  We present a set of experimentally feasible pulse sequences that implement
any single-qubit gate on a singlet-triplet spin qubit and demonstrate that
these new sequences are up to three times faster than existing sequences in the
literature. We show that these sequences can be extended to incorporate
built-in dynamical error correction, yielding gates that are robust to both
charge and magnetic field noise and up to twice as fast as previous dynamically
corrected gate schemes. We present a thorough comparison of the performance of
our new sequences with that of several existing ones using randomized
benchmarking, considering both quasistatic and $1/f^\alpha$ noise models. We
provide our results both as a function of evolution time and as a function of
the number of gates, which respectively yield both an effective coherence time
and an estimate of the number of gates that can be performed within this
coherence time. We determine which set of pulse sequences gives the best
results for a wide range of noise strengths and power spectra. Overall, we find
that the traditional, slower sequences perform best when there is no field
noise or when the noise contains significant high-frequency components;
otherwise, our new, fast sequences exhibit the best performance.
