In this Q&A: What or who were the Oracle and the Architect?, we find out what the Oracle is. In short, the Architect says:
Architect: ... Thus the answer was stumbled upon by another – an intuitive program, initially created to investigate certain aspects of the human psyche. If I am the father of the Matrix, she would undoubtedly be its mother.
Neo: The Oracle.
It also appears to be the case that she took the Merovingian's place, so presumably she now has a purpose similar to his purpose back when he wasn't an exile. See: What kind of program is the Merovingian?
However, what I'm struggling with is understanding this conversation Neo has with the Oracle after we meet Seraph:
Oracle: [The Architect] doesn’t understand [choices] – he can’t. To him they are variables in an equation. One at a time each variable must be solved and countered. That’s his purpose: to balance an equation.
Neo: What’s your purpose?
Oracle: To unbalance it.
According to the Architect, her purpose is to "investigate certain aspects of the human psyche", but she claims it is "to unbalance equations" (paraphrased). Of course, she was speaking more poetically, whereas the Architect was speaking more literally (I assume). I'm also assuming that the Architect is correct when he says what he says about why the Oracle was created, and I interpret that to mean that that is therefore her purpose.
So what is her purpose, exactly (i.e. is my understanding of the Architect's words above correct? Or is it now to effectively be the "new Merovingian"?), and how to reconcile what the Oracle said regarding unbalancing equations with her purpose?