Average Error: 0.0 → 0.0
Time: 6.9min
Precision: binary64
Cost: 14528
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{Vef + \left(\left(mu + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
\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}}}↓
\frac{NdChar}{1 + e^{\frac{Vef + \left(\left(mu + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
:precision binary64
(+
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
(/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
↓
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
:precision binary64
(+
(/ NdChar (+ 1.0 (exp (/ (+ Vef (- (+ mu EDonor) Ec)) KbT))))
(/ NaChar (+ 1.0 (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT))))))
double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
return (NdChar / (1.0 + exp(-(((Ec - Vef) - EDonor) - mu) / KbT))) + (NaChar / (1.0 + exp((((Ev + Vef) + EAccept) + -mu) / KbT)));
}
↓
double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
return (NdChar / (1.0 + exp((Vef + ((mu + EDonor) - Ec)) / KbT))) + (NaChar / (1.0 + exp((((Vef + Ev) + EAccept) - mu) / KbT)));
}
Try it out
Enter valid numbers for all inputs
Alternatives
| Alternative 1 |
|---|
| Error | 1.7 |
|---|
| Cost | 14728 |
|---|
\[\begin{array}{l}
\mathbf{if}\;mu \leq -2.211954645996467 \cdot 10^{+59} \lor \neg \left(mu \leq 4.72980683032022 \cdot 10^{+109}\right):\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(Vef + EDonor\right) - Ec}{KbT}}}\\
\end{array}\]
| Alternative 2 |
|---|
| Error | 2.2 |
|---|
| Cost | 15042 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Vef \leq -1.0415895093946856 \cdot 10^{+152}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\
\mathbf{elif}\;Vef \leq 4.117484678030446 \cdot 10^{-07}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + EDonor\right) - Ec}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(Vef + EDonor\right) - Ec}{KbT}}}\\
\end{array}\]
| Alternative 3 |
|---|
| Error | 2.1 |
|---|
| Cost | 14728 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Vef \leq -5.240816475062237 \cdot 10^{+154} \lor \neg \left(Vef \leq 8.886312827474003 \cdot 10^{+17}\right):\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + EDonor\right) - Ec}{KbT}}}\\
\end{array}\]
| Alternative 4 |
|---|
| Error | 2.0 |
|---|
| Cost | 14728 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Ec \leq -2.444642284531229 \cdot 10^{+17} \lor \neg \left(Ec \leq 6.979714506808102 \cdot 10^{+52}\right):\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu + \left(Vef + EDonor\right)}{KbT}}}\\
\end{array}\]
| Alternative 5 |
|---|
| Error | 3.2 |
|---|
| Cost | 14728 |
|---|
\[\begin{array}{l}
\mathbf{if}\;EDonor \leq -5.180250292725552 \cdot 10^{+186} \lor \neg \left(EDonor \leq 6.519050892948451 \cdot 10^{+243}\right):\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}\\
\end{array}\]
| Alternative 6 |
|---|
| Error | 14.2 |
|---|
| Cost | 16455 |
|---|
\[\begin{array}{l}
\mathbf{if}\;mu \leq -2.8525274116388735 \cdot 10^{+75}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\
\mathbf{elif}\;mu \leq -2.1016655503755895 \cdot 10^{-184}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;mu \leq -7.598254844362704 \cdot 10^{-276}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\
\mathbf{elif}\;mu \leq 5.401926993433478 \cdot 10^{-219}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;mu \leq 2.9443912014653054 \cdot 10^{-146}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\
\mathbf{elif}\;mu \leq 7.719657987282082 \cdot 10^{-31}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;mu \leq 2.5502619016227197 \cdot 10^{+147}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{-\frac{mu}{KbT}}}\\
