Given a table of values $x$, $y$ and $z$, find a formula that expresses $z$ as a function of $x$ and $y$

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I'm not really versed in this kind of mathematics, but I ran into this problem while programming, so I find myself turning to the hivemind. (Thus I don't even know the proper tags to use here... Feel free to correct them, whoever can..)

Given a table of values for $x$, $y$ and $z$, how would I go about finding a formula for $z$ that expresses $z$ as a function of $x$ and $y$?

Also, there is a chance that the values I have for $z$ in the table, are not exact (they may be close to $99\%$ accurate). Is there a way to account for some level of tolerance?

Any and all help is greatly appreciated!