Notes. Performance of the ENRKE routine, using bisection in the critical region, the rational seed, the efficient stopping condition (9), and one run of OG131 followed by CNR iterations. The accuracy is set to the value rad. These results correspond to different values of the eccentricity e and to a homogeneous set of N = 10⁸ values of M ∈ [0, 2π]. The average and maximum numbers of iterations (i.e., computations of Δ_n s, the first onewith OG131 and the rest with the CNR iterators, each implying the computation of a sine and a cosine), and , are shown in the second and third column, respectively. The last column presents the average CPU execution time per solution, (in nanoseconds), obtained with an optimized Cython implementation of the CNR method employing multithreaded loops and executed on the hardware previously specified. The bisection method is used for e > 0.99 and for M < 0.0045 rad or M > 2π − 0.0045 rad. The listed average and maximum number of bisection iterations, and (implying the computation of a sine), correspond to the same set of homogeneous values of M.