bigint-benchmark-rs VS herbie

Consider using a different big int crate if performance is concerned https://github.com/tczajka/bigint-benchmark-rs

Have you performed benchmarks for this? I imagine it would be nice to have something similar to the big integer benchmarks provided by ibig.

How does it compare in the bigint benchmark?

For big integers, ibig has worked well for me. rug requires libc and GMP (which may be a good or bad thing depending on needs), and ramp is no longer maintained. Some other options are mentioned in ibig's handful of benchmarks.

This benchmark indicates that num-bigint has pretty bad performance. It would be interesting if using a GMP wrapper like rug affects the outcome.

tczajka made a benchmark of the different bigint implementations.

The herbie project using egraphs to explore different ways of rewriting floating point expressions. https://herbie.uwplse.org/ One can also write custom rulesets in egglog (a new egraph rewriting system / language / datalog) https://egraphs-good.github.io/egglog/?example=herbie

The approach is not yet anywhere near being able to touch all the domains sympy can handle. Destructive term rewriting tends to be a bit more forgiving to unsoundness in the rules and still returning roughly meaningful results. EGraph rewriting (and other automated reasoning systems) tend to just return junk as soon as you aren't careful about your semantics. Associativity and commutativity are ubiquitous in CAS applications and encoding these concepts in general purpose terms is rather unsatisfying. The post above emphasizes specialty methods for polynomials, which it would be desirable to find a clean way to integrate into egraph techniques. Variable binding (which is treated in a rather mangled form in CAS systems) is seemingly important for treating summation, differentiation, and integration correctly. The status of doing variable binding efficiently and correctly in egraphs is also unclear imo.

As a starting point, check Herbie: https://herbie.uwplse.org/

Here is a really cool automatic tool that rewrites floating point expressions to be more accurate: https://herbie.uwplse.org/

On a related note, see tools like Herbie which rewrite floating point expressions to improve accuracy without altering the underlying data-type. It's worth being aware that sometimes you get really bad diminishing returns from using bigger floats and what you really need to do is to rewrite the calculation to avoid a weakness of floating point representation, see numerically unstable calculations.