Techniques for generating distribution approximations with low memory footprints are disclosed. In some embodiments, a system receives a first set of values that measure one or more metrics of at least one computing resource. A set of clusters are generated, within volatile or non-volatile memory, that approximate a distribution of the first set of values measuring the one or more metrics of the at least one computing resource. The set of clusters is transformed, within volatile or non-volatile memory, to a piecewise approximation of a function for the first set of values.