Numerical software is being reinvented to provide opportunities to tune dynamically the accuracy of computation to the requirements of the application, resulting in savings of memory, time, and energy. Floating point computation in science and engineering has a history of “oversolving” relative to expectations for many models. So often are real datatypes defaulted to double precision that GPUs did not gain wide acceptance until they provided in hardware operations not required in their original domain of graphics. However, computational science is now reverting to employ lower precision arithmetic where possible. Many matrix operations considered at a blockwise level allow for lower precision and many blocks can be approximated with low rank near equivalents. This leads to smaller memory footprint, which implies higher residency on memory hierarchies, leading in turn to less time and energy spent on data copying, which may even dwarf the savings from fewer and cheaper flops. We provide examples from several application domains, including a look at campaigns in geospatial statistics, seismic processing, genome wide association studies, and climate emulation that earned Gordon Bell Prize finalist status in 2022, 2023, and 2024.