Math Is Fun Forum

Does anyone have an efficient computational method, preferably recursive,  to calculate the following finite product series without compromising accuracy,

    \Prod_{j=1}^{k-1} (1-exp(-(t_k-t_{k-j}))

where the number of t_k's increases over time of the simulation,
t_k's are real positive numbers, and t_k > t_{k-1} (where k is an integer greater than 2).
Each time a new t_{k+1} is generated then the above finite product needs
to be re-calculated. One could use a brute force method but this is computational inefficient since you have an ever increasing number of exponential to evaluate.

In suggestions or solutions will be greatly appreciated