Initial program 0.0
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
- Using strategy
rm Applied *-un-lft-identity0.0
\[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{\color{blue}{1 \cdot KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Applied neg-mul-10.0
\[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{-1 \cdot \left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}}{1 \cdot KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Applied times-frac0.0
\[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-1}{1} \cdot \frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Applied exp-prod0.0
\[\leadsto \frac{NdChar}{1 + \color{blue}{{\left(e^{\frac{-1}{1}}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Simplified0.0
\[\leadsto \frac{NdChar}{1 + {\color{blue}{\left(e^{-1}\right)}}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
- Using strategy
rm Applied add-cube-cbrt0.0
\[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}\right) \cdot \sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
- Using strategy
rm Applied *-un-lft-identity0.0
\[\leadsto \frac{NdChar}{1 + \left(\sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}\right) \cdot \sqrt[3]{{\left(e^{\color{blue}{1 \cdot -1}}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Applied exp-prod0.0
\[\leadsto \frac{NdChar}{1 + \left(\sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}\right) \cdot \sqrt[3]{{\color{blue}{\left({\left(e^{1}\right)}^{-1}\right)}}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Applied pow-pow0.0
\[\leadsto \frac{NdChar}{1 + \left(\sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}\right) \cdot \sqrt[3]{\color{blue}{{\left(e^{1}\right)}^{\left(-1 \cdot \frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Simplified0.0
\[\leadsto \frac{NdChar}{1 + \left(\sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}\right) \cdot \sqrt[3]{{\left(e^{1}\right)}^{\color{blue}{\left(\frac{-1 \cdot \left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}\right)}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto \frac{NdChar}{1 + \left(\sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}\right) \cdot \sqrt[3]{\color{blue}{\sqrt{{\left(e^{1}\right)}^{\left(\frac{-1 \cdot \left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}\right)}} \cdot \sqrt{{\left(e^{1}\right)}^{\left(\frac{-1 \cdot \left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}\right)}}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Final simplification0.0
\[\leadsto \frac{NdChar}{1 + \left(\sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{-1}\right)}^{\left(\frac{\left(\left(Ec - Vef\right) - EDonor\right) - mu}{KbT}\right)}}\right) \cdot \sqrt[3]{\sqrt{{\left(e^{1}\right)}^{\left(\frac{-1 \cdot \left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}\right)}} \cdot \sqrt{{\left(e^{1}\right)}^{\left(\frac{-1 \cdot \left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}\right)}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
