Details

sample40.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	9	12
1	14	11
2	24	10
3	31	10
done	31	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite126.0ms

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:

14.0ms	(+ (* x x) (* y y))
50.0ms	(+ (+ (* x x) (* y y)) (* z z))
60.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series274.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ (* x x) (* y y))
60.0ms	(+ (+ (* x x) (* y y)) (* z z))
164.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.2s

Counts

59 → 59

Iterations

Useful iterations: 2 (230.0ms)

Iter	Nodes	Cost
0	80	808
1	253	677
2	1412	586
done	5000	586

prune380.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.9b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(hypot (sqrt (+ (* x x) (* y y))) z)
29.0b	(sqrt (+ (* x x) (* y y)))

rewrite39.0ms

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:

17.0ms	(+ (* x x) (* y y))
1.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
20.0ms	(sqrt (+ (* x x) (* y y)))

series344.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* x x) (* y y))
245.0ms	(hypot (sqrt (+ (* x x) (* y y))) z)
57.0ms	(sqrt (+ (* x x) (* y y)))

simplify644.0ms

Counts

51 → 51

Iterations

Useful iterations: done (642.0ms)

Iter	Nodes	Cost
0	65	571
1	168	374
2	763	312
done	5001	308

prune267.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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)

series276.0ms

Counts

1 → 3

Calls

1 calls:

276.0ms

(hypot (hypot x y) z)

simplify1.2s

Counts

13 → 13

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	19	88
1	24	86
2	27	76
3	32	76
4	40	76
5	74	76
6	154	76
7	328	76
8	1000	76
done	5000	76

prune70.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot (hypot x y) z))
0.0b	(hypot (hypot x y) z)
0.0b	(hypot (hypot x y) z)
0.6b	(* (sqrt (hypot (hypot x y) z)) (sqrt (hypot (hypot x y) z)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`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×	`hypot-udef`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

2.0ms	(sqrt (hypot (hypot x y) z))
0.0ms	(hypot (hypot x y) z)
0.0ms	(hypot (hypot x y) z)
26.0ms	(* (sqrt (hypot (hypot x y) z)) (sqrt (hypot (hypot x y) z)))

series1.4s

Counts

4 → 12

Calls

4 calls:

403.0ms	(sqrt (hypot (hypot x y) z))
310.0ms	(hypot (hypot x y) z)
352.0ms	(hypot (hypot x y) z)
305.0ms	(* (sqrt (hypot (hypot x y) z)) (sqrt (hypot (hypot x y) z)))

simplify1.0s

Counts

98 → 98

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	82	1186
1	183	783
2	812	691
done	5000	676

prune412.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes432.0ms

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

sample1.1s

Algorithm

intervals

Results

662.0ms

8000×

body

valid