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$hash{"$regexp"} = $value;

...
$value  = $hash{$key};
$regexp = qx/$key/;  # Expensive

$hash{"$regexp"} = [ $regexp, $value ];

...
$value  = $hash{$key}[1];
$regexp = $hash{$key}[0];

$hash{"$regexp"} = $value;
$regexps{"$regexp"} = $regexp;
...
...
$value = $hash{$key};
$regexp = $regexps{$key};