Converting piecewise functions into single expressions

Is it possible to express the below piecewise defined function as a single expression? If not, why? In what cases is it possible?

$$ e(x) := \begin{cases} 0, & x \in [0, 199] \\ 5, & x \in [200, 449] \\ 10, & x \in [450, 699] \\ 15, & x \in [700, 949] \\ 20, & x \in [950, 1200] \\ 25, & x \in [1200, \infty) \end{cases} $$

where $x \in \mathbb{N}$.

What I mean by "single expression" is that it should be possible to compute $e(x)$ on a calculator by blindly plugging in the value of $x$ into the the formula for $e(x)$ without having to think of in what interval $x$ falls. I am mainly interested in learning whether there is a general procedure for doing so and under what circumstances it is possible to produce a single expression that makes the function simpler to use rather than giving rise something "ugly and complicated".

This particular function could be defined using the floor function $\left\lfloor x\right\rfloor$ by

$$ e(x):=\begin{cases}10+5\left\lfloor\frac{x-450}{250}\right\rfloor\text{ for }0\le x\lt1200\\25\text{ for }x\ge1200\end{cases} $$

For cases where the $\Delta x$ and $\Delta y$ are constant this can be generalized to the form

$$ e(x):=\begin{cases}y_{\text{offset}}+\Delta y\left\lfloor\frac{x-\Delta x-x_{\text{offset}}}{\Delta x}\right\rfloor\text{ for }0\le x\lt x_{\text{max}}\\y_{\text{max}}\text{ for }x\ge x_{\text{max}}\end{cases} $$