Burnup calculation and nuclide inventory calculation may require solving detailed depletion chains with high computational accuracy and efficiency. NUIT (NUclide Inventory Tool) is a newly-developed nuclide inventory calculation code, which is capable of handling detailed depletion chains by implementing various advanced algorithms. Based on the NUIT code, this paper investigates the accuracy and efficiency of the Mini-Max Polynomial Approximation (MMPA) method, and compare it with the Chebyshev Rational Approximation Method (CRAM). It is concluded that both methods are numerically accurate and efficient for dealing with detailed depletion chains with extremely short half-lived nuclides.

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