Weyl tensor is a well-known object in general relativity which is similar to Riemann curvature tensor. Like Riemann curvature tensor, Weyl tensor also shines light upon the curvature of the manifold. A scalar term, known as Weyl-4 term, can be constructed out of Weyl tensors. This term appears in type-II String theory.
Currently, I am studying this term in the presence of Einstein and Gauss-Bonnet gravity. Although theoretically knowing about this term, I am not able to compute this term. I have written a code for this term which involves computing this term by summing over its 16 indices which run over n=5.
This should be a straight forward computation, but still, it’s taking quite a long time. Please suggest me any changes or ideas to improve the computation speed.
It’s a simple 2-cell code, which generates Riemann curvature tensor, Ricci tensor and Ricci scalar. Then in the second cell, it computes terms which are then weighted-summed to form Weyl-4 term. If you wish to run it, you are most welcome 
Please check the attached .nb program file
Weyl4 term.nb (25.1 KB)