Find maximum regular expression length. Note that I guess the maximum length could be different if other regular expression features are used.

maxregexp_node.js

var upper = 0x7fffffff; // maximum signed 32 bit integer
var lower = 0;

while (lower + 1 < upper) {
	var index = ((lower + upper) / 2)|0;
	try {
		new RegExp(new Array(index + 1).join('A'));
		lower = index;
		console.log(index + ' is ok');
	} catch(e) {
		console.log(index + ' is too big (' + e.constructor.name + ')');
		upper = index;
	}
}

console.log('maximum regular expression size is ' + lower + ' ASCII character');

maxregexp_web.js

var script = '\n' +
'self.onmessage = function (event) {\n' +
'if (event.data === "start") {\n' +
'var upper = 0x7fffffff; // maximum signed 32 bit integer\n' +
'var lower = 0;\n' +
'\n' +
'while (lower + 1 < upper) {\n' +
'	var index = ((lower + upper) / 2)|0;\n' +
'	try {\n' +
'		new RegExp(new Array(index + 1).join("A"));\n' +
'		lower = index;\n' +
'		self.postMessage({size:index, ok:true});\n' +
'	} catch(e) {\n' +
'		self.postMessage({size:index, ok:false, error: e.constructor.name});\n' +
'		upper = index;\n' +
'	}\n' +
'}\n' +
'self.postMessage({size:lower, ok:true, done:true});\n' +
'}};\n';

var blob = new Blob([script], {type:'text/javascript'});
var worker = new Worker(window.URL.createObjectURL(blob));
worker.onmessage = function(event) {
	if (event.data.done) {
		console.log('maximum regular expression size is ' + event.data.size + ' ASCII character');
	} else if (event.data.ok) {
		console.log(event.data.size + ' is ok');
	} else {
		console.log(event.data.size + ' is too big (' + event.data.error + ')');
	}
};

worker.postMessage('start');

Results.txt

Google Chrome 68.0.3440.84 64 bit Linux:  41943040
NodeJS v8.11.1 64 bit Linux:              41943040
Mozilla Firefox 61.0.1 64 bit Linux:     268435455