Find minimum element while transforming the elements

gistfile1.txt

// This is meant to minimic std::minimum_element, but allows you to transform the 
// element in some way. We could use std::minimum_element, but the transform function
// would be evaluated twice as many times as it needs to be as it's results aren't
// cached. This caches the value. 

template<class ForwardIt, class UnaryOperation>
ForwardIt min_transformed_element(ForwardIt first, ForwardIt last, UnaryOperation unary_op)
{
  if (first == last) return last;

  ForwardIt smallest = first;
  auto smallest_val = unary_op(*first);

  ++first;
  for (; first != last; ++first) {
    auto first_val = unary_op(*first);
    if (first_val < smallest_val) {
      smallest = first;
      smallest_val = first_val;
    }
  }
  return smallest;
}

// https://wandbox.org/permlink/Mvr69yFIMtxQB7yy