  The colored Jones polynomial is a knot invariant that plays a central role in
low dimensional topology. We give a simple and an efficient algorithm to
compute the colored Jones polynomial of any knot. Our algorithm utilizes the
walks along a braid model of the colored Jones polynomial that was refined by
Armond from the work of Huynh and L\^e. The walk model gives rise to ordered
words in a $q$-Weyl algebra which we address and study from multiple
perspectives. We provide a highly optimized Mathematica implementation that
exploits the modern features of the software. We include a performance analysis
for the running time of our algorithm. Our implementation of the algorithm
shows that our method usually runs in faster time than the existing state-of
the-art method by an order of magnitude.
