template BabyAdd() {
    signal input x1;
    signal input y1;
    signal input x2;
    signal input y2;
    signal output xout;
    signal output yout;

    signal beta;
    signal gamma;
    signal delta;
    signal epsilon;
    signal tau;

    var a = 168700;
    var d = 168696;

    beta <== x1*y2;
    gamma <== y1*x2;
    delta <== y1*y2;
    epsilon <== x1*x2;
    tau <== delta * epsilon;

    xout <-- (beta + gamma) / (1+ d*tau);
    (1+ d*tau) * xout === (beta + gamma);

    yout <-- (delta - a * epsilon) / (1-d*tau);
    (1-d*tau)*yout === (delta - a * epsilon);
}

template BabyDbl() {
    signal input x;
    signal input y;
    signal output xout;
    signal output yout;

    component adder = BabyAdd();
    adder.x1 <== x;
    adder.y1 <== y;
    adder.x2 <== x;
    adder.y2 <== y;

    adder.xout ==> xout;
    adder.yout ==> yout;
}


template BabyCheck() {
    signal input x;
    signal input y;

    signal x2;
    signal y2;

    var a = 168700;
    var d = 168696;

    x2 <== x*x;
    y2 <== y*y;

    a*x2 + y2 === 1 + d*x2*y2;
}