Kinematics of a particular five-axis milling machine can drastically change the machining accuracy. Therefore, the reduction of the kinematics error is an important problem associated with the tool path planning. Our new optimization method employs a closed form of the kinematics error represented as a function of the positions of the cutter contact points. The closed form is derived from the inverse kinematics associated with a particular five-axis machine and obtained through automatic symbolic calculations. The second component of the algorithm is the optimal setup of the part surface on the mounting table employed in an iterative loop with the generation of the cutter contact points. For a prescribed tolerance the proposed optimization allows for substantial reduction in the number of required cutter contact points. The reduction can be significant and may amount to long hours of machining if the machining time at the programmed feed is less than the sampling time of the controller. In turn, when the number of cutter location points is fixed, the error can be substantially reduced. However, this refers to commanded error wherein the dynamics of machine tool are not taken into account. We present an analysis, systematic numerical experiments and results of real cutting (ball nose and flat-end cutters) as an evidence of the efficiency and the accuracy increase produced by the proposed method. We also evaluate the relative contributions of the setup and the point optimization. The method is shown to work with advanced tool path generation techniques proposed earlier such as the adaptive space filling curves. The numerical and machining experiments demonstrate that the proposed procedure outperforms tool paths based on the equi-arclength principle and paths generated by MasterCam 9.