\end{array}\]
| Alternative 7 |
|---|
| Error | 15.5 |
|---|
| Cost | 16398 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Ev \leq -4.302669812138807 \cdot 10^{+56}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\
\mathbf{elif}\;Ev \leq -8.9160128013058 \cdot 10^{-102}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;Ev \leq 1.3647266724108177 \cdot 10^{-249}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{elif}\;Ev \leq 7.249915218194929 \cdot 10^{-228}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\
\mathbf{elif}\;Ev \leq 4.43886519707328 \cdot 10^{-177}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\
\mathbf{elif}\;Ev \leq 1.7137583404639804 \cdot 10^{-24}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;Ev \leq 7805795598.342865 \lor \neg \left(Ev \leq 1.866973410643373 \cdot 10^{+74}\right):\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\
\end{array}\]
| Alternative 8 |
|---|
| Error | 15.2 |
|---|
| Cost | 16398 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Ev \leq -3.74416382103057 \cdot 10^{+58}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\
\mathbf{elif}\;Ev \leq -6.2225306685150084 \cdot 10^{-96}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;Ev \leq 2.824107960749293 \cdot 10^{-303}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{elif}\;Ev \leq 6.964376844477491 \cdot 10^{-200}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\
\mathbf{elif}\;Ev \leq 6.320102651471274 \cdot 10^{-173}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;Ev \leq 6.377194615007919 \cdot 10^{-29}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;Ev \leq 27744969007.037086 \lor \neg \left(Ev \leq 9.718557464414122 \cdot 10^{+75}\right):\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\
\end{array}\]
| Alternative 9 |
|---|
| Error | 15.7 |
|---|
| Cost | 16077 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Ev \leq -1.6594247569357382 \cdot 10^{+97}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\
\mathbf{elif}\;Ev \leq 3.395818802270135 \cdot 10^{-309}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{elif}\;Ev \leq 1.3653746676395939 \cdot 10^{-205}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\
\mathbf{elif}\;Ev \leq 3.615493184676879 \cdot 10^{-178}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{elif}\;Ev \leq 1.9448003102295055 \cdot 10^{-28}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;Ev \leq 23627432342.815002 \lor \neg \left(Ev \leq 3.2459679302601303 \cdot 10^{+75}\right):\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\
\end{array}\]
| Alternative 10 |
|---|
| Error | 14.6 |
|---|
| Cost | 16391 |
|---|
\[\begin{array}{l}
\mathbf{if}\;mu \leq -2.6607303887100427 \cdot 10^{+76}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\
\mathbf{elif}\;mu \leq -4.203135521666346 \cdot 10^{-182}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\
\mathbf{elif}\;mu \leq -1.719587662696821 \cdot 10^{-273}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{elif}\;mu \leq 1.8570042913449023 \cdot 10^{-215}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\
\mathbf{elif}\;mu \leq 5.225341728215493 \cdot 10^{-170}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{elif}\;mu \leq 1.5242427725047761 \cdot 10^{+26}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;mu \leq 2.94843638165008 \cdot 10^{+165}:\\
\;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\
\end{array}\]
| Alternative 11 |
|---|
| Error | 14.6 |
|---|
| Cost | 16070 |
|---|
\[\begin{array}{l}
\mathbf{if}\;mu \leq -7.291560633812412 \cdot 10^{+59}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\
