> Exactly what constitutes "correct" varies from one situation to another. For example, fast inverse square root approximates multiplicative inverse: for situat

> Exactly what constitutes "correct" varies from one situation to another. For example, fast inverse square root approximates multiplicative inverse: for situations such as games, its fast nearly-correct answer is a better trade-off than a slow definitely-correct answer. Amazingly in topic, the famous constant 0x5f3759df from this algorithm was also thought to be derived from an approximate search algorithm because you need ~2^31 calls to determine the maximal relative error for a single constant---a big deal back in 1980s. A better constant 0x5f375a86 was only found in 2003, and took a few more years to be proven optimal (Robertson 2012, Moroz et al. 2016).