Simplify
Details and Options
- Simplify tries expanding, factoring, and doing many other transformations on expressions, keeping track of the simplest form obtained.
- Simplify can be used on equations, inequalities, and domain specifications.
- Quantities that appear algebraically in inequalities are always assumed to be real.
- FullSimplify does more extensive simplification than Simplify .
- You can specify default assumptions for Simplify using Assuming .
- The following options can be given:
-
- Assumptions can consist of equations, inequalities, domain specifications such as x∈Integers , and logical combinations of these.
- With the setting TimeConstraint->{tloc,ttot}, at most tloc seconds are spent for any particular transformation, and at most ttot seconds are spent for all transformations before the best result is returned.
- Simplify can be used with symbolic array expressions.
Examples
open all close allBasic Examples (3)
Simplify can get further if assumptions are made about x:
Scope (5)
Simplify a polynomial:
Simplify a rational expression:
Simplify a trigonometric expression:
Simplify an exponential expression:
Simplify an equation:
Simplify expressions using assumptions:
Use assumptions to prove inequalities:
Simplify symbolic array expressions:
Options (10)
Assumptions (3)
Assumptions can be given both as an argument and as an option value:
The default value of the Assumptions option is $Assumptions :
When assumptions are given as an argument, $Assumptions is used as well:
Specifying assumptions as an option value prevents Simplify from using $Assumptions :
ComplexityFunction (2)
The default ComplexityFunction counts the subexpressions and digits of integers:
LeafCount counts only the number of subexpressions:
With the default ComplexityFunction , Abs [x] is simpler than the FullForm of -x:
This complexity function makes Abs more expensive than Times :
ExcludedForms (1)
This gives no simplification:
Excluding transformations of (x-2)^10 allows Simplify to expand the remaining terms:
TimeConstraint (2)
This takes a long time, due to trigonometric expansion, but does not yield a simplification:
Use TimeConstraint to limit the time spent on any single transformation:
A similar example, where the transformation yields a simplification:
In this case, setting TimeConstraint prevents some simplification:
TransformationFunctions (1)
Applications (4)
Prove that a solution satisfies its equations:
Show that the arithmetic mean is larger than the geometric one:
This applies Fermat's little theorem:
Prove commutativity from Wolfram's minimal axiom for Boolean algebra:
Properties & Relations (3)
Use Assuming to propagate assumptions:
Use FullSimplify to simplify expressions involving special functions:
ArraySimplify performs only array transformations:
Simplify performs other transformations as well:
Possible Issues (2)
The Wolfram Language evaluates zero times a symbolic expression to zero:
This happens even if the symbolic expression is always infinite:
Because of this, results of simplification of expressions with singularities are uncertain:
In this case, FullSimplify recognizes the zero:
Results of simplification may depend on the names of symbols:
Related Guides
Related Links
History
Introduced in 1988 (1.0) | Updated in 1996 (3.0) ▪ 1999 (4.0) ▪ 2000 (4.1) ▪ 2002 (4.2) ▪ 2003 (5.0) ▪ 2014 (10.0) ▪ 2025 (14.2)
Text
Wolfram Research (1988), Simplify, Wolfram Language function, https://reference.wolfram.com/language/ref/Simplify.html (updated 2025).
CMS
Wolfram Language. 1988. "Simplify." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/Simplify.html.
APA
Wolfram Language. (1988). Simplify. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Simplify.html
BibTeX
@misc{reference.wolfram_2025_simplify, author="Wolfram Research", title="{Simplify}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/Simplify.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_simplify, organization={Wolfram Research}, title={Simplify}, year={2025}, url={https://reference.wolfram.com/language/ref/Simplify.html}, note=[Accessed: 17-November-2025]}