  We present IMRPhenomTPHM, a phenomenological model for the gravitational wave
signals emitted by the coalescence of quasi-circular precessing binary black
holes systems. The model is based on the "twisting up" approximation, which
maps non-precessing signals to precessing ones in terms of a time dependent
rotation described by three Euler angles, and which has been utilized in
several frequency domain waveform models that have become standard tools in
gravitational wave data analysis. Our model is however constructed in the time
domain, which allows several improvements over the frequency domain models: we
do not use the stationary phase approximation, we employ a simple approximation
for the precessing Euler angles for the ringdown signal, and we implement a new
method for computing the Euler angles through the evolution of the spin
dynamics of the system, which is more accurate and also computationally
efficient.
