This is very similar to dual numbers [1] which I find even easier to reason about.

There is an implementation of dual numbers in Julia [2] that is quite fun to play around with. The Optim.jl package [3] uses this to get better derivatives than finite differencing.

[1] http://en.wikipedia.org/wiki/Dual_number

[2] https://github.com/JuliaDiff/DualNumbers.jl

[3] https://github.com/JuliaOpt/Optim.jl