#include <iostream>
#include "StatTools/Funct/Variables.h"
#include "StatTools/Funct/FunctManip.h"
#include "StatTools/Funct/FunctIO.h"
using namespace std;
using namespace Funct;

int main() 
{
  X x;
  Y y;

  // test basic function sum
  cout << sin( x ) << " + " << cos( x ) << " = " << sin( x ) + cos( x ) << endl;
  cout << sin( x ) << " comp. " << cos( x ) << " = " << sin( cos( x ) ) << endl;

  // test minus
  cout << " -( " << sin( x ) << " ) = " << - sin( x ) << endl;
  cout << " - - ( " << sin( x ) << " ) = " << ( -( - sin( x ) ) ) << endl;
  cout << sin( x ) << " * "  << sin( x ) << " = " << sin( x ) * sin ( x ) << endl;
  cout << sin( x )<< " ^ " << num<3>() << " = " << pow( sin( x ), num<3>() ) << endl;

  cout << "2 * " << sin( x ) << " * "  << sin( x ) << " = " 
       << num<2>() * sin( x ) * sin ( x ) << endl;

  cout << sin( x ) << " * "  << cos( x ) << " * " << sin( x ) << " = " 
       << sin( x ) * cos( x ) * sin ( x ) << endl;

  cout << "( " << sin( x ) << " / "  << exp( x ) << " ) / " << cos( x ) << " = " 
       << ( sin( x ) / exp( x ) ) / cos ( x ) << endl;

  cout << sin( x ) << " / ( "  << exp( x ) << " / " << cos( x ) << " ) = " 
       << sin( x ) / ( exp( x ) / cos ( x ) ) << endl;

  cout << ( sin( x ) * exp( x ) ) << " / ( "  << sin( x ) << " ) = " 
       << ( sin( x ) * exp( x ) ) / sin ( x ) << endl;

  cout << ( sin( x ) * exp( x ) ) << " / ( "  << exp( x ) << " ) = " 
       << ( sin( x ) * exp( x ) ) / exp ( x ) << endl;

  cout << sin( x ) << " / " << ( sin( x ) * exp( x ) ) << " ) = " 
       << sin( x ) / ( sin( x ) * exp( x ) ) << endl;

  cout << exp( x ) << " / " << ( sin( x ) * exp( x ) ) << " ) = " 
       << exp( x ) / ( sin( x ) * exp( x ) ) << endl;

  cout << sin( x ) << " * "  << cos( x ) << " * " 
       << exp( x ) << " * " << pow( sin( x ), num<2>() ) << " = " 
       << sin( x ) * cos( x ) * exp( x ) * pow( sin( x ), num<2>() ) << endl;

  cout << num<8>() << " " << cos( x ) << " "  << sin( x ) << " " 
       << pow( cos( x ), num<3>() ) << " " << sin( x ) << " = " 
       << num<8>() * cos( x ) * sin( x ) * pow( cos( x ), num<3>() ) * sin( x ) << endl;

  cout << exp( x ) << " * " << sin( x ) << " = " 
       << ( exp( x ) * sin( x ) ) << endl;

  cout << "log( abs( x ) ) = " << log( abs( x ) ) << endl;

  cout << "exp( log( x ) ) = "  << exp( log( x ) ) << endl;
  cout << "log( x^2 ) = "  << log( pow( x, num<2>() ) ) << endl;

  cout << exp( x ) << " * " << sin( x ) << " * "  << cos( x ) << " = " 
       << ( ( exp( x ) * sin( x ) ) * cos ( x ) ) << endl;

  cout << sin( x ) << " * "  << pow( sin( x ), num<3>() ) << " = " 
       << sin( x ) * pow( sin( x ), num<3>() ) << endl;
  // difference with negative function
  cout << sin( x ) << " -( - " << cos( x ) << " ) = " << sin( x ) - ( -cos( x ) ) << endl;

  // simplification expression
  cout << sin( x ) << " * 1 = " << sin( x ) * num<1>() << endl;
  cout << sin( x ) << " / 1 = " << sin( x ) / num<1>() << endl;
  cout << sin( x ) << " / ( - 1 ) = " << sin( x ) / num<-1>() << endl;
  cout << sin( x ) << " * 0 = " << sin( x ) * num<0>() << endl;
  cout << sin( x ) << " * -1 = " << sin( x ) * num<-1>() << endl;
  cout << sin( x ) << " ^ 1 = " << pow( sin( x ), num<1>() ) << endl;
  cout << sin( x ) << " ^ 1/2 = " << pow( sin( x ), fract<1,2>() ) << endl;
  cout << sin( x ) << " ^ -1 = " << pow( sin( x ), num<-1>() ) << endl;

  cout << sqr( sin( x ) ) << " + " << sqr( cos( x ) ) << " = " << sqr( sin( x ) ) + sqr( cos( x ) ) << endl;
  cout << tan( x ) << " * " << cos( x ) << " = " << tan( x ) * cos( x ) << endl;
  cout << sin( x ) << " + " << sin( x ) << " = " << sin( x ) + sin( x ) << endl;
  cout << sin( x ) << " - " << sin( x ) << " = " << sin( x ) - sin( x ) << endl;
  cout << sin( x ) << " * " << sin( x ) << " = " << sin( x ) * sin( x ) << endl;
  cout << sin( x ) << " / " << sin( x ) << " = " << sin( x ) / sin( x ) << endl;
  cout << sin( x ) << " + " << sin( x ) << " + " << sin( x ) << " = " << sin( x ) + sin( x ) + sin( x ) << endl;
  cout << sin( x ) + cos( x ) << " / " << cos( x ) + sin( x ) << " = " 
       << ( sin( x ) + cos( x ) ) / ( cos( x ) + sin( x ) )<< endl;

  cout << sin( x ) * x << " + " << exp( x ) * x * cos( x ) << " = " 
       << sin( x ) * x + exp( x ) * x * cos( x ) << endl;

  cout << sin( x ) * x << " + " << cos( x ) * x * sin( x ) << " = " 
       << sin( x ) * x + cos( x ) * x * sin( x ) << endl;

  cout <<  x * exp( pow( x, num( 2 ) ) ) << " + " 
       << pow( x, num( 3 ) ) * exp( pow( x, num( 2 ) ) ) << " = " 
       << x * exp( pow( x, num( 2 ) ) ) + pow( x, num( 3 ) ) * exp( pow( x, num( 2 ) ) ) << endl;

  cout << x * sin( x ) << " + "  << pow( x, num( 3 ) ) * sin( x ) << " = " 
       << x * sin( x ) + pow( x, num( 3 ) ) * sin( x ) << endl;

  cout << sin( x ) * cos( x ) << " + "  << pow( cos( x ), num( 3 ) ) * sin( x ) << " = " 
       << sin( x ) * cos( x ) + pow( cos( x ), num( 3 ) ) * sin( x ) << endl;

  cout << pow( cos( x ), num( 3 ) ) << " + "  << 2 * pow( sin( x ), num( 2 ) ) * cos( x ) << " = " 
       << pow( cos( x ), num( 3 ) ) + 2 * pow( sin( x ), num( 2 ) ) * cos( x ) << endl;

  cout << pow( cos( x ), num( 3 ) ) << " - "  << 2 * pow( sin( x ), num( 2 ) ) * cos( x ) << " = " 
       << pow( cos( x ), num( 3 ) ) - 2 * pow( sin( x ), num( 2 ) ) * cos( x ) << endl;

  return 0;
}