As somebody who has implemented Hans Boehm's "Towards an API for the Real Numbers" paper I cannot agree that the floating point types are "less weird" than alte

As somebody who has implemented Hans Boehm's "Towards an API for the Real Numbers" paper I cannot agree that the floating point types are "less weird" than alternatives. They're much faster of course because they're implemented in hardware, but that's hardly surprising. In my (unpublished) toy calculator I added a mechanism to bring an f32 or f64 into existence and convert it to my Rational type and so that's why I had the exact value of the f32 we call 0.1 to hand earlier. But of course the API goes much further than that. Want to multiply the square root of 40 by the square root of 1000? No problem that's exactly 20. A bright teenager can figure that out, and so can a properly designed API for numbers. The ordinary human activities you talked about of course work just fine in this API, it has historically been how the calculator in an Android phone works for example. Symbolic approaches also have value in this space. In both cases, what you do not get is the problem where the programmer mistakenly believes these types will behave like the numbers in school but actually they behave in an entirely different way. You have to go really far off piste, by which point likely the programmer has appreciated that they do not understand what's going on, before you trip on a hazard we cannot manage with this approach - whereas in traditional floating point that happens without them realising.