very slow filters with couchDB even with erlang

I have a database (couchDB) with about 90k documents in it. The documents are very simple like this:

{
   "_id": "1894496e-1c9e-4b40-9ba6-65ffeaca2ccf",
   "_rev": "1-2d978d19-3651-4af9-a8d5-b70759655e6a",
   "productName": "Cola"
}

now I want one day to sync this database with a mobile device. Obviously 90k docs shouldn't go to the phone all at once. This is why I wrote filter functions. These are supposed to filter by "productName". At first in Javascript later in Erlang to gain performance. These Filter functions look like this in JavaScript:

{
   "_id": "_design/local_filters",
   "_rev": "11-57abe842a82c9835d63597be2b05117d",
   "filters": {
       "by_fanta": "function(doc, req){ if(doc.productName == 'Fanta'){ return doc;}}",
       "by_wasser": "function(doc, req){if(doc.productName == 'Wasser'){ return doc;}}",
       "by_sprite": "function(doc, req){if(doc.productName == 'Sprite'){ return doc;}}"
   }
}

and like this in Erlang:

{
   "_id": "_design/erlang_filter",
   "_rev": "74-f537ec4b6508cee1995baacfddffa6d4",
   "language": "erlang",
   "filters": {
       "by_fanta": "fun({Doc}, {Req}) ->  case proplists:get_value(<<\"productName\">>, Doc) of <<\"Fanta\">> -> true; _ -> false end end.",
       "by_wasser": "fun({Doc}, {Req}) ->  case proplists:get_value(<<\"productName\">>, Doc) of <<\"Wasser\">> -> true; _ -> false end end.",
       "by_sprite": "fun({Doc}, {Req}) ->  case proplists:get_value(<<\"productName\">>, Doc) of <<\"Sprite\">> -> true; _ -> false end end."       
   }
}

To keep it simple there is no query yet but a "hardcoded" string. The filter all work. The problem is they are way to slow. I wrote a testprogram first in Java later in Perl to test the time it takes to filter the documents. Here one of my Perl scripts:

$dt =