>> diary
>> format long
>> eps

ans =
     2.220446049250313e-16

>> bisection( 'myfunction', 0.0, pi/2, 1.0e-5, 100, 0)

ans =
   0.870153597984356

>> approx_root = bisection( inline( '2/pi*exp(2*x/pi)+(1-exp(1))*cos(x)' ), 0.0, pi/2, 1.0e-5, 100, 1)

iters       left end             midpt             right end        fun(midpt)  log_2(bracket)

  1    0.00000000000000    0.78539816339745    1.57079632679490    -1.654e-01     0.651
  2    0.78539816339745    1.17809724509617    1.57079632679490     6.902e-01    -0.349
  3    0.78539816339745    0.98174770424681    1.17809724509617     2.347e-01    -1.349
  4    0.78539816339745    0.88357293382213    0.98174770424681     2.724e-02    -2.349
  5    0.78539816339745    0.83448554860979    0.88357293382213    -7.100e-02    -3.349
  6    0.83448554860979    0.85902924121596    0.88357293382213    -2.235e-02    -4.349
  7    0.85902924121596    0.87130108751904    0.88357293382213     2.324e-03    -5.349
  8    0.85902924121596    0.86516516436750    0.87130108751904    -1.004e-02    -6.349
  9    0.86516516436750    0.86823312594327    0.87130108751904    -3.868e-03    -7.349
 10    0.86823312594327    0.86976710673116    0.87130108751904    -7.741e-04    -8.349
 11    0.86976710673116    0.87053409712510    0.87130108751904     7.743e-04    -9.349
 12    0.86976710673116    0.87015060192813    0.87053409712510    -2.762e-08   -10.349
 13    0.87015060192813    0.87034234952662    0.87053409712510     3.871e-04   -11.349
 14    0.87015060192813    0.87024647572737    0.87034234952662     1.935e-04   -12.349
 15    0.87015060192813    0.87019853882775    0.87024647572737     9.675e-05   -13.349
 16    0.87015060192813    0.87017457037794    0.87019853882775     4.836e-05   -14.349
 17    0.87015060192813    0.87016258615304    0.87017457037794     2.417e-05   -15.349
 18    0.87015060192813    0.87015659404058    0.87016258615304     1.207e-05   -16.349
 19    0.87015060192813    0.87015359798436    0.87015659404058     6.021e-06   -17.349

>> approx_root =
     0.870153597984356

>> exact_root = bisection( inline( '2/pi*exp(2*x/pi)+(1-exp(1))*cos(x)' ), 0.0, pi/2, 1.0e-14, 100, 0)

exact_root =
     0.870150615609478

>> approx_root - exact_root

ans =
     2.982374878057747e-06

>> exact_root = bisection( inline( '2/pi*exp(2*x/pi)+(1-exp(1))*cos(x)' ), 0.0, pi/2, 1.0e-20, 100, 0)
Warning: the tolerance is too small

> In bisection at 14
Error in ==> bisection at 13
if tol < 3*eps       %  The tolerance is too small

Output argument "r" (and maybe others) not assigned during call to "/home/npetrov/bisection.m>bisection".

>> exit