I like the Rust approach of adding operations like `algebraic_add` instead of supporting a compiler flag. This avoids undefined behaviour and keeps the complications from optimizations localized to code using these.

https://doc.rust-lang.org/std/primitive.f32.html#algebraic-o...

> Algebraic operators of the form a.algebraic_*(b) allow the compiler to optimize floating point operations using all the usual algebraic properties of real numbers – despite the fact that those properties do not hold on floating point numbers. This can give a great performance boost since it may unlock vectorization.

> The exact set of optimizations is unspecified but typically allows combining operations, rearranging series of operations based on mathematical properties, converting between division and reciprocal multiplication, and disregarding the sign of zero. This means that the results of elementary operations may have undefined precision, and “non-mathematical” values such as NaN, +/-Inf, or -0.0 may behave in unexpected ways, but these operations will never cause undefined behavior.

> Because of the unpredictable nature of compiler optimizations, the same inputs may produce different results even within a single program run. Unsafe code must not rely on any property of the return value for soundness. However, implementations will generally do their best to pick a reasonable tradeoff between performance and accuracy of the result.