A simple sunrise-sunset algorithm taken from http://williams.best.vwh.net/sunrise_sunset_algorithm.htm in JavaScript

computeSunrise.js

function computeSunrise(day, sunrise) {

    /*Sunrise/Sunset Algorithm taken from
        http://williams.best.vwh.net/sunrise_sunset_algorithm.htm
        inputs:
            day = day of the year
            sunrise = true for sunrise, false for sunset
        output:
            time of sunrise/sunset in hours */

    //lat, lon for Berlin, Germany
    var longitude = 13.408056;
    var latitude = 52.518611;
    var zenith = 90.83333333333333;
    var D2R = Math.PI / 180;
    var R2D = 180 / Math.PI;

    // convert the longitude to hour value and calculate an approximate time
    var lnHour = longitude / 15;
    var t;
    if (sunrise) {
        t = day + ((6 - lnHour) / 24);
    } else {
        t = day + ((18 - lnHour) / 24);
    };

    //calculate the Sun's mean anomaly
    M = (0.9856 * t) - 3.289;

    //calculate the Sun's true longitude
    L = M + (1.916 * Math.sin(M * D2R)) + (0.020 * Math.sin(2 * M * D2R)) + 282.634;
    if (L > 360) {
        L = L - 360;
    } else if (L < 0) {
        L = L + 360;
    };

    //calculate the Sun's right ascension
    RA = R2D * Math.atan(0.91764 * Math.tan(L * D2R));
    if (RA > 360) {
        RA = RA - 360;
    } else if (RA < 0) {
        RA = RA + 360;
    };

    //right ascension value needs to be in the same qua
    Lquadrant = (Math.floor(L / (90))) * 90;
    RAquadrant = (Math.floor(RA / 90)) * 90;
    RA = RA + (Lquadrant - RAquadrant);

    //right ascension value needs to be converted into hours
    RA = RA / 15;

    //calculate the Sun's declination
    sinDec = 0.39782 * Math.sin(L * D2R);
    cosDec = Math.cos(Math.asin(sinDec));

    //calculate the Sun's local hour angle
    cosH = (Math.cos(zenith * D2R) - (sinDec * Math.sin(latitude * D2R))) / (cosDec * Math.cos(latitude * D2R));
    var H;
    if (sunrise) {
        H = 360 - R2D * Math.acos(cosH)
    } else {
        H = R2D * Math.acos(cosH)
    };
    H = H / 15;

    //calculate local mean time of rising/setting
    T = H + RA - (0.06571 * t) - 6.622;

    //adjust back to UTC
    UT = T - lnHour;
    if (UT > 24) {
        UT = UT - 24;
    } else if (UT < 0) {
        UT = UT + 24;
    }

    //convert UT value to local time zone of latitude/longitude
    localT = UT + 1;

    //convert to Milliseconds
    return localT * 3600 * 1000;
}

@Tafkas Would you mind putting this code under an open source license? MIT would be handy for me.

Your source link for the algorithm is dead, but can still be found at https://web.archive.org/web/20161022214335/http://williams.best.vwh.net/sunrise_sunset_algorithm.htm or the original print: https://books.google.de/books?id=GbDC6AaH-kAC&hl=de&pg=SL2-PA5
Not entirely sure how much copyright from the book remains in your code.

BTW you might also wanna replicate that the algorithm was meant to be used in 1950-2000, and between 65°N and 65°S :)