Not a native speaker; I think I understand your point, though I fail to see a distinction between these two words: if the output is a number to the nth decimal, but it is not "accurate" (ie. the numbers are actually wrong), can it still be said to be "precise" ?
Precise means lots of fine-grained information; accurate means close to the truth. If the weather is 20° exactly and one thermometer reads 20.2° and another 20.562° the first can be described as more accurate and the latter as more precise. Hence the expression, “precisely wrong”.
