This method gets the user agent and parses it to find the browser. The browser name and version are extracted from the user agent through a regex. Based on these two, the <browser name> <version> is returned.

The four conditional blocks following the user agent matching code are meant to account for differences in the user agents of different browsers. For example, in case of opera, since it uses Chrome rendering engine, there is an additional step of ignoring that part.

Note that this method can be easily spoofed by a user.

navigator.sayswho= (function(){
    var ua= navigator.userAgent, tem,
    M= ua.match(/(opera|chrome|safari|firefox|msie|trident(?=\\/))\\/?\\s*(\\d+)/i) || [];
    if(/trident/i.test(M[1])){
        tem=  /\\brv[ :]+(\\d+)/g.exec(ua) || [];
        return 'IE '+(tem[1] || '');
    }
    if(M[1]=== 'Chrome'){
        tem= ua.match(/\\b(OPR|Edge)\\/(\\d+)/);
        if(tem!= null) return tem.slice(1).join(' ').replace('OPR', 'Opera');
    }
    M= M[2]? [M[1], M[2]]: [navigator.appName, navigator.appVersion, '-?'];
    if((tem= ua.match(/version\\/(\\d+)/i))!= null) M.splice(1, 1, tem[1]);
    return M.join(' ');
})();

Credit to kennebec