Tic toc command giving erroneous result

Here is my code

axis([0 5 -30 30]);
  c=0;
  theta=pi/6;
  dt=1e-5;                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
  nstep=round(5/dt);
  stheta=0;
  x1=theta;
  x2=stheta;
  dx1=x2;
  dx2=-c*x2-21.791*sin(x1);
  X=zeros(2,nstep);
  V=zeros(2,nstep);
  t=0:dt:(nstep-1)*dt;
  tic
  X(:,1)=[x1;x2];
  V(:,1)=[dx1;dx2];
  for i=2:(nstep)
      X(:,i)=(dt*(V(:,i-1)))+X(:,i-1);
      V(:,i)=[X(2,i);-c*X(2,i)-21.791*X(1,i)];
  end
  toc
  plot(t,(180/pi)*X(1,:))
  figure
  plot(t,X(2,:))

In the above case I am using tic before X(:,1)=[x1;x2] and in the code below I am using tic before the for loop.

axis([0 5 -30 30]);
  c=0;
  theta=pi/6;
  dt=1e-5;                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
  nstep=round(5/dt);
  stheta=0;
  x1=theta;
  x2=stheta;
  dx1=x2;
  dx2=-c*x2-21.791*sin(x1);
  X=zeros(2,nstep);
  V=zeros(2,nstep);
  t=0:dt:(nstep-1)*dt;
  X(:,1)=[x1;x2];
  V(:,1)=[dx1;dx2];
  tic
  for i=2:(nstep)
      X(:,i)=(dt*(V(:,i-1)))+X(:,i-1);
      V(:,i)=[X(2,i);-c*X(2,i)-21.791*X(1,i)];
  end
  toc
  plot(t,(180/pi)*X(1,:))
  figure
  plot(t,X(2,:))
But the time required in 1st case is less than that required in the second case and is varying. Why is it so I have plotted the histogram for both the case.

The code for histogram is

    axis([0 5 -30 30]);
      c=0;
      theta=pi/6;
      dt=1e-5;

      nstep=round(5/dt);
      stheta=0;
      x1=theta;
      x2=stheta;
      dx1=x2;
      dx2=-c*x2-21.791*sin(x1);
      X=zeros(2,nstep);
      V=zeros(2,nstep);
      t=0:dt:(nstep-1)*dt;
      comp_time = [];
      for j=1:50
          tic
          X(:,1)=[x1;x2];
          V(:,1)=[dx1;dx2];

          for i=2:(nstep)
              X(:,i)=(dt*(V(:,i-1)))+X(:,i-1);
              V(:,i)=[X(2,i);-c*X(2,i)-21.791*X(1,i)];
          end
          comp_time = [comp_time,toc];
      end
      hist(comp_time);
      title('Before X(:,1)=[x1;x2]');

      comp_time = [];
      for j=1:50

          X(:,1)=[x1;x2];
          V(:,1)=[dx1;dx2];
          tic
          for i=2:(nstep)
              X(:,i)=(dt*(V(:,i-1)))+X(:,i-1);
              V(:,i)=[X(2,i);-c*X(2,i)-21.791*X(1,i)];
          end
          comp_time = [comp_time,toc];
      end
      figure;
      hist(comp_time);
      title('Before for i=2:(nstep)');

Answer 1

[David Sanchez]

The time taken to run both scripts are insignificantly different. There are only two lines of code of difference between them:

    X(:,1)=[x1;x2];
    V(:,1)=[dx1;dx2];

Your system will fly through this two lines and will make almost no distinction between both scripts. Depending on the processes running in your system during the processing of the scripts ( most of them hidden processes ), the time taken will change.

You say

"But the time required in 1st case is less than that required in the second case and is varying."

You should be aware that it is faster sometimes ( I took the time to run it too several times ), and some others it is a bit slower. Your histogram shows it too.