Not in the slightest. For example, the output of a numerically unstable [1] algorithm, run on 64-bit floats, can diverge arbitrarily from the output of the same algorithm run on real numbers with infinite precision (which computers can't do). Often this will lead to obviously wrong outputs, but not always. There are numerically-stable versions of most of the workhorse linear algebra algorithms, but (1) sometimes it's possible to use a faster, numerically unstable algorithm, and this is a matter of judgment that can be mistaken and (2) it's easy to introduce numerical instability via subtle bugs, or even via the exact arithmetic steps you use to calculate a result (in particular, trying to add or subtract two numbers of very different orders of magnitude is a big no-no).

[1] https://en.wikipedia.org/wiki/Numerical_stability