= Natural interval extension
{title2=$f(X)\subseteq F(X)$}
A <natural interval extension> evaluates a chosen expression by replacing its <arithmetic operations> with <interval arithmetic operations>, its <constants> with enclosing <closed intervals>, and any additional <functions> with valid <interval enclosures>. Each intermediate result must remain defined on its inputs. The resulting $F(X)$ encloses the actual <image of a function> $f(X)$, but its width depends on the expression used. Rump's INTLAB tutorial describes this inclusion principle and warns that repeated inputs can produce severe overestimation.https://www.tuhh.de/ti3/rump/intlab/demos/html/dintval.html[Siegfried M. Rump, Interval computations in INTLAB, Overestimation of interval operations and A common misuse of interval arithmetic]{ref}
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