Step by Step solution about How to resolve the algorithm Time a function step by step in the Mathematica/Wolfram Language programming language

Wolfram Language (formerly known as Mathematica) is a proprietary computer algebra system developed by Wolfram Research. It is widely used in various fields, including scientific research, engineering, mathematics, and education.

The provided Wolfram Language code snippet demonstrates the use of the AbsoluteTiming function to measure the execution time of two different expressions.

Explanation:

1. AbsoluteTiming[x];: This line measures the execution time of the expression x and assigns the result to a variable called AbsoluteTiming[x]. In this example, x is not defined, so the result will be just the current time, which is used as a reference point.

2. AbsoluteTiming[N[Sqrt[3], 10^6]]: This line measures the execution time of the expression N[Sqrt[3], 10^6], which calculates the numerical value of the square root of 3 to one million decimal places using the N function. The result is assigned to a variable called AbsoluteTiming[N[Sqrt[3], 10^6]].

3. The output of the code is a list containing two values:

   • The first value is the execution time of the expression N[Sqrt[3], 10^6]. In this example, it is approximately 0.000657 seconds.
   • The second value is the result of the expression, which is the numerical value of the square root of 3 to one million decimal places. It starts with 1.7320508075688772935274463... and continues for many more digits.

This code demonstrates how to use the AbsoluteTiming function to measure the execution time of expressions in Wolfram Language. It can be useful for profiling and optimizing code or comparing the performance of different algorithms.

AbsoluteTiming[x];


AbsoluteTiming[N[Sqrt[3], 10^6]]


{0.000657, 1.7320508075688772935274463......}