Fast Expression Evaluator

fee is a fast and flexible library for evaluating mathematical expressions from strings. It focuses on runtime performance while keeping the parsing layer simple and efficient.

This crate was originally designed to power scientific and engineering software where expressions cannot be hardcoded:

• The source code may be unavailable for recompilation.
• You may want to ship closed/private tools with configurable formulas.

Over time, fee has grown into a more general-purpose expression engine. It already supports:

• f64 arithmetic
• Boolean logic
• Comparisons
• Bitwise operators

This makes it suitable not only for numerical/scientific use cases, but also for building DSLs, config evaluators, and high-performance runtimes.

Usage

First step is add the dependency to your Cargo.toml.

[dependencies]
fee = { version = "0.2.2" }

The following code shows the default use case

use fee::{prelude::*, DefaultResolver};

fn main()
{
    let expr = "max((2 + 4) * 6 / (p1 + 2), sqrt(p0^2 + p1^2)) + abs(-2)";

    let mut var_resolver = DefaultResolver::empty();
    var_resolver.insert("p0", 10.0);
    var_resolver.insert("p1", 4.0);

    let mut fn_resolver = DefaultResolver::empty();
    fn_resolver.insert("abs", ExprFn::new(abs));

    let context = Context::new(var_resolver, fn_resolver);
    let mut stack = Vec::with_capacity(10);

    let expr = Expr::compile(expr, &context).unwrap();

    let result = expr.eval(&context, &mut stack).unwrap();
    assert_eq!(result, 8.0);
}

fn abs(x: &[f64]) -> f64 {
   x[0].abs()
}

Resolvers

The resolvers are the objects that give meaning to the variables and functions used in an expression. They can be freely combined in a Context depending on your needs.

The current available resolvers are:

• DefaultResolver — No size or naming restrictions, but slower than specialized resolvers.
• IndexedResolver — No size restrictions, but requires specific naming patterns. Very fast.
• SmallResolver — Restricted size, but allows arbitrary names with good performance.
• ConstantResolver — Always resolves to the same value; offers the best performance.
• EmptyResolver — Always resolves to None; useful for expressions without variables or functions.

To learn more about their pros and cons read each struct's documentation.

Features

• Variables
• Functions with no limit in the number of arguments.
• f64 operations.

Supported Operators

Keywords

• true: Boolean literal, equivalent to 1.0 (Values greater than 0.0 are also considered true).
• false: Boolean literal, equivalent to 0.0.

Example of a valid expression:

((x + 3 * y) << 2 ) & 255 | ((10 ^ 2) % 7 )
^^ ((true && (z > 5 || false)) ? 1 : 0 )
+ max(a, b, c)
- min(1, 2, 3)
* abs(-42)

Note: short-circuit not yet implemented.

Smart compilation

One of the goals of this library is provide a simple but powerful API. To archive this, the Expr::compile() method, depending on the context provided and thanks to Rust’s type system, automatically picks the best Expr<T> for your Context. You only need to choose the right resolvers, and fee will compile to the most efficient form at compile time.

The different types of Expr are:

• RPN (Expr<Rpn>): Default and the slowest expression variant.
• Indexed Var RPN (Expr<IVRpn>): Compiled expression with indexed variable resolver.
• Indexed Fn RPN (Expr<IFRpn>): Compiled expression with indexed function resolver.
• Indexed RPN (Expr<IRpn>): Compiled expression with indexed variable and function resolver.
• Locked RPN (Expr<LRpn>): Compiled expression with locked context.

Locking

The context has a method called lock() that allows the context to lock the resolvers it holds. Locking implies that the resolvers will no longer be able to grow in size, avoiding any further reallocations. This enables the use of pointers to get and set the resolver's items values. Using a locked context, the expression can be compiled to a more optimized form, reducing the number of operations required to evaluate the expression in exchange of not being able to add new items to the resolvers.

When building this type of expression, the context should be able to resolve the expression's variables and functions at compile time instead of eval time.

let context = Context::new(var_resolver, fn_resolver).lock();
let expr = Expr::compile("abs(2 / p1) + abs(-2)", &context).unwrap();

Benchmarking

Benchmarking Recommendations

To get accurate and reproducible results, it is recommended to run benchmarks on isolated CPU cores with a fixed frequency and Turbo Boost disabled.

System Configuration Example

The following script executes the lib benches.

CORES=0
taskset -c $CORES cargo bench internal

The following script executes the benches related to comparations with other similar libraries available in crates.io.

CORES=0
taskset -c $CORES cargo bench cmp

• Simple Expr -> 3 * 3 - 3 / 3
• Power Expr -> 2 ^ 3 ^ 4
• Var Expr -> x0 * 2
• Trig Expr -> s0(x0) + c0(x0)
• Quadratic Expr -> (-x2 + (x2^2 - 4*x0*x1)^0.5) / (2*x0)
• Large Expr -> ((((87))) - 73) + (97 + (((15 / 55 _ ((31)) + 35))) + (15 - (9)) - (39 / 26) / 20 / 91 + 27 / (33 _ 26 + 28 - (7) / 10 + 66 _ 6) + 60 / 35 - ((29) - (69) / 44 / (92)) / (89) + 2 + 87 / 47 _ ((2)) _ 83 / 98 _ 42 / (((67)) _ ((97))) / (34 / 89 + 77) - 29 + 70 _ (20)) + ((((((92))) + 23 _ (98) / (95) + (((99) _ (41))) + (5 + 41) + 10) - (36) / (6 + 80 * 52 + (90))))

Additional Resources

• Roadmap
• Changelog
• Contributing