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Comment by stiff | Hacker News Reader

Actually, it's a pretty interesting idea. He basically wants to keep track of the last n operations with every given number and take advantage of this history to try to minimize the floating point error. To compare 2.2 with exp(6.5) or anything else you just evaluate the expression, but taking advantage of possible reorderings or simplifications.

Your critique really boils down to:

Most equations that aren't trivial cannot be simplified.

but this is not true, just take a look at what Wolfram Alpha or Mathematica can do.

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There are also numbers that can't _possibly_ be represented by this system using the elementary functions/operators, i.e. are "non-analytic".

This may actually not be a problem in most instances, however. It really depends on the use case, but outside of scientific computing/engineering design we're not usually doing computations to find roots of degree >= 5 polynomials.

OTOH, as pointed out by GP, it is easy to construct 'unsimplifiable' operations which after some time may grow too large.

My conclusions are, this certainly cannot be implemented on practical systems without some care -- it's not as straightforward as it looks at first -- and certainly not a better default as is right now.

If you have an equation in your program that can be effectively simplified, you should have simplified it before writing in the first place. The thing about equations that can be simplified is that 99.9% of the time, they can be simplified at compile time.

If you want to write a library to do it for you, great! But don't advertise it as a replacement for floating point number representations, because it isn't.

Hey, why have compilers, if you can just write hand-optimized assembly yourself!

Compilers aren't able to do similar optimizations, first of all the flow of data that finally leads to some computation might be non-trivial and I think most compilers deal well only with reasonably local (in space and in time) optimizations. Besides, compilers typically don't know much mathematics. If I have a function for taking a square root and a function for squaring the compiler most likely wont rewrite sqr(sqrt(x)) to just x. Certainly it wont rearrange a quadratic equation to minimize round-off.

You are basically totally dismissing an idea on very little evidence, which is typical of HN lately. It certainly isn't completely hopeless and trying it out will shed much more light on the problem than your know-it-all-in-advance comments not substantiated by any evidence (like the claim about not being able to simplify most expressions and now the claim of 99.9%).

He want more than compile-time simplification. He wants runtime simplification depending on the values encountered at runtime. For example in the quadratic equation.

And, he clearly isn't marketing it as a replacement for floating point. He says: "It is important to note, however, that the goal of the project is to make tools for symbolic calculations, not to create a viable alternative to the floating point." and he talks a lot about estimating numerical error and precision.

He says this about SymPy...

oops you're right. Nevertheless, he clearly intends to extend rather than replace floating point since one of the goals is to estimate the errors in the floating point calculations, and he rounds.

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