自适应辛普森法

证明省略

$$\int_{a}^{b}f\left ( x \right )dx\approx \frac{b-a}{6}\left [ f\left ( a \right ) +4f\left ( \frac{a+b}{2} \right )+f\left ( b \right )\right ]$$

#include<cstdio>
#include<cmath>
using namespace std;
const double eps=1e-10;
double a,b,c,d;
double F(double x)
{
    return (c*x+d)/(a*x+b);
}
double simpson(double l,double r)
{
    double mid=(l+r)/2.0;
    return (F(l)+F(mid)*4.0+F(r))*(r-l)/6.0;
}
double ASR(double l,double r,double ans)
{
    double mid=(l+r)/2.0;
    double L=simpson(l,mid);
    double R=simpson(mid,r);
    if (fabs(L+R-ans)<eps)
        return ans;
    else
        return ASR(l,mid,L)+ASR(mid,r,R);
}
int main()
{
    double ql,qr;
    scanf("%lf%lf%lf%lf",&a,&b,&c,&d);
    scanf("%lf%lf",&ql,&qr);
    printf("%.6lf",ASR(ql,qr,simpson(ql,qr)));
    return 0;
}