Add an example (comparing with Julia)

Cargo.toml

@@ -24,6 +24,7 @@ nightly = []
 [dev-dependencies]
 criterion = "0.3.5"
 roots = "0.0.7"
+rand = "0.8.5"
 
 [[example]]
 name = "basic"

examples/x_sinx_levels.jl

@@ -0,0 +1,25 @@
+using Pkg
+Pkg.add("NonlinearSolve")
+using NonlinearSolve
+
+N = 100_000
+levels = 1.5 * rand(N)
+out = zeros(N)
+
+f(x, lv) = x * sin(x) - lv
+
+function f(out, levels, u0)
+    for i in 1:N
+        out[i] = solve(NonlinearProblem{false}(
+                           NonlinearFunction{false}(f), u0, levels[i]),
+                           NewtonRaphson()).u
+    end
+end
+
+@time f(out, levels, 1.0)
+
+# Julia 1.9.4 (Intel Core i7-7500U CPU @ 2.70GHz)
+# 0.133063 seconds (1.30 M allocations: 141.891 MiB, 14.63% gc time)
+#
+# Note that, on the first run, the following was reported:
+# 299.023886 seconds (777.52 M allocations: 164.623 GiB, 1.72% gc time, 99.94% compilation time)

examples/x_sinx_levels.rs

@@ -0,0 +1,32 @@
+//! Compute level sets of x sin(x)
+//! See https://twitter.com/walkingrandomly/status/1544615360833507329
+//!     https://twitter.com/ChrisRackauckas/status/1544743542094020615
+//! and [Matlab R2023a][].
+//!
+//! [Matlab R2023a]: https://blogs.mathworks.com/matlab/2023/05/15/from-hpc-consultancy-to-a-faster-fzero-function-in-matlab-r2023a/
+
+use std::{error::Error, iter, time::Instant};
+use root1d::{toms748, bisect};
+use rand::prelude::*;
+
+fn main() -> Result<(), Box<dyn Error + 'static>> {
+    const N: usize = 100_000;
+    let levels: Vec<_> = iter::from_fn(|| Some(1.5 * random::<f64>()))
+        .take(N).collect();
+    let mut out = Vec::with_capacity(N);
+
+    let now = Instant::now();
+    for lv in &levels {
+        out.push(bisect(|x: f64| x * x.sin() - lv, 0., 2.).root()?);
+    }
+    println!("bisect: {} secs", now.elapsed().as_secs_f64());
+
+    out.clear();
+        let now = Instant::now();
+    for lv in &levels {
+        out.push(toms748(|x: f64| x * x.sin() - lv, 0., 2.).root()?);
+    }
+    println!("toms748: {} secs", now.elapsed().as_secs_f64());
+
+    Ok(())
+}