nrfind

nrfind provides a Newton-Raphson root finder for arbitrary differentiable functions, as well as convenient wrappers for common use cases like square roots.

Documentation is available on docs.rs

A simple example of usage to find the roots of x^{3 + x}2 + 1 in 18 iterations:

extern crate nrfind;

// The function for whose roots find_root will solve
fn f(x: f64) -> f64 {
    x.powi(3) + x.powi(2) + 1.0
}

// That function's derivative
fn fd(x: f64) -> f64 {
    (3.0 * x.powi(2)) + (2.0 * x)
}

fn main() {
    let initial_guess = 100.0;
    let precision = 0.1;
    let iterations = 18;

    println!("x^3 + x^2 + 1 = 0 when x ~= {}",
             nrfind::find_root(&f, &fd, 
                               initial_guess, 
                               precision, 
                               iterations).unwrap());
}

This will print: x^3 + x^2 + 1 = 0 when x ~= -1.4675327346575013.

Note that while this method is guaranteed to approximate a root, it may not be the root you care about! Changing the given x0 guess can have an impact on which root is approximated.