# Symbolic Expressions for Emulator Superiority

Name | Expression
--- | ---
advE | $\gamma_{1} \cdot \left(1 - e^{- 2 \cdot i \cdot \pi \cdot \phi}\right) + 1$
advI | $\frac{1}{- \gamma_{1} \cdot \left(1 - e^{- 2 \cdot i \cdot \pi \cdot \phi}\right) + 1}$
advA | $e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi}$
advH | $\theta_{0} \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi} + \theta_{1}$
advMagnitudeErrorE | $\cos{\left(\operatorname{atan}_{2}{\left(0,4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1 \right)} / 2 \right)} \cdot \sqrt{\left|{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}\right|} - 1$
advMagnitudeErrorI | $-1 + \frac{1}{\sqrt{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}}$
advPhaseErrorE | $\left|{\frac{\arg{\left(\gamma_{1} - \gamma_{1} \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi} + 1 \right)}}{\arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}}\right| - 1$
advPhaseErrorI | $\left|{\frac{\arg{\left(\frac{e^{2 \cdot i \cdot \pi \cdot \phi}}{- \gamma_{1} \cdot e^{2 \cdot i \cdot \pi \cdot \phi} + \gamma_{1} + e^{2 \cdot i \cdot \pi \cdot \phi}} \right)}}{\arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}}\right| - 1$
advISolTFirst | $- \frac{\gamma_{1}}{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1}$
advISolTSecond | $\frac{- 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + \gamma_{1} + 1}{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1}$
advASolTFirst | $- \frac{\sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)}}{\sin{\left(2 \cdot \pi \cdot \psi \right)}}$
advASolTSecond | $\frac{\sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)}}{\sin{\left(2 \cdot \pi \cdot \psi \right)}}$
advESolTFirst | $- \gamma_{1}$
advESolTSecond | $\gamma_{1} + 1$
advHE | $\gamma_{1} - \gamma_{1} \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi} + 1$
advHA | $\frac{\left(e^{2 \cdot i \cdot \pi \cdot \phi} \cdot \sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} - \sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)}\right) \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi}}{\sin{\left(2 \cdot \pi \cdot \psi \right)}}$
advHI | $\frac{\left(- \gamma_{1} + \left(- 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + \gamma_{1} + 1\right) \cdot e^{2 \cdot i \cdot \pi \cdot \phi}\right) \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi}}{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1}$
advSupMagIIA | $\frac{\sqrt{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1} \cdot \left(- 4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + \cos{\left(\operatorname{atan}_{2}{\left(0,- 16 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 16 \cdot \gamma_{1}^{2} \cdot \sin^{4}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 8 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1 \right)} / 2 \right)} \cdot \sqrt{\left|{- 16 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 16 \cdot \gamma_{1}^{2} \cdot \sin^{4}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 8 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1}\right|} - 1\right)}{\left(1 - \sqrt{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}\right) \cdot \left(4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1\right)}$
advSupMagAIA | $\frac{\left(\cos{\left(\operatorname{atan}_{2}{\left(0,\sin^{2}{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} - 2 \cdot \sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} \cdot \sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} \cdot \cos{\left(2 \cdot \pi \cdot \phi \right)} + \sin^{2}{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} \right)} / 2 \right)} \cdot \left|{\frac{\sqrt{\sin^{2}{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} - 2 \cdot \sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} \cdot \sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} \cdot \cos{\left(2 \cdot \pi \cdot \phi \right)} + \sin^{2}{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)}}}{\sin{\left(2 \cdot \pi \cdot \psi \right)}}}\right| - 1\right) \cdot \sqrt{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}}{1 - \sqrt{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}}$