\mathbf{elif}\;mu \leq -1.5282202350604305 \cdot 10^{-133}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;mu \leq 3.0720993295298158 \cdot 10^{-304}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{elif}\;mu \leq 8.882367407393645 \cdot 10^{-220}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{elif}\;mu \leq 9.030074765372135 \cdot 10^{-171}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{elif}\;mu \leq 1.554566754653333 \cdot 10^{-56}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\
\end{array}\]
| Alternative 12 |
|---|
| Error | 14.2 |
|---|
| Cost | 14472 |
|---|
\[\begin{array}{l}
\mathbf{if}\;Vef \leq -1.5537382809328836 \cdot 10^{+102} \lor \neg \left(Vef \leq 1.2723707612996735 \cdot 10^{+42}\right):\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\end{array}\]
| Alternative 13 |
|---|
| Error | 20.2 |
|---|
| Cost | 14472 |
|---|
\[\begin{array}{l}
\mathbf{if}\;EDonor \leq -3.1999162857086536 \cdot 10^{+25} \lor \neg \left(EDonor \leq 1.240510069331853 \cdot 10^{-232}\right):\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{\left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \left(\frac{mu}{KbT} + 2\right)\right)\right) - \frac{Ec}{KbT}}\\
\end{array}\]
| Alternative 14 |
|---|
| Error | 32.5 |
|---|
| Cost | 8840 |
|---|
\[\begin{array}{l}
\mathbf{if}\;NdChar \leq 4.7007220537757295 \cdot 10^{-23} \lor \neg \left(NdChar \leq 1.7319667664944906 \cdot 10^{+178}\right):\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{\left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \left(\frac{mu}{KbT} + 2\right)\right)\right) - \frac{Ec}{KbT}}\\
\mathbf{else}:\\
\;\;\;\;0\\
\end{array}\]
| Alternative 15 |
|---|
| Error | 36.0 |
|---|
| Cost | 8081 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -1.972876357359083 \cdot 10^{+86} \lor \neg \left(KbT \leq -6.755349909660575 \cdot 10^{-36} \lor \neg \left(KbT \leq 4.6504101422032904 \cdot 10^{-259}\right) \land KbT \leq 7.123442425127174 \cdot 10^{-87}\right):\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + NdChar \cdot 0.5\\
\mathbf{else}:\\
\;\;\;\;0\\
\end{array}\]
| Alternative 16 |
|---|
| Error | 37.4 |
|---|
| Cost | 8644 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -1.572496108760098 \cdot 10^{+86}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\left(Ev + EAccept\right) - mu}{KbT}}}\\
\mathbf{elif}\;KbT \leq -1.3277177870257392 \cdot 10^{-39}:\\
\;\;\;\;0\\
\mathbf{elif}\;KbT \leq 2.1690037964323533 \cdot 10^{-258}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\
\mathbf{elif}\;KbT \leq 9.501720778760614 \cdot 10^{-87}:\\
\;\;\;\;0\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + NdChar \cdot 0.5\\
\end{array}\]
| Alternative 17 |
|---|
| Error | 37.7 |
|---|
| Cost | 8644 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -1.20771197559279 \cdot 10^{+86}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + NdChar \cdot 0.5\\
\mathbf{elif}\;KbT \leq -2.4575348685467493 \cdot 10^{-35}:\\
\;\;\;\;0\\
\mathbf{elif}\;KbT \leq 7.747360134939159 \cdot 10^{-259}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\
\mathbf{elif}\;KbT \leq 4.621609581179345 \cdot 10^{-86}:\\
\;\;\;\;0\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + NdChar \cdot 0.5\\
\end{array}\]
| Alternative 18 |
|---|
| Error | 37.7 |
|---|
| Cost | 7953 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -1.20771197559279 \cdot 10^{+86} \lor \neg \left(KbT \leq -1.1372310781987923 \cdot 10^{-42} \lor \neg \left(KbT \leq 5.806414277556208 \cdot 10^{-258}\right) \land KbT \leq 7.42582470239374 \cdot 10^{-86}\right):\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}} + NdChar \cdot 0.5\\
\mathbf{else}:\\
\;\;\;\;0\\
\end{array}\]
| Alternative 19 |
|---|
| Error | 37.3 |
|---|
