#[macro_use]
extern crate itertools;

#[allow(non_snake_case)]

fn compute(range_1: (f64, f64), range_2: (f64, f64), range_3: (f64, f64), range_4: (f64, f64), epsilon: f64, mult: i32) -> Option<(f64, f64, f64, f64)> {

    let epsilon = (epsilon * mult as f64 * mult as f64) as i32;

    let range_1 = ((range_1.0 * mult as f64) as i32, (range_1.1 * mult as f64) as i32);
    let range_2 = ((range_2.0 * mult as f64) as i32, (range_2.1 * mult as f64) as i32);
    let range_3 = ((range_3.0 * mult as f64) as i32, (range_3.1 * mult as f64) as i32);
    let range_4 = ((range_4.0 * mult as f64) as i32, (range_4.1 * mult as f64) as i32);

    let A = 2 * mult * mult;
    let B = 3 * mult * mult;
    let C = 4 * mult * mult;
    let D = 5 * mult * mult;
    let E = 6 * mult * mult;

    for (a, b, c, d) in iproduct!(range_1.0..range_1.1, range_2.0..range_2.1, range_3.0..range_3.1, range_4.0..range_4.1) {

        if (A - a * b).abs() <= epsilon &&
           (B - a * c).abs() <= epsilon &&
           (C - a * d).abs() <= epsilon &&
           (D - b * c).abs() <= epsilon &&
           (E - b * d).abs() <= epsilon {
            return Some((a as f64 / mult as f64, b as f64 / mult as f64, c as f64 / mult as f64, d as f64 / mult as f64));
        }

    }

    None
}

fn main() {
    println!("{:?}", compute((1.0, 1.3), (1.6, 2.0), (2.7, 3.1), (3.0, 3.9), 0.11, 10000));
}