demo, C++ (clang) - rextester

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#include <iostream>
#include <type_traits>

using namespace std;

template <typename T>
class base {
public:
    base (T val = T())
        : m_val(val)
    {}
    base (const base &other)
        : base(other.m_val)
    {}
    virtual void base_specific_method()
    {
        cout << __func__ << " method called: " << m_val << endl;
    }
    void each_class_has_this() {
        cout << __func__ << " this is boring..." << endl;
    }
    T m_val;
};
class other {
public:
    void each_class_has_this() {
        cout << __func__ <<" this is boring..." << endl;
    }
};
class derived_i : public base <int>
{
public:
    derived_i () : base <int> (10)
    {}
    virtual void base_specific_method() override
    {
        cout << __func__ <<" Hey! I'm interesting derived! And 10 == " << m_val << endl;
    }
};

template <typename T, typename TT = void>
class caller {
public:
    caller (T val = T())
        : m_val(val)
    {}
    void call() {
        p_call(m_val);
    }
private:
    template <typename T1> typename std::enable_if<!std::is_base_of<base<TT>, T1>::value>::type p_call (T1 &val)
    {
        val.each_class_has_this();
    }
    template <typename T1> typename std::enable_if<std::is_base_of<base<TT>, T1>::value>::type p_call(T1& val)
    {
        val.base_specific_method();
    }

private:
    T m_val;
};

int main ()
{
    caller<other> c1;
    caller<base<double>, double> c2;
    caller<derived_i, int> c3;

c1.call();
    c2.call();
    c3.call();
}

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Compilation time: 0.62 sec, absolute running time: 0.14 sec, cpu time: 0 sec, memory peak: 3 Mb, absolute service time: 0,77 sec