The challenge here is knowing the shape of the manifold within an epsilon radius 65 Billion dimension sphere around the position being evaluated. To calculate t

The challenge here is knowing the shape of the manifold within an epsilon radius 65 Billion dimension sphere around the position being evaluated. To calculate this you would need to sample points within epsilon radius around the current point. As these points will be lower-precision by default, you would have minimal knowledge of the shape of the manifold within the sphere if epsilon is < the minimum precision. It might be possible to work around this by estimating the gradient volatility through the n^th order derivatives, but you would then also have to deal with mixed precision SIMD which hardware doesn't really support.