I'm trying to develop a architecture hardware to make a implementation of an algorithm that can be descompose in terms of sums, multiplications, subtractions and exponential functions. I'm trying to modelling $\exp(-x)$ through Taylor series. The domain of my function is bounded between $0$ and $1500$, but I want to use a particular Taylor approximation whose domain is bounded between $0$ and $0.5$.
Is there any way to get an approximation using the my tailor series whose domain is bounded between $0$ and $0.5$ to modelling the function whose domain is bounded between $0$ and $1500$?
The function I want to model for bounded domain is $\exp(-x)$. Thank you for your help.