#include<bits/stdc++.h> //4.9 DM
using namespace std;

double leibniz()
{
     double pi=0,x=1,y;

    for(double i=0;i<=1000000;i++)
    {
        int l=i;
        if(l%2==0)x=1;
        else x=-1;
        double val= (2*i+1);
        pi+=(x/val);
    }
    return 4*pi;
}

double better_leibniz()
{
     double pi=0,x=1.0,y,val,val1,z;

    for(double i=0;i<=1000000;i++)
    {
        val=(4.0*i+1.0);
        val1=(4.0*i+3.0);
        y=(1.0/val);
        z=(1.0/val1);
        pi+=z*y;

    }
    return 8.0*pi;
}


double marchins()
{
     double pi=0,x,y,val,val1,z;
     x=atan(1.0/5.0);
     y=atan(1.0/239.0);
     pi=16.0*x;
     x=4.0*y;
     pi=pi-x;
    return pi;
}


double david()
{
     double pi=0,x=1,y,val,val1,z,a,b,c,d;

    for(double i=0;i<=27;i++)
    {
        x*=16;
        a=4.0/(8.0*i+1.0);
        b=2.0/(8.0*i+4.0);
        c=1.0/(8.0*i+5.0);
        c=1.0/(8.0*i+6.0);
        z=(1.0/val1);
        y=a-b-c-d;
        pi+=(y/x*16.0);

    }
    return pi;
}




int main()
{
    double pi,x,y,z,w,av;
    pi=3.14159265358979323846264338327950288419716939937510;
    w=leibniz();
    x=better_leibniz();
    y=marchins();
    z=david();
    printf("normal leibniz pi= %.51f\n",w);
    printf("better leibniz pi= %.51f\n",x);
    printf("marchins pi= %.51f\n",y);
    printf("david pi= %.51f\n\n",z);
    printf("original pi= %.51f\n\n",pi);
    double p=1e9,index=1;

        if(abs(pi-w)<p) p=abs(pi-w),index=1,av=w;
        if(abs(pi-x)<p) p=abs(pi-x),index=2,av=x;
        if(abs(pi-y)<p) p=abs(pi-y),index=3,av=y;
        if(abs(pi-z)<p) p=abs(pi-z),index=4,av=z;
        if(index==1) printf("leibniz is better, pi= %.51f\n",w);
        if(index==2) printf("better leibniz is better, pi= %.51f\n",x);
        if(index==3) printf("marchins is better, pi= %.51f\n",y);
        if(index==4) printf("david is better, pi= %.51f\n",z);



}