A sanity test or "smoke test" is a brief run-through of the main functionality of a computer program or other product. It gives a measure of confidence that the system works as expected prior to a more exhaustive round of testing.
Also, the name sanity test has been used to refer to various order of magnitude and other rule-of-thumb devices applied to mathematical calculations. 7382 cannot be equal to 53,874 since 3002 is 90,000; the power output of a car cannot be 700 kJ since that is a unit of energy, not power (energy per unit time) and 918 x 155 is not 142135 since 918 divides by three but the answer does not (digits do not add up to a multiple of three).