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#### Using C++11 Lambda's

Since all the root finding functions accept a function-object, they can be made to work (often in a lot less code) with C++11 lambda's. Here's the much reduced code for our "toy" cube root function:

    template <class T>
    T cbrt_2deriv_lambda(T x)
    {
       // return cube root of x using 1st and 2nd derivatives and Halley.
       //using namespace std;  // Help ADL of std functions.
       using namespace boost::math::tools;
       int exponent;
       frexp(x, &exponent);                                // Get exponent of z (ignore mantissa).
       T guess = ldexp(1., exponent / 3);                    // Rough guess is to divide the exponent by three.
       T min = ldexp(0.5, exponent / 3);                     // Minimum possible value is half our guess.
       T max = ldexp(2., exponent / 3);                      // Maximum possible value is twice our guess.
       const int digits = std::numeric_limits<T>::digits;  // Maximum possible binary digits accuracy for type T.
       // digits used to control how accurate to try to make the result.
       int get_digits = static_cast<int>(digits * 0.4);    // Accuracy triples with each step, so stop when just
       // over one third of the digits are correct.
       boost::uintmax_t maxit = 20;
       T result = halley_iterate(
          // lambda function:
          [x](const T& g){ return std::make_tuple(g * g * g - x, 3 * g * g, 6 * g); },
          guess, min, max, get_digits, maxit);
       return result;
    }

Full code of this example is at root_finding_example.cpp,