Automatic Differentiation using the AutoDiff Library

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using AutoDiff;

namespace NewtonRaphsonSample
{
    class Program
    {
        static void Main(string[] args)
        {
            // define and compile our function
            var x = new Variable();
            var func = TermBuilder.Exp(-x) + x - 2;
            var compiledFunc = func.Compile(x);

            // compute the two solutions
            var solution1 = NewtonRaphson(compiledFunc, -1);
            var solution2 = NewtonRaphson(compiledFunc, 2);

            Console.WriteLine("X1 = {0}, X2 = {1}", solution1, solution2);
        }

        static double NewtonRaphson(ICompiledTerm function, double x0, int iterationsCount = 10)
        {
            double x = x0;
            for (int i = 0; i < iterationsCount; ++i)
            {
                var valueAndGradient = function.Differentiate(x);

                // take the function's value - f(x)
                var fx = valueAndGradient.Item2;

                // we are dealing with single-variable functions. Therefore the first gradient element is the derivative
                var dfx = valueAndGradient.Item1[0];

                x = x - fx / dfx;
            }

            return x;
        }
    }
}