How to measures script execution and *parsing* time?

You cannot accurately measure script parse time independent of execution time using web APIs alone. Different browsers have different strategies for when they do parsing, and some of them will parse progressively as the script is executed, or even do "partial parsing" in cases where it's assumed a block of code is unlikely to immediately be executed (e.g. a function that is not an IIFE, see some details in the optimize-js README).

Using separate <script> tags is the most accurate way to at least capture both parsing and execution time. The only modification I would make to your snippet is this:

<script>
  performance.mark('start');
</script>
<script src="myscript.js"></script>
<script>
  performance.mark('end');
  performance.measure('total', 'start', 'end');
</script>

Note the use of the high-precision User Timing API which, as an added bonus, will show visualizations in the Chrome/Edge/IE dev tools (and tools like Windows Performance Analyzer and WebPageTest if you're so inclined).

Technically the 3rd <script> is not necessary, as you can just append the mark/measure to the end of the 2nd script. But the 1st <script> is certainly necessary to capture all parse time. You can verify in the dev tools that the marks/measures encompass all initial parsing and execution time.

I know this is kind of an old question but I came across it while looking for a solution to this myself. You can use the dev tools in the browser of your choice to look at this but if you'd like to do it in code this is the method I ended up using.

The scriptLoadParseDuration function below will take a URL to a .js file, place it into a <script> element, and log the load/parse duration to the console.

Keep in mind that this will execute the <script> you are profiling within the current DOM context. So in the example below: jQuery is still accessible in the global scope even though the script was removed. The script could be extended to do all of this in an <iframe> to isolate it though.

function scriptLoadParseDuration(url) {
  var start;
  var script = document.createElement('script');
  
  // <script> must be attached to the document to actually load the file
  document.querySelector('html').appendChild(script);
  
  // Calculate load/parse duration once script has loaded
  script.addEventListener('load', function scriptLoad() {   
    // Calculate load/parse duration
    console.log('Duration: ' + (Date.now() - start) + 'ms');
    
    // Remove <script> from document
    script.parentElement.removeChild(script);
  }, false);
  
  // Get current time in milliseconds
  start = Date.now();
  
  // Setting the `src` starts the loading. Math.random is used to make sure it is an uncached request
  script.src = url + '?' + Math.floor(Math.random() * 9e9);
}

var url = 'https://code.jquery.com/jquery-3.0.0.min.js';

scriptLoadParseDuration(url);

Here is an example showing that jQuery is still in the global scope after the <script> removal.

function scriptLoadParseDuration(url) {
  var start;
  var script = document.createElement('script');
  
  console.log('`jQuery` before attaching: ' + typeof jQuery);
  
  // <script> must be attached to the document to actually load the file
  document.querySelector('html').appendChild(script);
  
  // Calculate load/parse duration once script has loaded
  script.addEventListener('load', function scriptLoad() {   
    // Calculate load/parse duration
    console.log('Duration: ' + (Date.now() - start) + 'ms');

    console.log('`jQuery` once attached: ' + typeof jQuery);
    // Remove <script> from document
    script.parentElement.removeChild(script);
    console.log('`jQuery` after detach: ' + typeof jQuery);
  }, false);
  
  // Get current time in milliseconds
  start = Date.now();
  
  // Setting the `src` starts the loading. Math.random is used to make sure it is an uncached request
  script.src = url + '?' + Math.floor(Math.random() * 9e9);
}

var url = 'https://code.jquery.com/jquery-3.0.0.min.js';

scriptLoadParseDuration(url);

Open up Chrome and open the developer tools, the go to the "Timeline" tab. If you press the record button (filled in circle, bottom left) then reload the page it'll give you a fairly detailed timeline, broken down into specific types of activity (Send Request, Parse, Evaluate), timed down to the microsecond.