I always end up going back to Rump's example (https://link.springer.com/article/10.1023/A:1015569431383 https://link.springer.com/article/10.1023/A:101556943138

I always end up going back to Rump's example (https://link.springer.com/article/10.1023/A:1015569431383 https://link.springer.com/article/10.1023/A:1015569431383): > Rump’s example is to compute the expression > ƒ = 333.75 * b^6 + a^2 * (11 * a^2 * b^2 − b^6 − 121 * b^4 − 2) + 5.5 * b^8 + a/(2b) > with a = 77617 and b = 33096. On an IBM S/370 main frame he computed ƒ in (1.1) using single, double, and extended-precision arithmetic, to produce the results: > Single precision: ƒ = 1.172603... > Double precision: ƒ = 1.1726039400531... > Extended precision: ƒ = 1.172603940053178... > This suggests a reliable result of approximately 1.172603 or even 1.1726039400532. In fact, however, the correct result (within one unit of the last digit) is > ƒ = −0. 827396059946821368141165095479816... (1.2) > Even the sign was wrong. It's worth remembering that computers are very fast, but also very, very stupid. They do exactly what you tell them (or teach them, if we're talking about MCL), which isn't always what you want. Just because you've got a very scientific looking algorithm doesn't mean it's correct. Just because you're aggregating all your data doesn't mean the results are truly meaningful.