Several things are off with the current structure:
A standard cubic spline interpolation in most cases refer to cubic splines where the curvature (second derivative) is continuous at the knots.
Akima spline is a special case, which prevents oscillations by dropping the curvature-continuity condition. The module should be named "Akima" not "Differentiable".
There is no reason to call the cubic spline "Simple" because in fact it is even more differentiable than the Akima version (Akima curvature is not defined at knots).
Proposed structure:
namespace Interpolation
module CubicSpline
// contains standard cubic spline interpolation
// Separate source file
module Akima
// contains Akima spline
Current structure of the Interpolation module
Several things are off with the current structure:
Proposed structure:
Both interpolating splines in action