  Cosmic Microwave Background lensing simulation by Taylor expansion has long
been considered impractical due to slow convergence, but a recent flat-sky
implementation shows that a simple trick eliminates this problem, making Taylor
lensing a fast and simple lensing algorithm for the flat sky. Here we
generalize the method to the full sky, and study its convergence and
performance relative to a commonly used numerical code, Lenspix, with extensive
benchmarks of both. Compared to the flat sky case, the method takes a speed hit
due to the slow speed of spherical harmonic transforms compared to fast Fourier
transforms, resulting in speeds of 1/3 to 2/3 of Lenspix for similar accuracy.
