Adaptive Gauss-Kronrod rules G10K21*, G20K41*, G30K61* (and R variants) never early-exit on low-degree polynomials – extremely slow in v0.41.0

[cnhornbeck]

Description

When using the higher-order adaptive Gauss-Kronrod integrators (G10K21*, G20K41*, G30K61* and their R versions), the adaptive subdivision loop never stops early even on functions that the rule should integrate exactly in the first step (e.g. any polynomial of degree ≤ 9 for G10K21, ≤ 19 for G20K41, ≤ 59 for G30K61).

Instead, it keeps subdividing all the way to max_iter, causing the integration to take seconds instead of microseconds.

Lower-order rules and non-adaptive methods work fine still.

Reproduction

use peroxide::fuga::*;
use std::time::Instant;

fn main() {
    let f = |x: f64| 3.0 * x.powi(2) + 2.0 * x + 5.0;

    let tol = 1.0e-4;
    let max_iter = 24u32;

    let methods = vec![
        ("G10K21 ", Integral::G10K21(tol, max_iter)),
        ("G20K41 ", Integral::G20K41(tol, max_iter)),
        ("G30K61 ", Integral::G30K61(tol, max_iter)),
        ("G10K21R", Integral::G10K21R(tol, max_iter)),
        ("G20K41R", Integral::G20K41R(tol, max_iter)),
        ("G30K61R", Integral::G30K61R(tol, max_iter)),
    ];

    for (name, method) in methods {
        let start = Instant::now();
        let res = integrate(f, (5.0, 10.0), method);
        let ms = start.elapsed().as_secs_f64() * 1000.0;
        println!("{} | {:.3} ms | {:.6}", name, ms, res);
    }
}

Output of code:

Method	Time (ms)	Result
G10K21	2424.726	975.000000
G20K41	3540.177	975.000000
G30K61	4663.384	975.000000
G10K21R	2438.282	975.000000
G20K41R	3583.130	975.000000
G30K61R	4864.546	975.000000

Expected behavior

The algorithm should detect that |G - K| ≈ 0 on the first interval and return immediately (exact integration).

Actual behavior

Error estimate never falls below tolerance → full subdivision to max_iter.

Environment

Peroxide: 0.41.0
Rust: stable, tested on 1.85+
OS: Windows 11