#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;

double diffFinieCentral(double x0, double h);

int main() {     
  const int STEPMAX = 21;
   
  double h, dfNum, dfCalc;
  double delta;
  double x0;
  cout << "Estimation de la derivee de f(x)=x^3 avec la differece finie centrale" << endl;
  cout << "entrez la valeur de x ou estimer f'(x) : ";
  cin >> x0;

  cout << endl;
  cout << "          h           ;    log(dfNum - dfAna)  ;         dfNum"
       << endl << endl;  
  for (int step=0; step<STEPMAX; step++) {
    h = pow(10.,-step);
    
    dfNum = diffFinieCentral(x0,h);   //derivee numerique
    dfCalc = 3.*x0;   //derivee analytique

    if (fabs(dfNum-dfCalc)!=0)
      delta = log10(fabs(dfNum-dfCalc));
    else
      delta = -9999.99;   //une valeur jamais atteint par le logarithme
   
    cout << setprecision(20) << fixed << h <<  " "
         << delta << " " << dfNum <<endl;
  }
  cout << endl;

  return 0;
}

double diffFinieCentral(double x0, double h) {
  double df = (pow(x0+h,3)-pow(x0-h,3)) / (2.*h);
  return df;
}