NAG Library Manual, Mark 29
```!   D04AAF Example Program Text
!   Mark 29.0 Release. NAG Copyright 2023.

Module d04aafe_mod

!     D04AAF Example Program Module:
!            Parameters and User-defined Routines

!     nder:     abs(nder) is largest order derivative required;
!               nder < 0 means only odd or even derivatives.
!     h_init:   initial step size.
!     h_reduce: reduction factor applied to successive step sizes.
!     xval:     derivatives evaluated at x=xval.

!     .. Use Statements ..
Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Accessibility Statements ..
Private
Public                           :: f
!     .. Parameters ..
Real (Kind=nag_wp), Parameter, Public :: h_init = 0.5_nag_wp
Real (Kind=nag_wp), Parameter, Public :: h_reduce = 0.1_nag_wp
Real (Kind=nag_wp), Parameter, Public :: xval = 0.5_nag_wp
Integer, Parameter, Public       :: nder = -7, nout = 6
Contains
Function f(x)

!       .. Function Return Value ..
Real (Kind=nag_wp)             :: f
!       .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: x
!       .. Intrinsic Procedures ..
Intrinsic                      :: exp
!       .. Executable Statements ..
f = 0.5_nag_wp*exp(2.0_nag_wp*x-1.0_nag_wp)
Return
End Function f
End Module d04aafe_mod
Program d04aafe

!     D04AAF Example Main Program

!     .. Use Statements ..
Use d04aafe_mod, Only: f, h_init, h_reduce, nder, nout, xval
Use nag_library, Only: d04aaf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: hbase
Integer                          :: i, ifail, j, k, l
!     .. Local Arrays ..
Real (Kind=nag_wp)               :: der(14), erest(14)
!     .. Intrinsic Procedures ..
Intrinsic                        :: abs, merge
!     .. Executable Statements ..
Write (nout,*) 'D04AAF Example Program Results'

Write (nout,*)
Write (nout,*)                                                           &
'Four separate runs to calculate the first four odd order ',           &
'derivatives of'
Write (nout,*) '   f(x) = 0.5*exp(2.0*X-1.0) at x = 0.5.'
Write (nout,*) 'The exact results are 1, 4, 16 and 64'
Write (nout,*)
Write (nout,*) 'Input parameters common to all four runs'
Write (nout,99999) '  xval = ', xval, '    nder = ', nder,               &
'    ifail = 0'
Write (nout,*)

hbase = h_init
l = abs(nder)

If (nder>=0) Then
j = 1
Else
j = 2
End If

Do k = 1, 4

ifail = 0
Call d04aaf(xval,nder,hbase,der,erest,f,ifail)

Write (nout,*)
Write (nout,99998) 'with step length', hbase, '  the results are'
Write (nout,*) 'Order        Derivative       Questionable?'

Do i = 1, l, j
Write (nout,99997) i, der(i), merge('Yes','No ',erest(i)<0._nag_wp)
End Do

hbase = hbase*h_reduce
End Do

99999 Format (1X,A,F4.1,A,I2,A)
99998 Format (1X,A,F9.4,A)
99997 Format (1X,I2,E21.4,13X,A)
End Program d04aafe
```