Is fasting three days sufficient as an expiation for not adhering to a severe diet promised to oneself?

Scholars have differed regarding what is necessitated by the phrase "I covenant with Allah." The preponderant opinion is that it constitutes a vow if what is committed to is an act of worship, and an oath if what is committed to is not an act of worship. Accordingly, this expression functions as an oath, and whoever breaks it must offer an expiation for an oath: feeding ten poor persons, or clothing them, or freeing a slave. If one is unable to do so, then fasting for three consecutive days. This applies if the covenant was made verbally; however, if it was merely an intention, then nothing is necessitated.