# Computing the error bound of floating-point expression

How should I compute the maximum absolute and relative error of the following IEEE-754 floating-point expression?

a.y + (x - a.x) * ((b.y - a.y) / (b.x - a.x))


Also, we assume, that

• the optimizer leaves the expression in the specified form
• the default rounding mode (round to nearest even)
• Hint: the absolute error on a sum/difference is the sum of the absolute errors and the relative error on a product/quotient is the sum of the relative errors. – Yves Daoust May 29 '18 at 12:27
• Why exactly is this question coming back? – gnasher729 Apr 25 '19 at 8:11