Result of the accuracy test. The difference between a map smoothed in spherical harmonic space and a map smoothed with our hybrid method is at most 1.5 × 10^-4 in a small number of outliers around the north pole (left panel). These are generated by numerical errors in the CUFFT library v. 3.1 for specific HEALPix ring lengths and are absent when using the slightly slower CUFFT v. 3.2. The larger scale error both at the pole and in the equatorial region (right panel) is caused by small inaccuracies in the kernel evaluation. In this test, a Gaussian kernel with 1° FWHM was used. Each patch is 10° on the side.