The next generation of video codecs incorporate multiple transforms as a part of their transform core. However, some of the new transform types introduced in state-of-the-art codecs are still lacking efficient optimization methods. This paper focuses on the optimization of Adaptive Multiple Transforms (AMTs) in the next generation of video decoders. Our solution consists in three main contributions aiming towards a real time software implementation of an AMTs inverse core transform. We first investigate AMTs usage and properties in a transform and quantization video coding context. In a second contribution we design a unified transform core decoding algorithm for AMTs relying on pruning strategies. Finally, in a third contribution we present a Single Input Multiple Data (SIMD) implementation using AVX2 extension set targeting x86 architecture. To the best of our knowledge this is the first software implementation of AMTs achieving real-time performance in a software video decoder.