# OptimizingFunctionRepresentationsForIntervalAnalysis

# 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.