In scientific computing, the acceleration of atomistic computer simulations by means of custom hardware is finding ever-growing application.A major limitation, however, is that the high efficiency in terms of performance and low power consumption entails the massive usage Mechanical pencil of low precision computing units.Here, based on the Military Socks approximate computing paradigm, we present an algorithmic method to compensate for numerical inaccuracies due to low accuracy arithmetic operations rigorously, yet still obtaining exact expectation values using a properly modified Langevin-type equation.