Average Error: 0.0 → 0.0
Time: 25.5s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NaChar}{e^{\frac{\left(\left(Ev - mu\right) + Vef\right) + EAccept}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1}\]
\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{NaChar}{e^{\frac{\left(\left(Ev - mu\right) + Vef\right) + EAccept}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r11928177 = NdChar;
        double r11928178 = 1.0;
        double r11928179 = Ec;
        double r11928180 = Vef;
        double r11928181 = r11928179 - r11928180;
        double r11928182 = EDonor;
        double r11928183 = r11928181 - r11928182;
        double r11928184 = mu;
        double r11928185 = r11928183 - r11928184;
        double r11928186 = -r11928185;
        double r11928187 = KbT;
        double r11928188 = r11928186 / r11928187;
        double r11928189 = exp(r11928188);
        double r11928190 = r11928178 + r11928189;
        double r11928191 = r11928177 / r11928190;
        double r11928192 = NaChar;
        double r11928193 = Ev;
        double r11928194 = r11928193 + r11928180;
        double r11928195 = EAccept;
        double r11928196 = r11928194 + r11928195;
        double r11928197 = -r11928184;
        double r11928198 = r11928196 + r11928197;
        double r11928199 = r11928198 / r11928187;
        double r11928200 = exp(r11928199);
        double r11928201 = r11928178 + r11928200;
        double r11928202 = r11928192 / r11928201;
        double r11928203 = r11928191 + r11928202;
        return r11928203;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r11928204 = NaChar;
        double r11928205 = Ev;
        double r11928206 = mu;
        double r11928207 = r11928205 - r11928206;
        double r11928208 = Vef;
        double r11928209 = r11928207 + r11928208;
        double r11928210 = EAccept;
        double r11928211 = r11928209 + r11928210;
        double r11928212 = KbT;
        double r11928213 = r11928211 / r11928212;
        double r11928214 = exp(r11928213);
        double r11928215 = 1.0;
        double r11928216 = r11928214 + r11928215;
        double r11928217 = r11928204 / r11928216;
        double r11928218 = NdChar;
        double r11928219 = Ec;
        double r11928220 = r11928219 - r11928208;
        double r11928221 = EDonor;
        double r11928222 = r11928220 - r11928221;
        double r11928223 = r11928206 - r11928222;
        double r11928224 = r11928223 / r11928212;
        double r11928225 = exp(r11928224);
        double r11928226 = r11928225 + r11928215;
        double r11928227 = r11928218 / r11928226;
        double r11928228 = r11928217 + r11928227;
        return r11928228;
}

Error

Bits error versus NdChar

Bits error versus Ec

Bits error versus Vef

Bits error versus EDonor

Bits error versus mu

Bits error versus KbT

Bits error versus NaChar

Bits error versus Ev

Bits error versus EAccept

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{EAccept + \left(\left(Vef + Ev\right) - mu\right)}{KbT}}} + \frac{NdChar}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.0

    \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(\left(Vef + Ev\right) - mu\right)}{\color{blue}{1 \cdot KbT}}}} + \frac{NdChar}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1}\]

  5. Applied associate-/r*0.0

    \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{\frac{EAccept + \left(\left(Vef + Ev\right) - mu\right)}{1}}{KbT}}}} + \frac{NdChar}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1}\]

  6. Simplified0.0

    \[\leadsto \frac{NaChar}{1 + e^{\frac{\color{blue}{EAccept + \left(\left(Ev - mu\right) + Vef\right)}}{KbT}}} + \frac{NdChar}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1}\]

  7. Final simplification0.0

    \[\leadsto \frac{NaChar}{e^{\frac{\left(\left(Ev - mu\right) + Vef\right) + EAccept}{KbT}} + 1} + \frac{NdChar}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  (+ (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))