advSupMagIEA | $\frac{- \left(\cos{\left(\operatorname{atan}_{2}{\left(0,4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1 \right)} / 2 \right)} \cdot \sqrt{\left|{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}\right|} - 1\right) \cdot \left(4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} - \cos{\left(\operatorname{atan}_{2}{\left(0,- 16 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 16 \cdot \gamma_{1}^{2} \cdot \sin^{4}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 8 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1 \right)} / 2 \right)} \cdot \sqrt{\left|{- 16 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 16 \cdot \gamma_{1}^{2} \cdot \sin^{4}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 8 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1}\right|} + 1\right) + \sin{\left(\operatorname{atan}_{2}{\left(0,4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1 \right)} / 2 \right)} \cdot \sin{\left(\operatorname{atan}_{2}{\left(0,- 16 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 16 \cdot \gamma_{1}^{2} \cdot \sin^{4}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 8 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1 \right)} / 2 \right)} \cdot \left|{\sqrt{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1} \cdot \sqrt{- 16 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 16 \cdot \gamma_{1}^{2} \cdot \sin^{4}{\left(\pi \cdot \psi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 8 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1}}\right|}{\left(4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1\right) \cdot \left(- 2 \cdot \cos{\left(\operatorname{atan}_{2}{\left(0,4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1 \right)} / 2 \right)} \cdot \sqrt{\left|{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}\right|} + \left|{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}\right| + 1\right)}$
advSupMagAEA | $\frac{\left(\cos{\left(\operatorname{atan}_{2}{\left(0,4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1 \right)} / 2 \right)} \cdot \sqrt{\left|{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}\right|} - 1\right) \cdot \left(\cos{\left(\operatorname{atan}_{2}{\left(0,\sin^{2}{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} - 2 \cdot \sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} \cdot \sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} \cdot \cos{\left(2 \cdot \pi \cdot \phi \right)} + \sin^{2}{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} \right)} / 2 \right)} \cdot \left|{\frac{\sqrt{\sin^{2}{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} - 2 \cdot \sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} \cdot \sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} \cdot \cos{\left(2 \cdot \pi \cdot \phi \right)} + \sin^{2}{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)}}}{\sin{\left(2 \cdot \pi \cdot \psi \right)}}}\right| - 1\right) + \sin{\left(\operatorname{atan}_{2}{\left(0,4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1 \right)} / 2 \right)} \cdot \sin{\left(\operatorname{atan}_{2}{\left(0,\sin^{2}{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} - 2 \cdot \sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} \cdot \sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} \cdot \cos{\left(2 \cdot \pi \cdot \phi \right)} + \sin^{2}{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} \right)} / 2 \right)} \cdot \left|{\frac{\sqrt{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}}{\sin{\left(2 \cdot \pi \cdot \psi \right)}} \cdot \sqrt{\sin^{2}{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} - 2 \cdot \sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)} \cdot \sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} \cdot \cos{\left(2 \cdot \pi \cdot \phi \right)} + \sin^{2}{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)}}}\right|}{- 2 \cdot \cos{\left(\operatorname{atan}_{2}{\left(0,4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1 \right)} / 2 \right)} \cdot \sqrt{\left|{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}\right|} + \left|{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}\right| + 1}$
advSupMagEIA | $\frac{\left(- \cos{\left(\operatorname{atan}_{2}{\left(0,4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1 \right)} / 2 \right)} \cdot \sqrt{\left|{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}\right|} + 1\right) \cdot \sqrt{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}}{\sqrt{4 \cdot \gamma_{1}^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1} - 1}$
advSupMagEAA | $\text{NaN}$
advSupPhaseIIA | $\frac{\arg{\left(\left(- \gamma_{1} + \left(- 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + \gamma_{1} + 1\right) \cdot e^{2 \cdot i \cdot \pi \cdot \phi}\right) \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi} \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}{\arg{\left(\frac{e^{2 \cdot i \cdot \pi \cdot \phi}}{- \gamma_{1} \cdot e^{2 \cdot i \cdot \pi \cdot \phi} + \gamma_{1} + e^{2 \cdot i \cdot \pi \cdot \phi}} \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}$
