The discussion revolves around the concept of simplifying mathematical expressions, exploring what it means to simplify, the criteria involved, and the subjective nature of determining simplicity. Participants consider both theoretical and practical aspects, including programming implications.
Participants express varying opinions on what constitutes a simpler expression, indicating that there is no clear consensus on the criteria for simplicity. The discussion remains unresolved regarding the subjective nature of simplification.
Participants acknowledge that the definition of simplicity may depend on context, such as numerical evaluation or programming considerations, and that there may be multiple valid approaches to simplification.
You also often cancel terms in a fraction when you know ( or assume) they are not zero.Fascheue said:What exactly does it mean to simplify an expression. I understand that an expression becomes more simple when you combine like terms but what other conditions are there? Is x(5x+1) more or less simple than 5x^2 +x? Do square roots need to be moved to the numerator?
Do these compiler contain optimizers in the way SQL Server does? Optimizer in SQL Server looks at query format, usage statistics, indexes and decides on best way of running query. Would be nice to have similar for other software.eys_physics said:As a side note, from the point of view of evaluating the expression numerically (on a computer) the first expression might be better. The reason is that the first one requires 4 operations (2 multiplications and 1 addition) but the second one 5 (3 multiplications and 1 addition). Many compilers are doing this kind of optimizations but it could have importance for script languages, if this sort of expressions are evaluated many times.
It's like art -- you know it when you see it.mfb said:It is not always unambiguous which expression is the easiest, but typically there are not many options.