自适应辛普森公式模版

暴力求解一重定积分。

形如 ans = 积分从a->b F(x) 的公式

黑匣子调用：

先修改函数 double F(double x){}

然后ans = ars(a, b, eps);

double F(double x){
    return 1;
}
double simpson(double a, double b){
    double c = a + (b-a)/2.0;
    return (F(a) +4*F(c) + F(b)) * (b-a) / 6.0;
}
double asr(double a, double b, double eps, double A){
    double c = a + (b-a) / 2.0;
    double L = simpson(a, c), R = simpson(c, b);
    if(fabs(L+R-A) <= 15*eps) return L+R+(L+R-A)/15.0;
    return asr(a, c, eps/2.0, L) + asr(c, b, eps/2.0, R);
}
double asr(double a, double b, double eps){
    return asr(a, b, eps, simpson(a,b));
}