Algorithmic Chemistries are Artificial Chemistries that aim at algorithms. In this contribution we present a new algorithm to execute Algorithmic Chemistries during evolution. This algorithm ensures synthesizes of the whole program and cuts off execution of unneeded instructions without restricting the stochastic way of execution. We demonstrate benefits of the new algorithm for evolution of Algorithmic Chemistries and discuss the relation of Algorithmic Chemistries with Estimation of Distribution Algorithms. Categories and Subject Descriptors I.2.2 [Artificial Intelligence]: Automatic Programming General Terms Algorithms Keywords Algorithmic Chemistries, Genetic Programming, Total Synthesis