自适应辛普森

struct Simpson
{
    static const double eps=1e-8;
    static double f(double x)
    {
        return (c*x+d)/(a*x+b);
    }
    double simpson(double l,double r)
    {
        return (r-l)*(f(l)+f(r)+4*f((l+r)/2))/6;
    }
    double integral(double l,double r,double ans=1e18)
    {
        double mid=(l+r)/2;
        double le=simpson(l,mid),ri=simpson(mid,r);
        if(fabs(le+ri-ans)<eps)return le+ri;
        return integral(l,mid,le)+integral(mid,r,ri);
    }
}S;