  In Run 3 of the LHC the LHCb experiment faces very high data rates containing
beauty and charm hadron decays. Thus the task of the trigger is not to select
any beauty and charm events, but to select those containing decays interesting
for the LHCb physics programme. LHCb has therefore implemented a real-time data
processing strategy to trigger directly on reconstructed events. The first
stage of the purely software-based trigger is implemented on GPUs performing a
partial event reconstruction. In the second stage of the software trigger, the
full, offline-quality event reconstruction is performed on CPUs, with a crucial
part being track reconstruction, balancing track finding efficiency, fake track
rate and event throughput. LHCb's CPU-based track reconstruction sequence for
Run 3 is presented, highlighting the "Forward Tracking", which is the algorithm
that reconstructs trajectories of charged particles traversing all of LHCb's
tracking detectors. To meet event throughput requirements, the "Forward
Tracking" uses SIMD instructions in several core parts of the algorithm, such
as the Hough transform and the cluster search. These changes led to an
improvement of the algorithm's event throughput by 60%.
