Extending String.prototype performance shows that function calls are 10x faster

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This is most likely because you are not using strict mode, and the this value inside your method is getting coerced to a String instance instead of being a primitive string. This coercion, and further method calls or property accesses on the String object, are slower than using primitive values.

You can (Edit: could, at least, in 2016) confirm this by repeating your measurement on var STR = new String('01101011…') which should have less overhead.

Then fix your implementation:

String.prototype.count = function (char) {
    "use strict";
//  ^^^^^^^^^^^^
    var n = 0;
    for (var i = 0; i < this.length; i++)
        if (this[i] == char)
            n++;
    return n;
};

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