is an option for Simplify and other functions which gives a function to rank the complexity of different forms of an expression.
ComplexityFunction
is an option for Simplify and other functions which gives a function to rank the complexity of different forms of an expression.
Details
- With the default setting ComplexityFunction->Automatic , forms are ranked primarily according to their LeafCount , with corrections to treat integers with more digits as more complex.
- Simplify [expr,ComplexityFunction->f] applies f to each intermediate expression generated by Simplify , treating the one which yields the smallest numerical value as simplest.
Examples
open all close allBasic Examples (2)
The default ComplexityFunction counts the subexpressions and digits of integers:
LeafCount counts only the number of subexpressions:
By default this expression is not simplified:
This complexity function makes ChebyshevT more expensive than other functions:
Scope (1)
With the default ComplexityFunction , Abs [x] is simpler than the FullForm of -x:
This complexity function counts characters in the InputForm of the expression:
Now -x is simpler than Abs [x]:
Properties & Relations (1)
The automatic complexity function:
Tech Notes
Related Guides
History
Introduced in 1996 (3.0)
Text
Wolfram Research (1996), ComplexityFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexityFunction.html.
CMS
Wolfram Language. 1996. "ComplexityFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComplexityFunction.html.
APA
Wolfram Language. (1996). ComplexityFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComplexityFunction.html
BibTeX
@misc{reference.wolfram_2025_complexityfunction, author="Wolfram Research", title="{ComplexityFunction}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexityFunction.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_complexityfunction, organization={Wolfram Research}, title={ComplexityFunction}, year={1996}, url={https://reference.wolfram.com/language/ref/ComplexityFunction.html}, note=[Accessed: 17-November-2025]}