advSupPhaseAIA | $\frac{\arg{\left(\frac{\left(e^{2 \cdot i \cdot \pi \cdot \phi} \cdot \sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} - \sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)}\right) \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi}}{\sin{\left(2 \cdot \pi \cdot \psi \right)}} \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}{\arg{\left(\frac{e^{2 \cdot i \cdot \pi \cdot \phi}}{- \gamma_{1} \cdot e^{2 \cdot i \cdot \pi \cdot \phi} + \gamma_{1} + e^{2 \cdot i \cdot \pi \cdot \phi}} \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}$
advSupPhaseIEA | $\frac{\arg{\left(\left(- \gamma_{1} + \left(- 4 \cdot \gamma_{1} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + \gamma_{1} + 1\right) \cdot e^{2 \cdot i \cdot \pi \cdot \phi}\right) \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi} \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}{\arg{\left(\gamma_{1} - \gamma_{1} \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi} + 1 \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}$
advSupPhaseAEA | $\frac{\arg{\left(\frac{\left(e^{2 \cdot i \cdot \pi \cdot \phi} \cdot \sin{\left(2 \cdot \pi \cdot \psi \cdot \left(\gamma_{1} + 1\right) \right)} - \sin{\left(2 \cdot \pi \cdot \gamma_{1} \cdot \psi \right)}\right) \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi}}{\sin{\left(2 \cdot \pi \cdot \psi \right)}} \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}{\arg{\left(\gamma_{1} - \gamma_{1} \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi} + 1 \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}$
advSupPhaseEIA | $\frac{\arg{\left(\gamma_{1} - \gamma_{1} \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi} + 1 \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}{\arg{\left(\frac{e^{2 \cdot i \cdot \pi \cdot \phi}}{- \gamma_{1} \cdot e^{2 \cdot i \cdot \pi \cdot \phi} + \gamma_{1} + e^{2 \cdot i \cdot \pi \cdot \phi}} \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}}$
advSupPhaseEAA | $\tilde{\infty} \cdot \left(\arg{\left(\gamma_{1} - \gamma_{1} \cdot e^{- 2 \cdot i \cdot \pi \cdot \phi} + 1 \right)} - \arg{\left(e^{2 \cdot i \cdot \pi \cdot \gamma_{1} \cdot \phi} \right)}\right)$
diffE | $\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 1$
diffI | $\frac{1}{- \gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 1}$
diffA | $e^{- 2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}}$
diffH | $\theta \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 1$
diffMagnitudeErrorE | $\left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 1\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} - 1$
diffMagnitudeErrorI | $\frac{- 2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} - 1}{2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} + 1}$
diffISol | $\frac{\gamma_{2}}{2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1}$
diffASol | $\frac{\left(1 - e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}\right) \cdot e^{- 2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}}{\cos{\left(2 \cdot \pi \cdot \psi \right)} - 1}$
diffESol | $\gamma_{2}$
diffHI | $\frac{\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1}{2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1}$
diffHA | $\frac{\left(\left(1 - e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}\right) \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + \left(\cos{\left(2 \cdot \pi \cdot \psi \right)} - 1\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}\right) \cdot e^{- 2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}}{\cos{\left(2 \cdot \pi \cdot \psi \right)} - 1}$
diffHE | $\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 1$
diffSupMagIIA | $\frac{\left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) - 1\right) \cdot \left(2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + \left(2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} - 1\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} + 1\right)}{\left(2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1\right) \cdot \left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} - 1\right)}$
diffSupMagAIA | $- \frac{\left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) - 1\right) \cdot \left(- \left(\left(e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}} - 1\right) \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) - \left(\cos{\left(2 \cdot \pi \cdot \psi \right)} - 1\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} + 2 \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}} \cdot \sin^{2}{\left(\pi \cdot \psi \right)}\right) \cdot e^{- 2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}}{\left(\cos{\left(2 \cdot \pi \cdot \psi \right)} - 1\right) \cdot \left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} - 1\right)}$
