FP /


Optimizing function representations for interval analysis

MSc thesis project idea, Cezar Ionescu, 2015-03-17

The arithmetical operations on real (or floating-point) numbers can be easily extended to intervals. For example, adding two intervals I a b and I c d gives I (a + c) (b + d), or multiplying I a b with a negative constant alpha < 0 gives I (alpha*b) (alpha*a). A function that is built out of arithmetical operations is also easily extended, but sometimes the resulting extension is bad. For example, extending f x = x + (-1*x) with the previous formulas results in "big" intervals, instead of just the singleton I 0 0. It would have obviously been much better to extend the equivalent function f x = 0. Theses in this area will explore automatic optimization of representations for less obvious cases.