Details

Time bar (total: 3.7s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify2.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
28.5b
(sqrt (+ (* x x) (* y y)))

rewrite25.0ms

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 flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
12.0ms
(+ (* x x) (* y y))
12.0ms
(sqrt (+ (* x x) (* y y)))

series92.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(+ (* x x) (* y y))
54.0ms
(sqrt (+ (* x x) (* y y)))

simplify110.0ms

Counts
32 → 32

prune114.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (+ (* x x) (* y y))))
28.5b
(sqrt (+ (* x x) (* y y)))
28.5b
(sqrt (+ (* x x) (* y y)))
28.5b
(sqrt (+ (* x x) (* y y)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 61
Calls
4 calls:
8.0ms
(cbrt (sqrt (+ (* x x) (* y y))))
12.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(sqrt (+ (* x x) (* y y)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(cbrt (sqrt (+ (* x x) (* y y))))
55.0ms
(sqrt (+ (* x x) (* y y)))
53.0ms
(sqrt (+ (* x x) (* y y)))
56.0ms
(sqrt (+ (* x x) (* y y)))

simplify75.0ms

Counts
73 → 73

prune311.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.3b

localize28.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (+ (* x x) (* y y)))
28.5b
(sqrt (+ (* x x) (* y y)))
28.5b
(sqrt (+ (* x x) (* y y)))
28.5b
(sqrt (+ (* x x) (* y y)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
12.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(sqrt (+ (* x x) (* y y)))
18.0ms
(sqrt (+ (* x x) (* y y)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(sqrt (+ (* x x) (* y y)))
47.0ms
(sqrt (+ (* x x) (* y y)))
53.0ms
(sqrt (+ (* x x) (* y y)))
48.0ms
(sqrt (+ (* x x) (* y y)))

simplify152.0ms

Counts
72 → 72

prune318.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
5.7b
(exp (log (sqrt (+ (* x x) (* y y)))))
28.5b
(sqrt (+ (* x x) (* y y)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 log-prod exp-prod exp-sum sqrt-prod
5×add-log-exp
4×sqrt-div
3×add-exp-log flip3-+ log-pow add-cbrt-cube flip-+
2×log-div sqrt-pow1 pow1/2 exp-diff
1×+-commutative rem-sqrt-square sum-log rem-exp-log
Counts
3 → 48
Calls
3 calls:
12.0ms
(+ (* x x) (* y y))
15.0ms
(exp (log (sqrt (+ (* x x) (* y y)))))
13.0ms
(sqrt (+ (* x x) (* y y)))

series152.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(+ (* x x) (* y y))
52.0ms
(exp (log (sqrt (+ (* x x) (* y y)))))
58.0ms
(sqrt (+ (* x x) (* y y)))

simplify121.0ms

Counts
57 → 57

prune163.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.3b

regimes379.0ms

Accuracy

58.9% (9.9b remaining)

Error of 17.7b against oracle of 7.8b and baseline of 31.9b

bsearch55.0ms

Steps
ItersRangePoint
10
1.2073698495971617e+61
3.217811591970086e+74
2.7153468834491098e+73
5
-1.7457635943519997e+137
-5.665103565004941e+136
-1.2876568362185878e+137

simplify2.0ms

end0.0ms

sample911.0ms

Algorithm
intervals
Results
656.0ms8000×body80valid