diffSupMagIEA | $\frac{- 2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + \left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} - 1}{\left(2 \cdot \gamma_{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} + 1\right) \cdot \left(\left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 1\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} - 1\right)}$
diffSupMagAEA | $\frac{\left(\left(\left(1 - e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}\right) \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + \left(\cos{\left(2 \cdot \pi \cdot \psi \right)} - 1\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} + 2 \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}} \cdot \sin^{2}{\left(\pi \cdot \psi \right)}\right) \cdot e^{- 2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \psi^{2}}}{\left(\left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 1\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} - 1\right) \cdot \left(\cos{\left(2 \cdot \pi \cdot \psi \right)} - 1\right)}$
diffSupMagEIA | $- \frac{\left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) - 1\right) \cdot \left(\left(\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + 1\right) \cdot e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} - 1\right)}{\gamma_{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right) + e^{2 \cdot \pi^{2} \cdot \gamma_{2} \cdot \phi^{2}} - 1}$
poissFD | $\frac{1}{2 - 2 \cdot \cos{\left(2 \cdot \pi \cdot \phi \right)}}$
poissA | $\frac{1}{4 \cdot \pi^{2} \cdot \phi^{2}}$
poissIter | $\frac{0.5 - 0.5 \cdot \cos^{q}{\left(2 \cdot \pi \cdot \phi \right)}}{1 - \cos{\left(2 \cdot \pi \cdot \phi \right)}}$
poissH | $\frac{\theta}{2 - 2 \cdot \cos{\left(2 \cdot \pi \cdot \phi \right)}}$
poissMagnitudeErrorFD | $\frac{\pi^{2} \cdot \phi^{2}}{\sin^{2}{\left(\pi \cdot \phi \right)}} - 1$
poissMagnitudeErrorIter | $2.0 \cdot \pi^{2} \cdot \phi^{2} \cdot \left|{\frac{\cos^{q}{\left(2 \cdot \pi \cdot \phi \right)} - 1}{\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1}}\right| - 1.0$
poissMagnitudeErrorIterAgainstFD | $2.0 \cdot \sin^{2}{\left(\pi \cdot \phi \right)} \cdot \left|{\frac{\cos^{q}{\left(2 \cdot \pi \cdot \phi \right)} - 1}{\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1}}\right| - 1$
poissIterSol | $1.0 - \cos^{q}{\left(6.28318530717959 \cdot \psi \right)}$
poissFDSol | $1$
poissASol | $\frac{\sin^{2}{\left(\pi \cdot \psi \right)}}{\pi^{2} \cdot \psi^{2}}$
poissHIter | $\frac{\cos^{q}{\left(6.28318530717959 \cdot \psi \right)} - 1.0}{2 \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right)}$
poissHFD | $- \frac{1}{2 \cdot \cos{\left(2 \cdot \pi \cdot \phi \right)} - 2}$
poissHA | $- \frac{\sin^{2}{\left(\pi \cdot \psi \right)}}{2 \cdot \pi^{2} \cdot \psi^{2} \cdot \left(\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right)}$
poissSupMagIterFDA | $\frac{2 \cdot \left(\pi^{2} \cdot \phi^{2} \cdot \left|{\frac{\cos^{q}{\left(6.28318530717959 \cdot \psi \right)} - 1.0}{\sin^{2}{\left(\pi \cdot \phi \right)}}}\right| - 1\right) \cdot \sin^{2}{\left(\pi \cdot \phi \right)}}{2 \cdot \pi^{2} \cdot \phi^{2} + \cos{\left(2 \cdot \pi \cdot \phi \right)} - 1}$
poissSupMagIterIterA | $\frac{\pi^{2} \cdot \phi^{2} \cdot \left|{\frac{\cos^{q}{\left(6.28318530717959 \cdot \psi \right)} - 1.0}{\sin^{2}{\left(\pi \cdot \phi \right)}}}\right| - 1}{2.0 \cdot \pi^{2} \cdot \phi^{2} \cdot \left|{\frac{\cos^{q}{\left(2 \cdot \pi \cdot \phi \right)} - 1}{\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1}}\right| - 1.0}$
poissSupMagFDIterA | $\frac{1.0 \cdot \left(\frac{\pi^{2} \cdot \phi^{2}}{\sin^{2}{\left(\pi \cdot \phi \right)}} - 1\right)}{\pi^{2} \cdot \phi^{2} \cdot \left|{\frac{\left(- (2 \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 1)\right)^{q} - 1}{\sin^{2}{\left(\pi \cdot \phi \right)}}}\right| - 1}$
poissSupMagFDFDA | $1$
poissSupMagIterIterFD | $\frac{1.0 \cdot \left(\sin^{2}{\left(\pi \cdot \phi \right)} \cdot \left|{\frac{\cos^{q}{\left(6.28318530717959 \cdot \psi \right)} - 1.0}{\sin^{2}{\left(\pi \cdot \phi \right)}}}\right| - 1\right)}{2 \cdot \sin^{2}{\left(\pi \cdot \phi \right)} \cdot \left|{\frac{\cos^{q}{\left(2 \cdot \pi \cdot \phi \right)} - 1}{\cos{\left(2 \cdot \pi \cdot \phi \right)} - 1}}\right| - 1}$
poissSupMagAIterA | $\frac{1.0 \cdot \left(\frac{\phi^{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)}}{\sin^{2}{\left(\pi \cdot \phi \right)}} - \psi^{2}\right)}{\psi^{2} \cdot \left(\pi^{2} \cdot \phi^{2} \cdot \left|{\frac{\left(- (2 \cdot \sin^{2}{\left(\pi \cdot \phi \right)} - 1)\right)^{q} - 1}{\sin^{2}{\left(\pi \cdot \phi \right)}}}\right| - 1\right)}$
poissSupMagAFD2A | $\frac{2 \cdot \left(\phi^{2} \cdot \sin^{2}{\left(\pi \cdot \psi \right)} - \psi^{2} \cdot \sin^{2}{\left(\pi \cdot \phi \right)}\right)}{\psi^{2} \cdot \left(2 \cdot \pi^{2} \cdot \phi^{2} + \cos{\left(2 \cdot \pi \cdot \phi \right)} - 1\right)}$