If you need to do this operation many times on an unchanging array, you can use a hash to store the indices. You'd have to re-set the hash any time the array contents changed. You could use an object to encapsulate this mess. :-)

my @array = ( ... );

my %array_element_index;
@array_element_index{ @array } = (0 .. $#array);

my $i = $array_element_index{ $value_of_interest };
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Of course, this method and the repeated-greps method both have their own idiosyncratic costs, so which one is more effective/efficient for you really depends on your situations.