db.logs.aggregate([
    {$match:
        { date:
            { $regex: "^((2012-(1[0-2]|0[5-9]))|(2013-(0[1-5]))).*$" }
        }
    },
    {$group:
        {_id:
            {
                day :  "$date",
                service: "$service"
            },
            count: {$sum:1}
        }
    },
    {
        $sort: {_id:1}
    }
])