Maybe the students could appreciate the exp() example from the ?numapprox[remez] help-page?

I notice, in passing, that it's not obvious how to get the help-page ?array in the commandline and Classic interfaces. Issuing ?array gets to the ?Array help-page. It turns out that it can be obtained by instead querying for the help-topic,

array(deprecated)

There doesn't appear to be a link to ?array(deprecated) from ?Array. The only mention of the deprecated array in ?Array is not an active help-link.

But numapprox[remez] still needs an array, and doesn't accept an Array, for the critical points argument. There's no link from ?numapprox[remez] to ?array(deprecated) either.

acer

May be the following is towards what you have in mind, I once did that
in Visual Basic (for Excel to get values for negatives more exact), it
should be understandable: to get exp(x) one takes a presentation in
base 2, for higher powers one uses stored, pre-computed values and for
the rest - which is close to 0 - the Taylor series should do.

So it is done by a quite brute argument reduction.

  Attribute VB_Name = "Modul2"
  Option Explicit
  Option Base 0
  
  Function ExpExcel(x As Variant) As Variant
  ExpExcel = CStr(CDec(Exp(CDec(x)))) ' hat nur 15 Stellen
  End Function
  
  Function localExp(x As Variant) As Variant
  Dim i, j As Integer
  Dim absx As Variant
  Dim intx, fracx As Variant
  Dim binx(0 To 5) As Integer
  'Dim eps(0 To 5) As Integer
  Dim z, b, pow As Integer
  Dim v(0 To 6) As Variant
  Dim expintx As Variant
  Dim F(0 To 32) As Variant
  Dim sum As Variant
  Dim tst
  
  If (0 < x) Then
    localExp = Exp(x)
    Exit Function
  End If
  If (x <= -64) Then
    localExp = Exp(x)
    Exit Function
  End If
  
  ' -64 < x <= 0
  
  pow = Int(5)
  
  v(0) = CDec(0.367879441171442) + CDec(0.3215955237702 * 0.000000000000001)
  v(1) = CDec(0.135335283236612) + CDec(0.691893999495 * 0.000000000000001)
  v(2) = CDec(0.018315638888734) + CDec(0.1802937180213 * 0.000000000000001)
  v(3) = CDec(0.000335462627902) + CDec(0.5118388213891 * 0.000000000000001)
  v(4) = CDec(0.000000112535174) + CDec(0.7192591145138 * 0.000000000000001)
  v(5) = CDec(0.000000000000012) + CDec(0.6641655490942 * 0.000000000000001)
  v(6) = CDec(0#) + CDec(0.0000000000002 * 0.000000000000001)
  
  absx = -CDec(x)
  intx = Int(absx)
  fracx = CDec(absx - intx)
  
  ' binary
  z = intx
  b = 32 ' Int(2 ^ pow)
  tst = ""
  expintx = CDec(1)
  For i = pow To 0 Step -1
    binx(i) = Int(z / b)
    If (binx(i) = 1) Then
      expintx = expintx * CDec(binx(i)) * v(i)
    End If
    'tst = tst & CStr(i) & ": " & CStr(binx(i)) & " "
    z = z - binx(i) * b
    b = Int(b / 2)
    'tst = tst & CStr(binx(i))
  Next i
  'MsgBox (tst)
  
  F(0) = CDec(1)
  For i = 1 To 32
    F(i) = -fracx * CDec(F(i - 1)) / CDec(i) ' Mist: 7<a: berechnen!
    'sum = sum + F(i) * h ^ i
  Next i
  
  'Horner Form
  sum = CDec(0)
  For i = 0 To 32
    sum = CDec(F(32 - i) + sum)
  Next i
  
  
  localExp = CStr(expintx * sum)
  
  End Function

CDec is a data type, which is more precise than usual floats, but the
use is a bit limited - especially one has to convert to strings to see
it in full length in Excel sheets.