Generating a C++ function from a list of argument

I am writing a function f to be used in a Runge Kutta integrator.

output RungeKutta(function f, initial conditions IC, etc.)

Since the function will be called many times, I am looking for a way to generate the function f at compile time.

In this case, function f depends on a fixed list of parameters vector p, where p is sparse and is fixed before the code is compiled. To be concrete,

double function f(vector<double> x) {
    return x dot p;
}

Since p is sparse, taking the dot product in f is not the most efficient. Hard-coding x dot p seems to be the way to go, but p can be very long (1000).

What are my options?

Is writing another program (taking p as input) to generate a .cpp file my only option?

Thanks for the comments. Here is a more concrete example for the differential equation.

dy/dx = f_p(x)

One example for f_p(x):

p = [0, 1, 0]; x = [x1, x2, x3]

double f_p(vector<double> x) {
     return x2;  // This is what I meant by hard-coding
}

instead of:

   double f(vector<double> p, vector<double> x) {
       double r = 0;
       for (i=0; i < p.length(); i++) {
              r += p[i]*x[i];
        }
        return r;
   }