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 add-log-exp0.1
\[\leadsto \frac{NaChar}{1 + \color{blue}{\log \left(e^{e^{\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}}}\right)}} + \frac{NdChar}{e^{\frac{-\left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}{KbT}} + 1}\]
Applied add-log-exp0.1
\[\leadsto \frac{NaChar}{\color{blue}{\log \left(e^{1}\right)} + \log \left(e^{e^{\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}}}\right)} + \frac{NdChar}{e^{\frac{-\left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}{KbT}} + 1}\]
Applied sum-log0.1
\[\leadsto \frac{NaChar}{\color{blue}{\log \left(e^{1} \cdot e^{e^{\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}}}\right)}} + \frac{NdChar}{e^{\frac{-\left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}{KbT}} + 1}\]
Simplified0.1
\[\leadsto \frac{NaChar}{\log \color{blue}{\left(e \cdot e^{e^{\frac{Ev - \left(\left(mu - Vef\right) - EAccept\right)}{KbT}}}\right)}} + \frac{NdChar}{e^{\frac{-\left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}{KbT}} + 1}\]
Final simplification0.1
\[\leadsto \frac{NaChar}{\log \left(e \cdot e^{e^{\frac{Ev - \left(\left(mu - Vef\right) - EAccept\right)}{KbT}}}\right)} + \frac{NdChar}{1 + e^{-\frac{Ec - \left(EDonor + \left(mu + Vef\right)\right)}{KbT}}}\]
