Approximate computing is an emerging energy-efficient paradigm for error-resilient applications. Approximate logic synthesis (ALS) is an important field of it. To improve the existing ALS flows, one key issue is to derive a more accurate and efficient batch error estimation technique for all approximate transformations under consideration. In this work, we propose a novel batch error estimation method based on Monte Carlo simulation and local change propagation. It is generally applicable to any statistical error measurement such as error rate and average error magnitude. We applied the technique to an existing state-of-the-art ALS approach and demonstrated its effectiveness in deriving better approximate circuits.