"High precision" refers to the degree of accuracy or exactness in measurements, calculations, or actions. It means being very careful and diligent to ensure the smallest possible error or discrepancy. Full definition
Several theories predict the relation between contact area and normal force, but so far these theories could not be tested with high precision. (sciencedaily.com)
This phenomenon is often used for high precision measurements, for instance in atomic clocks. (sciencedaily.com)