Engineering enzyme biocatalysts for higher efficiency is key to enabling sustainable, ‘green’ production processes for the chemical and pharmaceutical industry. This challenge can be tackled from two angles: by directed evolution, based on labor-intensive experimental testing of enzyme variant libraries, or by computational methods, where sequence-function data are used to predict biocatalyst improvements. Here, we combine both approaches into a two-week workflow, where ultra-high throughput screening of a library of imine reductases (IREDs) in microfluidic devices provides not only selected ‘hits’, but also long-read sequence data linked to fitness scores of >17 thousand enzyme variants. We demonstrate engineering of an IRED for chiral amine synthesis by mapping functional information in one go, ready to be used for interpretation and extrapolation by protein engineers with the help of machine learning (ML). We calculate position-dependent mutability and combinability scores of mutations and comprehensively illuminate a complex interplay of mutations driven by synergistic, often positively epistatic effects. Interpreted by easy-to-use regression and tree-based ML algorithms designed to suit the evaluation of random whole-gene mutagenesis data, 3-fold improved ‘hits’ obtained from experimental screening are extrapolated further to give up to 23-fold improvements in catalytic rate after testing only a handful of designed mutants. Our campaign is paradigmatic for future enzyme engineering that will rely on access to large sequence-function maps as profiles of the way a biocatalyst responds to mutation. These maps will chart the way to improved function by exploiting the synergy of rapid experimental screening combined with ML evaluation and extrapolation.