// russian : cp1251 encoding
#include <iostream>
#include <cmath>
#include "ext_value.h"
using namespace std;

int main()
{
double x1=2.7, x2=1.32, x3=5.1;
// Внимание! Самая важная строчка!
// Инициализация независимых переменных
// Всего 3 независимых переменных (значение первого параметра): 
// значит индексы 0,1,2 (значения третьего параметра)
ext_value3 a1(3,x1,0),a2(3,x2,1),a3(3,x3,2);
ext_value3 res; // Здесь будет вычисленный результат
    res=asin(a2/sqrt(a1*a1+a2*a2+a3*a3));

double r,r2,r4,r6,s,s2,s3,s5,w,x12,x22,x32,x14,x24,x34,x16,x36;
  s2=x1*x1+x3*x3; s=sqrt(s2); s3=s*s2; s5=s2*s3;
  x12=x1*x1; x22=x2*x2; x32=x3*x3;
  x14=x12*x12; x24=x22*x22; x34=x32*x32;
  x16=x14*x12; x36=x34*x32;
  r2=x1*x1+x2*x2+x3*x3; r=sqrt(r2); r4=r2*r2; r6=r2*r4;

w=asin(x2/r);
cout<<"res   "<<res.get()<<"\t"<<w-res.get()<<endl;
w=-x1*x2/(s*r2);
cout<<"dx1   "<<res.get(0)<<"\t"<<w-res.get(0)<<endl;
w=s/r2;
cout<<"dx2   "<<res.get(1)<<"\t"<<w-res.get(1)<<endl;
w=-x2*x3/(s*r2);
cout<<"dx3   "<<res.get(2)<<"\t"<<w-res.get(2)<<endl;
w=-x2/(s*r2)+3*x1*x1*x2/(s*r4)+x1*x1*x2*x2*x2/(s3*r4) ;
cout<<"dx11  "<<res.get(0,0)<<"\t"<<w-res.get(0,0)<<endl;
w=-x1*(x3*x3-x2*x2+x1*x1)/(s*r4);
cout<<"dx12  "<<res.get(0,1)<<"\t"<<w-res.get(0,1)<<endl;
w=x1*x2*x3*(3*x3*x3+x2*x2+3*x1*x1)/(s3*r4);
cout<<"dx13  "<<res.get(0,2)<<"\t"<<w-res.get(0,2)<<endl;
w=-2*x2*s/r4;
cout<<"dx22  "<<res.get(1,1)<<"\t"<<w-res.get(1,1)<<endl;
w=-x3*(x3*x3-x2*x2+x1*x1)/(s*r4);
cout<<"dx23  "<<res.get(1,2)<<"\t"<<w-res.get(1,2)<<endl;
w=x2*(2*x3*x3*x3*x3+x1*x1*x3*x3-x1*x1*x2*x2-x1*x1*x1*x1)/(s3*r4);
cout<<"dx33  "<<res.get(2,2)<<"\t"<<w-res.get(2,2)<<endl;
w=x1*x2*(9*x36+12*x22*x34+12*x12*x34+3*x24*x32+14*x12*x22*x32-3*x14*x32+2*x14*x22-6*x16)/(s5*r6);
cout<<"dx111 "<<res.get(0,0,0)<<"\t"<<w-res.get(0,0,0)<<endl;
w=-(x36-x24*x32+6*x12*x22*x32-3*x14*x32+6*x14*x22-2*x16)/(s3*r6);
cout<<"dx112 "<<res.get(0,0,1)<<"\t"<<w-res.get(0,0,1)<<endl;
w=x2*x3*(3*x36+4*x22*x34-6*x12*x34+x24*x32-2*x12*x22*x32-21*x14*x32-2*x12*x24-6*x14*x22-12*x16)/(s5*r6);
cout<<"dx113 "<<res.get(0,0,2)<<"\t"<<w-res.get(0,0,2)<<endl;
w=2*x1*x2*(3*x32-x22+3*x12)/(s*r6);
cout<<"dx122 "<<res.get(0,1,1)<<"\t"<<w-res.get(0,1,1)<<endl;
w=x1*x3*(3*x34-6*x22*x32+6*x12*x32-x24-6*x12*x22+3*x14)/(s3*r6);
cout<<"dx123 "<<res.get(0,1,2)<<"\t"<<w-res.get(0,1,2)<<endl;
w=-x1*x2*(12*x36+6*x22*x34+21*x12*x34+2*x24*x32+2*x12*x22*x32+6*x14*x32-x12*x24-4*x14*x22-3*x16)/(s5*r6);
cout<<"dx133 "<<res.get(0,2,2)<<"\t"<<w-res.get(0,2,2)<<endl;
w=-2*s*(x32-3*x22+x12)/r6;
cout<<"dx222 "<<res.get(1,1,1)<<"\t"<<w-res.get(1,1,1)<<endl;
w=2*x2*x3*(3*x32-x22+3*x12)/(s*r6);
cout<<"dx223 "<<res.get(1,1,2)<<"\t"<<w-res.get(1,1,2)<<endl;
w=(2*x36-6*x22*x34+3*x12*x34-6*x12*x22*x32+x12*x24-x16)/(s3*r6);;
cout<<"dx233 "<<res.get(1,2,2)<<"\t"<<w-res.get(1,2,2)<<endl;

w=-x2*x3*(6*x36-2*x22*x34+3*x12*x34-14*x12*x22*x32-12*x14*x32-3*x12*x24-12*x14*x22-9*x16)/(s5*r6);
cout<<"dx333 "<<res.get(2,2,2)<<"\t"<<w-res.get(2,2,2)<<endl;
return 0;
}