I am trying to determine whether a line segment (i.e. between two points) intersects a sphere. I am not interested in the position of the intersection, just whether or not t
you sorta have to work that the position anyway if you want accuracy. The only way to improve speed algorithmically is to switch from ray-sphere intersection to ray-bounding-box intersection.
Or you could go deeper and try and improve sqrt and other inner function calls
http://wiki.cgsociety.org/index.php/Ray_Sphere_Intersection