The simplify(expr, size) calling sequence is used to attempt simplifying the expression size, performing only collections and simple decomposition of fractional powers in the coefficients - sometimes taking advantage of linear factors when they exist. No other mathematical simplifications of the expression or its subexpressions is performed. These operations, while simple and with low computational cost, may remarkably structure the expression and reduce its size.

The concept of size used by these routines is close to the concept of length, but function calls and radicals are considered of bigger size than mathematically simpler objects of the same length. In this framework size partly includes the idea of mathematical complexity (for advanced users, see the routines `simplify/size/size` and `simplify/size/size/object`).

The approach used consists of collecting subexpressions using an ordering based on size, then searching for possible fractional decompositions or linear factors that lead to coefficients of smaller size. Functions are handled by first simplifying in size their arguments, followed by re-evaluating the function when the simplification leads to simpler arguments. To avoid re-evaluating the functions, use the optional argument evaluate_known_functions=false.

Expressions given as a ratio between two subexpressions have the numerator and denominator simplified in size separately, and the returned result constructed by dividing the expressions obtained (whenever this result is simpler than the given expression).

The simplification of the expression size is performed automatically by the simplify command, as part of its default operation, for all calling sequences. To perform only simplification of the expression size, and no other simplifications, invoke the routines by calling simplify with the extra argument size. Alternatively, the simplification of size is an option in the context menu (Simplify > Size).

To disable simplification of the expression size, you can pass the option size = false to the simplify command. The option size = false can be included with any simplify calling sequence. Other simplifications cannot be turned off in the same way: this feature is exclusive to simplification with respect to size.

$\mathrm{e1}≔\frac{1}{4}\exp \left(-\frac{1}{4}{x}^2\right)2^{\frac{1}{4}}{x}^{\frac{3}{2}}+\frac{1}{8}\exp \left(\frac{1}{4}{x}^2\right)2^{\frac{3}{4}}\mathrm{sqrt}\left(x\right)\mathrm{sqrt}\left(\mathrm{\pi }\right)\mathrm{erf}\left(\frac{1}{2}\mathrm{sqrt}\left(2\right)x\right)+\frac{1}{8}\exp \left(\frac{1}{4}{x}^2\right)2^{\frac{3}{4}}{x}^{\frac{5}{2}}\mathrm{sqrt}\left(\mathrm{\pi }\right)\mathrm{erf}\left(\frac{1}{2}\mathrm{sqrt}\left(2\right)x\right)\:$

$\mathrm{simplify}\left(\mathrm{e1}\right)$

$\frac{2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\sqrt{x}\left(2{\ⅇ}^{-\frac{x^2}{4}}x+{\ⅇ}^{\frac{x^2}{4}}\sqrt{\mathrm{\pi }}\mathrm{erf}\left(\frac{\sqrt{2}x}{2}\right)\sqrt{2}\left(x^2+1\right)\right)}{8}$

$\mathrm{simplify}\left(\mathrm{e1}\,\mathrm{size}\right)$

$\frac{2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\sqrt{x}\left(2{\ⅇ}^{-\frac{x^2}{4}}x+{\ⅇ}^{\frac{x^2}{4}}\sqrt{\mathrm{\pi }}\mathrm{erf}\left(\frac{\sqrt{2}x}{2}\right)\sqrt{2}\left(x^2+1\right)\right)}{8}$

$\mathrm{e2}≔-3{\sin \left(x\right)}^{\frac{1}{2}}{\cos \left(x\right)}^2{\sin \left(x\right)}^m+3{\sin \left(x\right)}^{\frac{1}{2}}{\cos \left(x\right)}^2{\cos \left(x\right)}^n+4{\sin \left(x\right)}^{\frac{1}{2}}{\cos \left(x\right)}^4{\sin \left(x\right)}^m-4{\sin \left(x\right)}^{\frac{1}{2}}{\cos \left(x\right)}^4{\cos \left(x\right)}^n$

$\mathrm{e2}≔-3\sqrt{\sin \left(x\right)}{\cos \left(x\right)}^2{\sin \left(x\right)}^m+3\sqrt{\sin \left(x\right)}{\cos \left(x\right)}^2{\cos \left(x\right)}^n+4\sqrt{\sin \left(x\right)}{\cos \left(x\right)}^4{\sin \left(x\right)}^m-4\sqrt{\sin \left(x\right)}{\cos \left(x\right)}^4{\cos \left(x\right)}^n$

$\mathrm{simplify}\left(\mathrm{e2}\right)$

$-4\sqrt{\sin \left(x\right)}{\cos \left(x\right)}^2\left({\cos \left(x\right)}^n-{\sin \left(x\right)}^m\right)\left({\cos \left(x\right)}^2-\frac{3}{4}\right)$

$\mathrm{simplify}\left(\mathrm{e2}\,\mathrm{size}\right)$

$-4\sqrt{\sin \left(x\right)}{\cos \left(x\right)}^2\left({\cos \left(x\right)}^n-{\sin \left(x\right)}^m\right)\left({\cos \left(x\right)}^2-\frac{3}{4}\right)$

$\mathrm{simplify}\left(\mathrm{e2}\,\mathrm{size}=\mathrm{false}\right)$

$\left(-4{\cos \left(x\right)}^2+3\right)\left({\cos \left(x\right)}^n-{\sin \left(x\right)}^m\right)\sqrt{\sin \left(x\right)}{\cos \left(x\right)}^2$

$\mathrm{e3}≔{\sin \left(x\right)}^2+{\cos \left(x\right)}^2$

$\mathrm{e3}≔{\sin \left(x\right)}^2+{\cos \left(x\right)}^2$

$\mathrm{simplify}\left(\mathrm{e3}\right)$

$1$

$\mathrm{simplify}\left(\mathrm{e3}\,\mathrm{size}\right)$

${\sin \left(x\right)}^2+{\cos \left(x\right)}^2$

$\mathrm{simplify}\left(\mathrm{e3}\,\mathrm{size}=\mathrm{false}\right)$

$1$

$\mathrm{one}≔\exp \left(xa-a-\left(x-1\right)a\right)$

$\mathrm{one}≔{\ⅇ}^{xa-a-\left(x-1\right)a}$

$\mathrm{one}=\mathrm{simplify}\left(\mathrm{one}\,\mathrm{size}\right)$

${\ⅇ}^{xa-a-\left(x-1\right)a}=1$

$\mathrm{one}=\mathrm{simplify}\left(\mathrm{one}\,\mathrm{size}\,\mathrm{evaluate\_known\_functions}=\mathrm{false}\right)$

${\ⅇ}^{xa-a-\left(x-1\right)a}={\ⅇ}^0$

${\ⅇ}^{xa-a-\left(x-1\right)a}=1$