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    my @output =
      map { $_->[0] }
      sort { $a->[1] cmp $b->[1] }
      map { [$_, expensive_func($_)] }
    @input;

    foreach $_ (@input) {
        $result_for{$_} = expensive_func($_);
    }
...
    my @output
        = sort { $result_for{$a} cmp $result_for{$b}
               } @input;