76
4	38	76
5	58	76
6	117	76
7	342	76
8	1173	76
done	5001	76

prune32.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (hypot x y) z)
0.0b	(sqrt (hypot (hypot x y) z))
0.0b	(sqrt (hypot (hypot x y) z))
0.5b	(* (sqrt (hypot (hypot x y) z)) (sqrt (hypot (hypot x y) z)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `hypot-udef` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

0.0ms	(hypot (hypot x y) z)
1.0ms	(sqrt (hypot (hypot x y) z))
1.0ms	(sqrt (hypot (hypot x y) z))
10.0ms	(* (sqrt (hypot (hypot x y) z)) (sqrt (hypot (hypot x y) z)))

series906.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(hypot (hypot x y) z)
264.0ms	(sqrt (hypot (hypot x y) z))
261.0ms	(sqrt (hypot (hypot x y) z))
198.0ms	(* (sqrt (hypot (hypot x y) z)) (sqrt (hypot (hypot x y) z)))

simplify1.7s

Counts

103 → 103

Iterations

Useful iterations: 3 (378.0ms)

Iter	Nodes	Cost
0	82	1262
1	152	831
2	418	747
3	2301	725
done	5001	725

prune205.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
done	5	5

end0.0ms

sample411.0ms

Algorithm

intervals

Results

247.0ms

8000×

body

valid