Acceleration of electrons by lasers in a vacuum was considered impossible based on the fact that plane-wave and phase symmetric wave packets cannot transfer energy to electrons apart from Thomson or Compton scattering or the Kapitza–Dirac effect. The nonlinear nature of the electrodynamic forces of the fields to the electrons, expressed as nonlinear forces including ponderomotion or the Lorentz force, permits an energy transfer if the conditions of plane waves in favor of the beams and/or the phase symmetry are broken. The resulting electron acceleration by lasers in a vacuum is now well understood as “free wave acceleration”, as “ponderomotive scattering”, as “violent acceleration”, or as “vacuum beat wave acceleration”. The basic understanding of these phenomena relates to an accuracy principle of nonlinearity for explaining numerous discrepancies on the way to the mentioned achievement of “vacuum laser acceleration”, which goes beyond the well-known experience of necessary accuracy in both modeling and experimental work experiences among theorists and experimentalists in the field of nonlinearity. From mathematically designed beam conditions, an absolute maximum of electron energy per laser interaction has been established. It is shown here how numerical results strongly (both essentially and gradually) depend on the accuracy of the used laser fields for which examples are presented and finally tested by the criterion of the absolute maximum.