Applications ranging from the Internet of Things (IoT) to high-performance computing demand energy-efficient hardware for processing and storage. Reducing computation accuracy has shown the potential to achieve high energy efficiency in hardware implementations. In recent years, several automatic approximate logic synthesis techniques have been proposed to build an approximate circuit systematically, trading off accuracy for hardware cost. In this paper, we propose a novel approximate logic synthesis technique to simplify circuits using mutual information by considering the input distribution. Our experimental result shows that our proposed methodology demonstrates improvements in terms of area, delay, and error compared to the state-of-the-art.