# Accuracy

Accuracy[x]

gives the effective number of digits to the right of the decimal point in the number x.

# Examples

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## Basic Examples(3)

Machine-precision number:

Arbitrary-precision number:

Exact number:

## Scope(4)

Accuracy is the effective number of digits known to the right of the decimal point:

A zero known to accuracy 20:

The precision of z+1 is the same as the accuracy of z:

Accuracy of a machine zero:

The uncertainty in 0. equals the uncertainty in the smallest positive normalized machine number:

Specify accuracy as the goal for N:

## Generalizations & Extensions(1)

The accuracy of a symbolic expression is the minimum of the accuracies of its numbers:

## Applications(2)

Check the quality of a result:

Track loss of accuracy in a repetitive calculation:

## Properties & Relations(4)

For normalized machineprecision numbers, Accuracy[x] is the same as \$MachinePrecision-Log[10,Abs[x]]:

No machine number has a higher accuracy than \$MinMachineNumber:

Real and imaginary parts of complex numbers can have different accuracies:

Arithmetic operations will typically mix them:

But note that real and imaginary parts may still have different accuracies:

The accuracy of the whole number is always less than or equal to either of these two accuracies:

For machine numbers, accuracy generally increases with decreasing magnitude, with a maximum at \$MinMachineNumber:

For approximate numbers, Precision[x]==RealExponent[x]+Accuracy[x]:

## Possible Issues(1)

Subnormal machine numbers violate the relationship Precision[x]==RealExponent[x]+Accuracy[x]:

Instead, all subnormal numbers have the same uncertainty as \$MinMachineNumber:

## Neat Examples(1)

Accuracy and Precision in iterating the logistic map:

Wolfram Research (1988), Accuracy, Wolfram Language function, https://reference.wolfram.com/language/ref/Accuracy.html (updated 2018).

#### Text

Wolfram Research (1988), Accuracy, Wolfram Language function, https://reference.wolfram.com/language/ref/Accuracy.html (updated 2018).

#### CMS

Wolfram Language. 1988. "Accuracy." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2018. https://reference.wolfram.com/language/ref/Accuracy.html.

#### APA

Wolfram Language. (1988). Accuracy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Accuracy.html

#### BibTeX

@misc{reference.wolfram_2024_accuracy, author="Wolfram Research", title="{Accuracy}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/Accuracy.html}", note=[Accessed: 13-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_accuracy, organization={Wolfram Research}, title={Accuracy}, year={2018}, url={https://reference.wolfram.com/language/ref/Accuracy.html}, note=[Accessed: 13-September-2024 ]}