The thing recalled in your definition of faithfully recount seems to need sharpening since any successful pattern completion of such a thing (episodic event) is conditioned on its distinct pattern separation during its initial encoding and storage. In psychology the right term should be engram (aka memory trace). Simply mentioning mundane things or events such as brushing teeth and washing face won't be useful for your purpose to be qualified as faithful recount of the whole day $d$.
Another difficulty here is usually our hippocampus is adequate to very quickly store today or yesterday's most episodes which are ready anytime to be further retrieved for working memory use, but to form long term memory, system consolidation needs weeks, months, even years of retrieval and rehearsal as confirmed by this online source which cites several references as sampled below. Thus it's not uncommon that $x$ cannot recall 2 things of $d$ of this past week but can recall clearly for a day $d'$ of last year! Thus it's hard to apply the definition formulated in OP in practical experiments.
Finally for your purpose under further narrower assumptions such as ignore long term memory effect and for an average healthy person there're at least 2 distinct episodic events occur every day (time is not wasted in vein), then according to above reference such person may on average faithfully recount up to several weeks and its variance could be as large as several months even years as reflected by the hyperthymestic syndrome.
Dudai, Y. (2004). "The Neurobiology of Consolidations, Or, How Stable is the Engram?". Annual Review of Psychology. 55: 51–86. doi:10.1146/annurev.psych.55.090902.142050. PMID 14744210.