| Cost | 7953 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -1.20771197559279 \cdot 10^{+86} \lor \neg \left(KbT \leq -1.1567124161789221 \cdot 10^{-94} \lor \neg \left(KbT \leq 2.0784199699835478 \cdot 10^{-306}\right) \land KbT \leq 9.734350965828783 \cdot 10^{-86}\right):\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + EAccept}{KbT}}}\\
\mathbf{else}:\\
\;\;\;\;0\\
\end{array}\]
| Alternative 20 |
|---|
| Error | 41.4 |
|---|
| Cost | 9030 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -3.382842957065655 \cdot 10^{+157}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\
\mathbf{elif}\;KbT \leq -2.8194100310502743 \cdot 10^{-96}:\\
\;\;\;\;0\\
\mathbf{elif}\;KbT \leq -2.420044892571763 \cdot 10^{-200}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + NdChar \cdot 0.5\\
\mathbf{elif}\;KbT \leq -5.380029471084397 \cdot 10^{-203}:\\
\;\;\;\;0\\
\mathbf{elif}\;KbT \leq 3.9416950146059094 \cdot 10^{-258}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\
\mathbf{elif}\;KbT \leq 5.227341922479223 \cdot 10^{+53}:\\
\;\;\;\;0\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + NdChar \cdot 0.5\\
\end{array}\]
| Alternative 21 |
|---|
| Error | 41.8 |
|---|
| Cost | 8388 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -3.382842957065655 \cdot 10^{+157}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\
\mathbf{elif}\;KbT \leq -1.463211507506255 \cdot 10^{-95}:\\
\;\;\;\;0\\
\mathbf{elif}\;KbT \leq 4.129030372152245 \cdot 10^{-259}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\
\mathbf{elif}\;KbT \leq 4.804543485017373 \cdot 10^{+89}:\\
\;\;\;\;0\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\
\end{array}\]
| Alternative 22 |
|---|
| Error | 41.7 |
|---|
| Cost | 7885 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -3.4793180087654653 \cdot 10^{+157}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(\left(\frac{EAccept}{KbT} \cdot \frac{Ev}{KbT} + \left(0.5 \cdot \left(\frac{Ev}{KbT} \cdot \frac{Ev}{KbT}\right) + \left(\frac{Vef}{KbT} \cdot \frac{Ev}{KbT} + \left(0.5 \cdot \left(\frac{EAccept}{KbT} \cdot \frac{EAccept}{KbT}\right) + \left(2 + 0.5 \cdot \left(\frac{mu}{KbT} \cdot \frac{mu}{KbT} + \frac{Vef}{KbT} \cdot \frac{Vef}{KbT}\right)\right)\right)\right)\right)\right) + \frac{Vef}{KbT} \cdot \left(1 + \frac{EAccept}{KbT}\right)\right)\right)\right) - \left(\frac{mu}{KbT} \cdot \left(\frac{Vef}{KbT} + \frac{EAccept}{KbT}\right) + \frac{mu}{KbT} \cdot \left(1 + \frac{Ev}{KbT}\right)\right)}\\
\mathbf{elif}\;KbT \leq -3.6894905577944727 \cdot 10^{-113} \lor \neg \left(KbT \leq 1.3880082105001485 \cdot 10^{-306}\right) \land KbT \leq 8.98697964078289 \cdot 10^{+88}:\\
\;\;\;\;0\\
\mathbf{else}:\\
\;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\
\end{array}\]
| Alternative 23 |
|---|
| Error | 41.6 |
|---|
| Cost | 6785 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -3.768743163864897 \cdot 10^{+157}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(\left(\frac{EAccept}{KbT} \cdot \frac{Ev}{KbT} + \left(0.5 \cdot \left(\frac{Ev}{KbT} \cdot \frac{Ev}{KbT}\right) + \left(\frac{Vef}{KbT} \cdot \frac{Ev}{KbT} + \left(0.5 \cdot \left(\frac{EAccept}{KbT} \cdot \frac{EAccept}{KbT}\right) + \left(2 + 0.5 \cdot \left(\frac{mu}{KbT} \cdot \frac{mu}{KbT} + \frac{Vef}{KbT} \cdot \frac{Vef}{KbT}\right)\right)\right)\right)\right)\right) + \frac{Vef}{KbT} \cdot \left(1 + \frac{EAccept}{KbT}\right)\right)\right)\right) - \left(\frac{mu}{KbT} \cdot \left(\frac{Vef}{KbT} + \frac{EAccept}{KbT}\right) + \frac{mu}{KbT} \cdot \left(1 + \frac{Ev}{KbT}\right)\right)}\\
\mathbf{elif}\;KbT \leq 3.837821608208131 \cdot 10^{+97}:\\
\;\;\;\;0\\
\mathbf{else}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{2}\\
