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Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of compositionally-rich functions, concentrating on transformer inference. Based on the rounding error analysis of a composition $f(g(\mathrm{x}))$, we provide an adaptive strategy that selects a small subset of components of $g(\mathrm{x})$ to be computed more accurately while all other computations can be carried out with lower accuracy. We then explain how this strategy can be applied to different compositions within a transformer and illustrate its overall effect on transformer inference. We study the effectiveness of this algorithm numerically on GPT-2 models and demonstrate that already very low recomputation rates allow for improvements of up to two orders of magnitude in accuracy.