Compile expressions for repeated calculation

compile(expr) turns a parsed mathematical expression into an object that can be evaluated repeatedly. It is useful when an expression is fixed but its variables change: compile once, then provide a different scope for each calculation. This avoids repeatedly parsing text and keeps application code clear.

How compilation fits the workflow

Start with an expression such as x^2 + 2*x + 1, compile it, and evaluate it with a scope where x has a value. For a single, direct calculation, evaluate is usually simpler. Use parse when you need to inspect or transform the expression tree first, and simplify when a reduced symbolic form is helpful.

Practical example

A pricing rule can be compiled once and evaluated for many orders: subtotal * (1 - discount) + shipping. Supplying a fresh scope for each order is preferable to changing global variables. The same pattern works for simulations, plotted functions, and reusable formulas. If a formula contains constants such as pi, they can normally be resolved along with values in the supplied scope.

Inputs and safe use

The expression must use valid calculator syntax. Compilation does not make an invalid expression valid; syntax errors should be handled before evaluation. Treat expressions received from users as code-like input: only expose the names and functions you intend to allow, and do not blindly evaluate untrusted formulas in a sensitive environment. For symbolic tasks, pair compilation with derivative or integrate; use resolve when names in an expression need to be examined.

When to choose another function

Use evaluate for an ad-hoc answer, and compilation when the expression will be run again. Keeping those two jobs distinct makes formulas easier to test and reuse.