// The following functions are a replacement for expm1 and log1p, which are
// in C99, but not provided by MSVC 9.0 Express compiler.

// returns more accurate e^x-1 for x near 0 than calculating directly
double lcl_expm1(double fX)
{
    return tanh(fX/2)*(exp(fX)+1);
}
//another version
double lcl2_expm1(double x)
    {
        double u = exp(x);
        if (u == 1.0)
            return x;
        if (u-1. == -1.0)
            return -1.0;
        return (u-1.0)*x/log(u);
    }

// returns more accurate log(1+x) for x near 0 than calculating directly
double lcl_log1p(double fX)
{
double fU = 1.0+fX;
if (fU == 1.0)
    return fX;
else
    return log(fU)*fX/(fU-1);
}

=======
Correct values for exp(x)-1 and for log(1+x) for testing, whether the ersatz will work for you.

x	exp(x)-1 with MuPad	ln(1+x) with MuPad
-1,00000000000000E-001	-9.51625819640404E-002	-1.05360515657826E-001
-2,00000000000000E-005	-1.99998000013333E-005	-2.00002000026667E-005
-2,98700000000000E-007	-2.98699955389159E-007	-2.98700044610854E-007
-3,00000000000000E-010	-2.99999999955000E-010	-3.00000000045000E-010
-3,20000000000000E-012	-3.19999999999488E-012	-3.20000000000512E-012
-3,50000000000000E-015	-3.49999999999999E-015	-3.50000000000001E-015
-4,00000000000000E-020	-4.00000000000000E-020	-4.00000000000000E-020
-5,00000000000000E-050	-5.00000000000000E-050	-5.00000000000000E-050
-8,00000000000000E-300	-8.00000000000000E-300	0.00000000000000E+000
0,00000000000000E+000	0.00000000000000E+000	0.00000000000000E+000
8,00000000000000E-300	8.00000000000000E-300	0.00000000000000E+000
5,00000000000000E-050	5.00000000000000E-050	5.00000000000000E-050
4,00000000000000E-020	4.00000000000000E-020	4.00000000000000E-020
3,50000000000000E-015	3.50000000000001E-015	3.49999999999999E-015
3,20000000000000E-012	3.20000000000512E-012	3.19999999999488E-012
3,00000000000000E-010	3.00000000045000E-010	2.99999999955000E-010
2,98700000000000E-007	2.98700044610849E-007	2.98699955389164E-007
2,00000000000000E-005	2.00002000013333E-005	1.99998000026666E-005
1,00000000000000E-001	1.05170918075648E-001	9.53101798043249E-002
-5,00000000000000E+000	-9.93262053000915E-001	not in domain
-2,00000000000000E+000	-8.64664716763387E-001	not in domain
-1,00000000000000E+000	-6.32120558828558E-001	not in domain
1,00000000000000E+000	1.71828182845905E+000	6.93147180559945E-001
2,00000000000000E+000	6.38905609893065E+000	1.09861228866811E+000
5,00000000000000E+000	1.47413159102577E+002	1.79175946922805E+000