In two decades of intense algorithmic development, the Wolfram Language has established a new level of numerical computation. Particularly notable are its many original highly efficient algorithms, its methodology for automatic algorithm selection, and its systemwide support for automatic error tracking and arbitrary-precision arithmetic.

N — numerical evaluation to any precision

Major Numerics Functions

NSolve  ▪  NDSolve  ▪  NIntegrate  ▪  NMinimize  ▪  NSum

Complex Numbers »

I()  ▪  Abs  ▪  Re  ▪  Im  ▪  Conjugate  ▪  ...

Representation of Numbers »

IntegerDigits  ▪  RealDigits  ▪  FromDigits  ▪  IntegerQ  ▪  ...

Display of Numbers »

NumberForm  ▪  NumberMarks  ▪  InputForm  ▪  CForm  ▪  ...

Precision & Accuracy Control »

Precision  ▪  Accuracy  ▪  PrecisionGoal  ▪  AccuracyGoal  ▪  ...

Algorithm Control & Analysis

Method  ▪  StepMonitor  ▪  EvaluationMonitor  ▪  Norm

Compiled — control machine-precision compilation optimization