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As Olivier mentioned, it's not safe in general to apply algebraic optimizations to floating-point math, as floating point doesn't actually obey associativity rules due to roundoff error. $(a + b) - b$ will not be equal to $a$, if the intermediate result $(a + b)$ had to be rounded; nor will $a \cdot (b + c)$ be equal to $a \cdot b + a \cdot c$ in general, ...


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