There's a link in there to future directions for Herbie which talks about the intriguing idea of out-sourcing the translation of a high level "I want to do this real number math" to the lower level "Here's some floating point arithmetic" via Herbie.

That is, the physicist writes the two line equation they want for electromagnetic force into their program, the same way they'd write a for-each style loop in the program if that's what they needed.

Obviously the CPU doesn't understand how to compute the appropriate approximation for this electromagnetic force equation, but nor does it understand how to iterate over each item in a container. Tools convert the for-each loop into machine code, why shouldn't other, smart, tools convert the physicist's equation into the FP instructions ?

Today the for-each loop thing just works, loads of programming languages do that, if a language can't do it (e.g. C) that's because it is old or only intended for experts or both.

But every popular language insists that physicist should laboriously convert the equation into the code to compute an approximation, which isn't really their skill set, so why not automate that problem?