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Recently McCullough (1998) proposed a collection of intermediate-level tests for assessing the numerical reliability of a statistical package in three areas: estimation (both nonlinear and linear); random number generaion; and statistical distributions (e.g., for calculating p-values). Estimation is assessed via the Statistical Reference Datasets (StRD), which recently was released by the American "National Institute of Standards and Technology" (NIST). The output of the random number generator (RNG) is assessed using Marsaglia's (1996) "DIEHARD" battery of statistical tests for randomness. The accuracy of statistical distributions is assessed by comparison to results from a specialized software such as Knüsel's (1989) ELV or Brown's (1998) DCDFLIB. This methodology has been applied formally to the statistical packages SAS, SPSS, and S-PLUS (McCullough, 1999a) econometric packages EViews, LIMDEP, SHAZAM, and TSP (McCullough, 1999b) and GAUSS (Vinod, 2000), and the spreadsheet package Microsoft Excel 97 (McCullough and Wilson, 1999). Results on additional packages can be found in the working paper by Altman and MacDonald (1999). For all these packages, flaws were uncovered. This same methodology is applied to Mathematica (occasionally referred to as "Mma"), whose developer is Wolfram Research.
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