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    What is your concern and why are you bothering with x * x == 0 instead of just x == 0? For x such that x * x == 0, I would expect sin(q) and sinh(q) to return q because the actual value of sin q and sinh q is so close to q that q is the closest representable value. Then both sin (q) / q and sinh (q) / q produce 1, as does 1 - x / 6 (because x is so small that 1 is the closest representable value to 1 − x/6). So what are you gaining with x * x == 0 instead of just x == 0? Commented May 10, 2025 at 14:41
  • @EricPostpischil My concern was that when |x| is small, then there is "not enough" information in the sub-normal mantissa to yield results in the error margin. Commented May 15, 2025 at 11:05

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