You could be calculating until the end of the universe if you have to check out every path. Fortunately, there are ways to choose the calculations most worth doing. That's those which make the most difference.
You'll already have noticed that sometimes arrows line up and sometimes curl up. When the arrows are all lined up, they contribute a lot. When the arrows curl up, they contribute only a little.
So to save calculating time, work first on paths for which nearby triplets line up. Avoid triplets of paths resulting in arrows which curl up.
Choose to work with the most significant paths; you make a prediction good enough to test in a reasonable time. Think carefully about the space between source and detector to choose waypoints paths which identify such paths.