\end{array}\]
| Alternative 24 |
|---|
| Error | 41.6 |
|---|
| Cost | 3713 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -3.382842957065655 \cdot 10^{+157}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{\left(\frac{Ev}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right) \cdot \left(\frac{Ev}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right) - \frac{EAccept - mu}{KbT} \cdot \frac{EAccept - mu}{KbT}} \cdot \left(\left(\frac{Ev}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right) - \frac{EAccept - mu}{KbT}\right)\\
\mathbf{elif}\;KbT \leq 7.290195372060466 \cdot 10^{+88}:\\
\;\;\;\;0\\
\mathbf{else}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{2}\\
\end{array}\]
| Alternative 25 |
|---|
| Error | 41.6 |
|---|
| Cost | 1409 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -3.382842957065655 \cdot 10^{+157}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{\frac{EAccept - mu}{KbT} + \left(\frac{Ev}{KbT} + 2\right)}\\
\mathbf{elif}\;KbT \leq 2.5205305407857637 \cdot 10^{+95}:\\
\;\;\;\;0\\
\mathbf{else}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{2}\\
\end{array}\]
| Alternative 26 |
|---|
| Error | 41.6 |
|---|
| Cost | 1153 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -3.382842957065655 \cdot 10^{+157}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{2 + \frac{EAccept - mu}{KbT}}\\
\mathbf{elif}\;KbT \leq 2.8192610073421836 \cdot 10^{+94}:\\
\;\;\;\;0\\
\mathbf{else}:\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{2}\\
\end{array}\]
| Alternative 27 |
|---|
| Error | 41.6 |
|---|
| Cost | 776 |
|---|
\[\begin{array}{l}
\mathbf{if}\;KbT \leq -3.382842957065655 \cdot 10^{+157} \lor \neg \left(KbT \leq 2.658658861181577 \cdot 10^{+99}\right):\\
\;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{2}\\
\mathbf{else}:\\
\;\;\;\;0\\
\end{array}\]
| Alternative 28 |
|---|
| Error | 50.2 |
|---|
| Cost | 64 |
|---|
\[0\]
| Alternative 29 |
|---|
| Error | 61.9 |
|---|
| Cost | 64 |
|---|
\[1\]
Error
Time
Derivation
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
\[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}}\]
- Using strategy
rm Applied add-sqr-sqrt_binary64_282832.1
\[\leadsto \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{\color{blue}{\sqrt{KbT} \cdot \sqrt{KbT}}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Applied add-sqr-sqrt_binary64_282848.1
\[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{\sqrt{mu - \left(\left(Ec - Vef\right) - EDonor\right)} \cdot \sqrt{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}}{\sqrt{KbT} \cdot \sqrt{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Applied times-frac_binary64_281248.1
\[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\sqrt{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt{KbT}} \cdot \frac{\sqrt{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt{KbT}}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Taylor expanded around 0 0.0
\[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Simplified0.0
\[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{Vef + \left(\left(mu + EDonor\right) - Ec\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Simplified0.0
\[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{Vef + \left(\left(mu + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}}\]
Final simplification0.0
\[\leadsto \frac{NdChar}{1 + e^{\frac{Vef + \left(\left(mu + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Reproduce
herbie shell --seed 2021045
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
:name "Bulmash initializePoisson"
:precision binary64
(+ (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
