Matrix multiplication (MM) is pivotal in fields from deep learning to scientific computing, driving the quest for improved computational efficiency. Accelerating MM encompasses strategies like complexity reduction, parallel and distributed computing, hardware acceleration, and approximate computing techniques, namely AMM algorithms. Amidst growing concerns over the resource demands of large language models (LLMs), AMM has garnered renewed focus. However, understanding the nuances that govern AMM’s effectiveness remains incomplete. This study delves into AMM by examining algorithmic strategies, operational specifics, dataset characteristics, and their application in real-world tasks. Through comprehensive testing across diverse datasets and scenarios, we analyze how these factors affect AMM’s performance, uncovering that the selection of AMM approaches significantly influences the balance between efficiency and accuracy, with factors like memory access playing a pivotal role. Additionally, dataset attributes are shown to be vital for the success of AMM in applications. Our results advocate for tailored algorithmic approaches and careful strategy selection to enhance AMM’s effectiveness. To aid in the practical application and ongoing research of AMM, we introduce LibAMM —a toolkit offering a wide range of AMM algorithms, benchmarks, and tools for experiment management. LibAMM aims to facilitate research and application in AMM, guiding future developments towards more adaptive and context-aware computational solutions.