We observed that Eagle2 achieved 12–38x speedups over SHAPEIT2 for performing reference-based phasing using panels of size Nref = 15,000–100,000 (Fig. 2a and Supplementary Tables 2 and 3). Moreover, unlike the other methods we benchmarked, the computation time Eagle2 required to phase each target sample was nearly independent of the reference size. (For very large reference panels with Nref >> 100,000, the computational cost of Eagle2 will eventually increase with Nref; see Online Methods and the Supplementary Note.) Eagle2 achieved running times similar to Eagle1 and ≈2x faster than SHAPEIT2 –no–mcmc (both of which are much less accurate methods than Eagle2 and SHAPEIT2 when used with reference panels of these sizes; see below). All methods had low memory costs (<7GB for M=57,753 SNPs on chromosome 1 with Nref = 100,000; Supplementary Table 3).