By the final battle between Agent Smith and Neo in The Matrix Revolutions, Smith had taken over the Oracle, so the resulting hybrid must have been influenced in part by the Oracle.
Evidence which suggests this:
- At the beginning of the final battle, Smith claims to know the outcome of the fight, something only the Oracle would have a chance of knowing
Neo: It ends tonight.
Smith/Oracle: I know it does – I’ve seen it. That’s why the rest of me is just going to enjoy the show – we already know that I’m the one that beats you.
But then Smith becomes scared and doesn't understand what is happening
Smith/Oracle: Wait… I’ve seen this. This is it, this is the end. Yes, you were laying right there, just like that, and I… I… I stand here, right here, I’m… I’m supposed to say something. I say… Everything that has a beginning has an end, Neo.
{Neo begins to get up again}
Smith/Oracle: What? What did I just say? No… No, this isn’t right, this can’t be right. Get away from me!
Neo: What are you afraid of?
Smith/Oracle: It’s a trick!
The Matrix Revolutions
Smith is overconfident in his abilities, as only one Smith fights Neo, as opposed to all Smiths (which we assume Neo could not have defeated from his battle with Smith in The Matrix Reloaded). This suggests Smith knew he would defeat Neo, so this is closely related to point 1.
Once Smith is killed, the Oracle lies where Smith was defeated. So the Oracle was part of Smith during the whole battle.
My theory, which goes beyond the scope of this question, is that the Oracle orchestrated a lot of what happened in the Matrix trilogy; guiding humans to imbalance the Architect's equations, which ultimately led to peace between humans and machines (a goal most likely in line with the Oracle's motivations given she was developed to understand the "human psyche")
Did the Oracle corrupt Smith by giving him false premonitions that he would win?
If so, this ultimately led to Smith's defeat, due to his false sense of security.