> The main cause for the lower performance of GA is the Gaigen’s soft typing of the geometric algebra objects at compile-time: all types of objects (scalars, vectors, bivectors, trivectors, rotors and so on) are represented by a single data type in Gaigen. When a product or operation has to be computed, Gaigen first checks the grade usage of the argument(s) and then acts accordingly. This conditional step between function call and actual computation is largely responsible for the drop in performance.

So, I blame the library. Writing out the 3-4 datatypes for 3D GA by hand as real types costs some development effort but should give equivalent performance.