In this paper we study the calculus of circuits $\X$, as first presented in \cite{Lengrand'03} and studied in detail in \cite{vBLL'05}. We will present improvements on the implementation for $\X$ using term graph rewriting techniques that was presented in \cite{vBR-TermGraph'04}, which result in a far more efficient running of the reduction engine. We show that alpha conversion can be dealt with `on the fly', by implementing the avoidance of capture by modifying the rewrite rules. We then study two different approaches to garbage collection, and compare the various implementations by presenting benchmarks.
