Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \sqrt{{e}^{\left(\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}\right)}} \cdot \sqrt{{e}^{\left(\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}\right)}}}\]
\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{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \sqrt{{e}^{\left(\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}\right)}} \cdot \sqrt{{e}^{\left(\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}\right)}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r243165 = NdChar;
        double r243166 = 1.0;
        double r243167 = Ec;
        double r243168 = Vef;
        double r243169 = r243167 - r243168;
        double r243170 = EDonor;
        double r243171 = r243169 - r243170;
        double r243172 = mu;
        double r243173 = r243171 - r243172;
        double r243174 = -r243173;
        double r243175 = KbT;
        double r243176 = r243174 / r243175;
        double r243177 = exp(r243176);
        double r243178 = r243166 + r243177;
        double r243179 = r243165 / r243178;
        double r243180 = NaChar;
        double r243181 = Ev;
        double r243182 = r243181 + r243168;
        double r243183 = EAccept;
        double r243184 = r243182 + r243183;
        double r243185 = -r243172;
        double r243186 = r243184 + r243185;
        double r243187 = r243186 / r243175;
        double r243188 = exp(r243187);
        double r243189 = r243166 + r243188;
        double r243190 = r243180 / r243189;
        double r243191 = r243179 + r243190;
        return r243191;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r243192 = NdChar;
        double r243193 = 1.0;
        double r243194 = Ec;
        double r243195 = Vef;
        double r243196 = r243194 - r243195;
        double r243197 = EDonor;
        double r243198 = r243196 - r243197;
        double r243199 = mu;
        double r243200 = r243198 - r243199;
        double r243201 = -r243200;
        double r243202 = KbT;
        double r243203 = r243201 / r243202;
        double r243204 = exp(r243203);
        double r243205 = r243193 + r243204;
        double r243206 = r243192 / r243205;
        double r243207 = NaChar;
        double r243208 = exp(1.0);
        double r243209 = Ev;
        double r243210 = r243209 + r243195;
        double r243211 = EAccept;
        double r243212 = r243210 + r243211;
        double r243213 = -r243199;
        double r243214 = r243212 + r243213;
        double r243215 = r243214 / r243202;
        double r243216 = pow(r243208, r243215);
        double r243217 = sqrt(r243216);
        double r243218 = r243217 * r243217;
        double r243219 = r243193 + r243218;
        double r243220 = r243207 / r243219;
        double r243221 = r243206 + r243220;
        return r243221;
}

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. Using strategy rm

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

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

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

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

  5. Applied times-frac0.0

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

  6. Applied exp-prod0.0

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

  7. Simplified0.0

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

  9. Applied add-sqr-sqrt0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020033 
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  :precision binary64
  (+ (/ NdChar (+ 1 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))