What is the best method for 1D numeric differentiation? Something as glorious as Gaussian quadrature for numeric integration.

Maybe differential quadrature is such a method? What is its accuracy?

I'm well aware that it is really easy to have symbolic differentiation in the program (automatic differentiation or truly symbolic algorithm). However to use such methods it is necessary to rewrite all functions to be differentiated. Thus one can't differentiate functions imported from libraries.

I need differentiation almost with the machine precision.