The simulation of genealogical trees backwards in time, from observations up to the most recent common ancestor (MRCA), is hindered by the fact that, while approaching the root of the tree, coalescent events become rarer, with a corresponding increase in computation time. The recently proposed “Time Machine” tackles this issue by stopping the simulation of the tree before reaching the MRCA and correcting for the induced bias. We present a computationally efficient implementation of this approach that exploits multithreading.