The verify(expr1, expr2, sign) calling sequence returns true if any of the following is true:

The arguments are equal.

Multiplying pairs of multiplicands by $\mathrm{-1}$ results in equal arguments.

Given $a^n$ and $b^n$ where $n$ is even, $a=b$ or $a=-b$.

This verification is more memory and computationally intensive than checking whether the normal of the difference is zero, but it ensures that the two arguments have similar forms.

This verification is symmetric.

$\mathrm{verify}\left(-\frac{x}{a-b}\,\frac{x}{b-a}\,\mathrm{sign}\right)$

$\mathrm{true}$

$p≔\frac{3{\left(x-y\right)}^2\left(x-2y-xy\right)\left(x-y-4x\right)\left(x{y}^2+2x-2y\right)}{y-3x}$

$p≔\frac{3{\left(x-y\right)}^2\left(-xy+x-2y\right)\left(-3x-y\right)\left(x{y}^2+2x-2y\right)}{y-3x}$

$q≔\frac{3{\left(y-x\right)}^2\left(xy+2y-x\right)\left(4x-y-x\right)\left(2y-x{y}^2-2x\right)}{3x-y}$

$q≔3{\left(y-x\right)}^2\left(xy-x+2y\right)\left(-x{y}^2-2x+2y\right)$

$\mathrm{verify}\left(p\,q\,\mathrm{sign}\right)$

$\mathrm{false}$