The phaseamp conversion attempts to locate subexpressions of the form $aF\left(t\right)\cos \left(\mathrm{omega}t\right)\+bF\left(t\right)\sin \left(\mathrm{omega}t\right)$ in expr, and converts them to the form $\sqrt{a^2\+b^2}F\left(t\right)\cos \left(\mathrm{omega}t-\arctan \left(b\,a\right)\right)$. Here, the coefficients $a$ and $b$ are independent of the variable $t$, which must be passed as a parameter to the conversion.

The strength of the conversion is sensitive to the values of the environment variables Testzero and Normalizer.

$\mathrm{convert}\left(a\exp \left(ct\right)\cos \left(\mathrm{\omega }t\right)+b\exp \left(ct\right)\sin \left(\mathrm{\omega }t\right)\,\mathrm{phaseamp}\,t\right)$

$\sqrt{a^2+b^2}{\ⅇ}^{ct}\cos \left(\mathrm{\omega }t-\arctan \left(b\,a\right)\right)$

$\mathrm{convert}\left(a\left(s\right)\exp \left(st\right)\cos \left(st\right)+b\left(s\right)\exp \left(st\right)\sin \left(st\right)\,\mathrm{phaseamp}\,t\right)$

$\sqrt{{a\left(s\right)}^2+{b\left(s\right)}^2}{\ⅇ}^{st}\cos \left(st-\arctan \left(b\left(s\right)\,a\left(s\right)\right)\right)$

$\mathrm{convert}\left(a\left(s\right)\exp \left(st\right)\cos \left(st\right)+b\left(s\right)\exp \left(st\right)\sin \left(st\right)\,\mathrm{phaseamp}\,s\right)$

$a\left(s\right){\ⅇ}^{st}\cos \left(st\right)+b\left(s\right){\ⅇ}^{st}\sin \left(st\right)$