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is an option for various numerical operations that specifies how many digits of precision should be maintained in internal computations.
Details Examplesopen allclose all Basic Examples (2)Find a root using 60-digit precision arithmetic:
Solve a differential equation using 24-digit precision arithmetic:
Scope (4)Evaluate the function using 24-digit precision arithmetic:
Without higher precision you see mainly numerical roundoff error:
Approximate an integral using 24-digit precision arithmetic:
The PrecisionGoal is automatically increased to be 10 less than the working precision:
Find a minimum of a function, adaptively increasing the precision up to 50 digits:
The PrecisionGoal and AccuracyGoal are automatically set to be half the final precision:
Solve a differential equation with 32-digit precision arithmetic:
The PrecisionGoal and AccuracyGoal are set to be half of the working precision:
Using InterpolationOrder->All will reduce the errors between steps:
Applications (1)Check the quality of a solution to Duffing's equation by using a sequence of solution precisions:
Make a sequence of solutions at successively higher working precision:
A plot shows that some of the solutions deviate toward the end:
Plot the solution x[100] as a function of working precision:
Convergence to the solution at the highest precision indicates about 6 digits can be trusted:
Possible Issues (2)Low-precision parameters in functions may invalidate the use of higher-precision arithmetic:
The result is a poor approximation to :
Use of exact parameters allows comparison at different precisions:
Expect solution times to increase exponentially as a function of working precision:
A log plot of the computation time as a function of working precision:
HistoryIntroduced in 1988 (1.0) | Updated in 2003 (5.0)
Wolfram Research (1988), WorkingPrecision, Wolfram Language function, https://reference.wolfram.com/language/ref/WorkingPrecision.html (updated 2003). TextWolfram Research (1988), WorkingPrecision, Wolfram Language function, https://reference.wolfram.com/language/ref/WorkingPrecision.html (updated 2003).
CMSWolfram Language. 1988. "WorkingPrecision." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/WorkingPrecision.html.
APAWolfram Language. (1988). WorkingPrecision. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WorkingPrecision.html
BibTeX@misc{reference.wolfram_2025_workingprecision, author="Wolfram Research", title="{WorkingPrecision}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/WorkingPrecision.html}", note=[Accessed: 12-July-2025 ]}
BibLaTeX@online{reference.wolfram_2025_workingprecision, organization={Wolfram Research}, title={WorkingPrecision}, year={2003}, url={https://reference.wolfram.com/language/ref/WorkingPrecision.html}, note=[Accessed: 12-July-2025 ]}
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