#include <kaysha/kaysha.hpp>
#include <iostream>

int main()
{
    constexpr auto x  = kaysha::variable<double>{};
    constexpr auto _2 = kaysha::constant<double>{2.0};
    constexpr auto _1 = kaysha::constant<double>{1.0};

    constexpr auto f = x * x + _2 * x + _1;

    std::cout << "f(x) = x^2 + 2x + 1" << std::endl;
    std::cout << "f(1) = " << f(1.0)   << std::endl;
    std::cout << "f(2) = " << f(2.0)   << std::endl;
    std::cout << "f(3) = " << f(3.0)   << std::endl;
    std::cout << "f(4) = " << f(4.0)   << std::endl;

    constexpr auto df = kaysha::differentiate(f);

    std::cout << "f'(x) = 2x + 2"       << std::endl;
    std::cout << "f'(1) = " << df(1.0)  << std::endl;
    std::cout << "f'(2) = " << df(2.0)  << std::endl;
    std::cout << "f'(3) = " << df(3.0)  << std::endl;
    std::cout << "f'(4) = " << df(4.0)  << std::endl;

    constexpr auto ddf = kaysha::differentiate(df);

    std::cout << "f''(x) = 2"            << std::endl;
    std::cout << "f''(1) = " << ddf(1.0) << std::endl;
    std::cout << "f''(2) = " << ddf(2.0) << std::endl;
    std::cout << "f''(3) = " << ddf(3.0) << std::endl;
    std::cout << "f''(4) = " << ddf(4.0) << std::endl;

    return 0;
}

template<typename L, typename R>
struct addition
{
    value_type operator()(const value_type x) {return lhs(x) + rhs(x);}

    L lhs;
    R rhs;
};
template<typename L, typename R>
struct differentiation<addition<L, R>>
{
    // d(f(x) + g(x)) / dx = df/dx + dg/dx
    using type = addition<typename differentiation<L>::type,
                          typename differentiation<R>::type>;
};

template<typename L, typename R>
addition<L, R> operator+(const L&, const R&);

template<typename L, typename R>
addition<typename differentiation<L>::type, typename differentiation<R>::type>
differentiate(const addition<L, R>&);