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Sacado Speed: Second Derivative of a Polynomial

Operation Sequence
Note that the polynomial evaluation operation sequence does not depend on the argument to the polynomial. Yet there does not seem to be a way to reuse the DAG to compute derivatives for other values of z.

compute_poly
Routine that computes the derivative of a polynomial using Sacado:
 
# include <cppad/vector.hpp>
# include <cppad/poly.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <Sacado.hpp>

bool compute_poly(
	size_t                     size     , 
	size_t                     repeat   , 
	CppAD::vector<double>     &a        ,  // coefficients of polynomial
	CppAD::vector<double>     &z        ,  // polynomial argument value
	CppAD::vector<double>     &ddp      )  // second derivative w.r.t z  
{
	// -----------------------------------------------------
	// setup
	typedef Sacado::Tay::Taylor<double>  ADScalar;
	CppAD::vector<ADScalar>              A(size);

	size_t i;               // temporary index     
	ADScalar   Z;           // domain space AD value
	ADScalar   P;           // range space AD value 
	unsigned int order = 2; // order of Taylor coefficients
	Z.resize(order+1, false);
	P.resize(order+1, false);

	// choose the polynomial coefficients
	CppAD::uniform_01(size, a);

	// AD copy of the polynomial coefficients
	for(i = 0; i < size; i++)
		A[i] = a[i];

	// ------------------------------------------------------
	while(repeat--)
	{	// get the next argument value
		CppAD::uniform_01(1, z);

		// independent variable value
		Z.fastAccessCoeff(0)   = z[0]; // argument value
		Z.fastAccessCoeff(1)   = 1.;   // first order coefficient
		Z.fastAccessCoeff(2)   = 0.;   // second order coefficient

		// AD computation of the dependent variable
		P = CppAD::Poly(0, A, Z);

		// second derivative is twice second order Taylor coefficient
		ddp[0] = 2. * P.fastAccessCoeff(2);
	}
	// ------------------------------------------------------
	return true;
}

Input File: speed/sacado/poly.cpp