Sample-count feedback from bus functional models and a binary convergence algorithm are to generate optimal sampling values for an accelerator, or hardware assisted simulator. The simulator includes a bus functional model and a driver program. A software readable register maintains a count of a number of samples provided the simulator in execution of a transaction on the bus functional model. For each supported bus functional model, a sample count retrieved from the bus functional model and a last sampling value given the hardware assisted simulator is maintained, and a binary convergence algorithm applied to generate sampling values based on the last sampling value given to the hardware assisted simulator and the last actual sampling value used by a given bus functional model for a transaction.