Initial program 0.0
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Simplified0.0
\[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}}} + \frac{NdChar}{e^{\frac{-\left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}{KbT}} + 1}}\]
- Using strategy
rm Applied *-un-lft-identity0.0
\[\leadsto \frac{NaChar}{1 + e^{\color{blue}{1 \cdot \frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}}}} + \frac{NdChar}{e^{\frac{-\left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}{KbT}} + 1}\]
Applied exp-prod0.0
\[\leadsto \frac{NaChar}{1 + \color{blue}{{\left(e^{1}\right)}^{\left(\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}\right)}}} + \frac{NdChar}{e^{\frac{-\left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}{KbT}} + 1}\]
Simplified0.0
\[\leadsto \frac{NaChar}{1 + {\color{blue}{e}}^{\left(\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}\right)}} + \frac{NdChar}{e^{\frac{-\left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}{KbT}} + 1}\]
- Using strategy
rm Applied neg-sub00.0
\[\leadsto \frac{NaChar}{1 + {e}^{\left(\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}\right)}} + \frac{NdChar}{e^{\frac{\color{blue}{0 - \left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}}{KbT}} + 1}\]
Applied div-sub0.0
\[\leadsto \frac{NaChar}{1 + {e}^{\left(\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}\right)}} + \frac{NdChar}{e^{\color{blue}{\frac{0}{KbT} - \frac{Ec - \left(\left(Vef + mu\right) + EDonor\right)}{KbT}}} + 1}\]
Applied exp-diff0.0
\[\leadsto \frac{NaChar}{1 + {e}^{\left(\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}\right)}} + \frac{NdChar}{\color{blue}{\frac{e^{\frac{0}{KbT}}}{e^{\frac{Ec - \left(\left(Vef + mu\right) + EDonor\right)}{KbT}}}} + 1}\]
Simplified0.0
\[\leadsto \frac{NaChar}{1 + {e}^{\left(\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}\right)}} + \frac{NdChar}{\frac{\color{blue}{1}}{e^{\frac{Ec - \left(\left(Vef + mu\right) + EDonor\right)}{KbT}}} + 1}\]
- Using strategy
rm Applied add-cbrt-cube0.0
\[\leadsto \frac{NaChar}{\color{blue}{\sqrt[3]{\left(\left(1 + {e}^{\left(\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}\right)}\right) \cdot \left(1 + {e}^{\left(\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}\right)}\right)\right) \cdot \left(1 + {e}^{\left(\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}\right)}\right)}}} + \frac{NdChar}{\frac{1}{e^{\frac{Ec - \left(\left(Vef + mu\right) + EDonor\right)}{KbT}}} + 1}\]
Final simplification0.0
\[\leadsto \frac{NaChar}{\sqrt[3]{\left(\left({e}^{\left(\frac{EAccept + \left(\left(Vef + Ev\right) - mu\right)}{KbT}\right)} + 1\right) \cdot \left({e}^{\left(\frac{EAccept + \left(\left(Vef + Ev\right) - mu\right)}{KbT}\right)} + 1\right)\right) \cdot \left({e}^{\left(\frac{EAccept + \left(\left(Vef + Ev\right) - mu\right)}{KbT}\right)} + 1\right)}} + \frac{NdChar}{1 + \frac{1}{e^{\frac{Ec - \left(\left(Vef + mu\right) + EDonor\right)}{KbT}}}}\]
