specific cubic-cubic intersection not detected

[hamoid]

I found some cases in which intersections between cubic curves are not detected.
As the algorithm is iterative it is harder for me to figure out at which point something goes wrong.

Here a test program that can be dropped into src/io/lacuna/artifex:

package io.lacuna.artifex;

import io.lacuna.artifex.utils.Intersections;

public class TEST2 {
    public static void main(String[] args) {
        Vec2 s0 = new Vec2(435.3194971681168, 905.231313655894);
        Vec2 a0 = new Vec2(436.60194226635423, 904.5228510213844);
        Vec2 b0 = new Vec2(438.3935801257989, 904.1857845636355);
        Vec2 e0 = new Vec2(440.3919343740061, 904.1270373708342);

        Vec2 s1 = new Vec2(435.198246034818, 896.3191997888123);
        Vec2 a1 = new Vec2(436.84762896823827, 898.9951604687135);
        Vec2 b1 = new Vec2(438.2241643938649, 902.5923131816958);
        Vec2 e1 = new Vec2(439.1164972433261, 906.1884150468093);

        // SVG for debugging
        System.out.println("<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n" +
                "<svg width=\"420mm\" height=\"297mm\" version=\"1.1\" viewBox=\"0 0 420 297\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n" +
                " <g fill=\"none\" stroke=\"#000\" stroke-width=\".01\">");
        System.out.println("<path d=\"M " + s0.x + "," + s0.y +
                " L " + a0.x + "," + a0.y +
                " L " + b0.x + "," + b0.y +
                " L " + e0.x + "," + e0.y + "\" />");

        System.out.println("<path d=\"M " + s1.x + "," + s1.y +
                " L " + a1.x + "," + a1.y +
                " L " + b1.x + "," + b1.y +
                " L " + e1.x + "," + e1.y + "\" />");
        System.out.println(" </g>\n" + "</svg>\n");

        Bezier2.CubicBezier2 curve0 = (Bezier2.CubicBezier2) Bezier2.curve(s0, a0, b0, e0);
        Bezier2.CubicBezier2 curve1 = (Bezier2.CubicBezier2) Bezier2.curve(s1, a1, b1, e1);
        test2(curve0, curve1);
    }

    private static void test2(Bezier2.CubicBezier2 curve0, Bezier2.CubicBezier2 curve1) {
        System.out.println("\n# Intersections between");
        System.out.println("curve 0: " + curve0);
        System.out.println("curve 1: " + curve1);

        Vec2[] intersections = Intersections.intersections(curve0, curve1);
        System.out.println(intersections.length + " intersections");
        for (Vec2 intersection : intersections) {
            System.out.println(intersection);
        }
    }
}

The output of the program:

<?xml version="1.0" encoding="UTF-8"?>
<svg width="420mm" height="297mm" version="1.1" viewBox="0 0 420 297" xmlns="http://www.w3.org/2000/svg" xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
 <g fill="none" stroke="#000" stroke-width=".01">
<path d="M 435.3194971681168,905.231313655894 L 436.60194226635423,904.5228510213844 L 438.3935801257989,904.1857845636355 L 440.3919343740061,904.1270373708342" />
<path d="M 435.198246034818,896.3191997888123 L 436.84762896823827,898.9951604687135 L 438.2241643938649,902.5923131816958 L 439.1164972433261,906.1884150468093" />
 </g>
</svg>


# Intersections between
curve 0: p0=[x=435.3194971681168, y=905.231313655894], p1=[x=436.60194226635423, y=904.5228510213844], p2=[x=438.3935801257989, y=904.1857845636355], p3=[x=440.3919343740061, y=904.1270373708342]
curve 1: p0=[x=435.198246034818, y=896.3191997888123], p1=[x=436.84762896823827, y=898.9951604687135], p2=[x=438.2241643938649, y=902.5923131816958], p3=[x=439.1164972433261, y=906.1884150468093]
0 intersections

And the produced svg (bounding boxes, vertices and colors rendered by Inkscape)