Somewhat recent experience doing robotics work really highlighted the dangers of dividing by small numbers. As a robot arm approaches a singular configuration,

Somewhat recent experience doing robotics work really highlighted the dangers of dividing by small numbers. As a robot arm approaches a singular configuration, the matrix used to calculate motor torques starts to get very bad and, left unaddressed, will likely result in some pretty wild behaviour. I would argue that dividing by very tiny numbers is also something that you should probably be catching, since the output very large numbers are likely not going to do what you’re expecting...