I think that the "traces" of Descartes' (unattained) project in the Regulae ad directionem ingenii of an "universally applicable" method for the discovery of truth can be found in the three scientific works published with the Discours de la méthode.
In particular, in La Géométrie we can find what remains of the project of a Mathesis universalis.
You can see : Chikara Sasaki, Descartes's Mathematical Thought (2003), Ch.4 : The Mathematical Background of the Regulae, page 159-on.
At least, Descartes claimed to have found "the method" for himself ... but he was quite reticent about it.
He gives us "specimens" of it : we have to judge from them about its "soundness".
For sure, Descartes' promise, if any, of a sort of "systematic procedure" (an algorithm, in modern sense) for discovering the truth has been fulfilled only in a limited way by modern science.