Can someone explain how is this different from lambda calculus, it seems like you can derive the same in both. I don't understand both well enough and hence the question.

Lamda kind of does this in an analogous form, but does not allow you to derive this particular binary expression as a basis for elementary functions. There is a related concept with Iota [1], which allows you express every combinatoric SKI term and in turn every lambda definable function. But similar to this particular minimalist scientific function expression, it is mostly of interest for reductionist enthusiasts and not for any practical purpose.

[1] https://en.wikipedia.org/wiki/Iota_and_Jot

Any lambda term is equivalent to a combinatory term over a one-point basis (like λxλyλz. x z (y (λ_.z)) [1]). One difference is that lambda calculus doesn't distinguish between functions and numbers, and in this case no additional constant (like 1) is needed.

[1] https://github.com/tromp/AIT/blob/master/ait/minbase.lam

Lambda calculus talks about computable functions, where the types of the inputs are typically something discrete, like `Bool` or `Nat`. Here, the domain is the real numbers.

The short answer is that the lambda calculus computes transformations on digital values while this is for building functions that can transform continuous (complex) values.