  We present a fast Gauss transform in one dimension using nearly optimal
sum-of-exponentials approximations of the Gaussian kernel. For up to about
ten-digit accuracy, the approximations are obtained via best rational
approximations of the exponential function on the negative real axis. As
compared with existing fast Gauss transforms, the algorithm is straightforward
for parallelization and very simple to implement, with only twenty-four lines
of code in MATLAB. The most expensive part of the algorithm is on the
evaluation of complex exponentials, leading to three to six complex
exponentials FLOPs per point depending on the desired precision. The
performance of the algorithm is illustrated via several numerical examples.
