pricesEquationParts = (p_start, p_final) => {
const q0 = calcFractionBlueEyed(p_start);
const q1 = 1 - q0;
const qp0 = calcFractionBlueEyed(p_final);
const qp1 = 1 - qp0;
const dq0 = qp0 - q0;
const dq1 = qp1 - q1;
const z0 = q0 * z_blue;
const z1 = q1 * z_brown;
const zp0 = qp0 * z_blue;
const zp1 = qp1 * z_brown;
const dz0 = zp0 - z0;
const dz1 = zp1 - z1;
const dz_selection = dq0 * z0 + dq1 * z1;
const dz_transmission = qp0 * dz0 + qp1 * dz1;
const dz = dz_selection + dz_transmission;
return { dz, dz_selection, dz_transmission }
}