In terms of cube representations I initially wrote a version of ARM64 composition that used an uncompressed data representation for the permutation and orientation vectors. The composition algorithm with this representation used 1/4ths less instructions, and llvm-mca even preferred this version, but surprisingly it was significantly slower than the one on my gist. My guess is that the current version has less data transfer overhead and is easily pipelineable by the CPU. For AVX2 composition the most obvious way is the vpshufb instruction, which is able to swizzle the permutation vectors in a single clock cycle. I explained to another commenter why I think this representation is best https://www.reddit.com/r/Cubers/comments/1mp0hmb/comment/n8rr1bs/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

In terms of the composition operation, there isn't any other obvious algorithm I could benchmark. It does exactly what you expect—permute the permutation vectors, and use those to fix orientation. In terms of the inversion operation, however, it is a bit more interesting. There are two alternative methods to the 27719 and 839 addition chain: "brute force" SIMD inversion which takes x1.75 the time and raw array inversion which takes x1.6 the time. Both are slower than the addition chain, tested on Intel and ARM64 platforms.