Override a member function with different return type

Consider the example below:

#include <iostream>

using namespace std;

class base
{
   public:
      virtual int func()
      {
         cout << "vfunc in base class\n";
         return 0;
      }
};

class derived: public base
{
   public:
      double func()
      {
         cout << "vfunc in derived class\n";
         return 0;
      }
};

int main()
{
   base *bptr = new derived;
   bptr->func();

   return 0;
}

The compiler gives an error for the above code that there is conflicting type for the overriden function. Why is it not possible to override a function in the derived class with a different return type ?

I believe, in-order to override a function, the base class virtual method needs to be redefined in the derived class. To redefine a method, the signatures of the methods has to be the same. Since return type is not part of the signature, i believe even if there is difference in return type, the method will still be redefined? In that case for the code above, virtual function func is redefined in the derived class with a different return type. But the compiler throws an error. Is my understanding correct?

Overriding essentially means that either the Base class method or the Derived class method will be called at run-time depending on the actual object pointed by the pointer.
It implies that:
i.e: Every place where the Base class method can be called can be replaced by call to Derived class method without any change to calling code.

In order to achieve this the only possible way is to restrict the return types of the overriding virtual methods to return the same type as the Base class or a type derived from that(co-variant return types) and the Standard enforces this condition.

If the above condition was not in place it would leave a window to break the existing code by addition of new functionality.