Interchangeability of IEEE 754 floating-point addition and multiplication

Is the addition x + x interchangeable by the multiplication 2 * x in IEEE 754 (IEC 559) floating-point standard, or more generally speaking is there any guarantee that case_add and case_mul always give exactly the same result?

#include <limits>

template <typename T>
T case_add(T x, size_t n)
{
    static_assert(std::numeric_limits<T>::is_iec559, "invalid type");

    for (size_t i = 1; i < n; ++i)
    {
        x += x;
    }

    return x;
}

template <typename T>
T case_mul(T x, size_t n)
{
    static_assert(std::numeric_limits<T>::is_iec559, "invalid type");

    return x * static_cast<T>(n);
}