Programming is harder than rocket science, because it still doesn't have a firm mathematical machinery behind it. Yes, there is lambda calculus and other calculi, theory of infinite and finite automata, Boolean algebra, and other strands in mathematics that define the entire field. But what we miss is useful things rocket engineers can use: analysis and algebra. Set up the initial conditions and requirements as equations, and derive a solution, for instance (say) solving Newton's laws of motion for an accelerating rocket engine. We don't have any of that, much less laws of motion.

There are several reasons why there is no such thing:

Social resistance. Your job is secure if you don't frame and divulge your knowledge explicitly.

Artificial complexity. It seems to be human nature to create order where it is not really needed (in terms of reaching the goal).

Real complexity. Many requirements are impossible to express with mathematical precision; some are fuzzy, some change frequently, some have temporal qualities that cannot be encoded in predicate logic, etc.

A part of programming is an art. Perhaps due to inadequate notation, or deficiencies in education, or simply because it requires a certain way of thinking that not everyone can do, you do need tacit knowledge to do anything.

So even if you tried to be precise about the requirements, you will be swamped by (unnecessary) detail and complexity. Perhaps we just need to develop better abstractions.