While the Characteristic Multivector (CM) method within Geometric Algebra provides accurate 3D rotation estimation, its computational expense motivated the use of GAALOP (Geometric Algebra Algorithms Optimizer) symbolic optimization to create efficient standard and Common Subexpression Elimination (CSE) variants. We evaluated these optimized versions against the original MATLAB CM implementation provided by the Clifford Multivector Toolbox for the Absolute Orientation (AO) problem and benchmarked them against both the original CM and a standard SVD based method within the Iterative Closest Point (ICP) framework. The evaluation revealed significant runtime improvements with GAALOP and demonstrated speeds competitive with SVD, while preserving the inherent high accuracy of the Geometric Algebra approach and establishing it as a viable 3D registration alternative.