Average Error: 0.0 → 0.0
Time: 43.6s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + {\left({\left(e^{\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\right)}^{\left(\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}\right)}^{\left(\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}\right)}}\]
\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 + {\left({\left(e^{\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\right)}^{\left(\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}\right)}^{\left(\sqrt[3]{\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 r201129 = NdChar;
        double r201130 = 1.0;
        double r201131 = Ec;
        double r201132 = Vef;
        double r201133 = r201131 - r201132;
        double r201134 = EDonor;
        double r201135 = r201133 - r201134;
        double r201136 = mu;
        double r201137 = r201135 - r201136;
        double r201138 = -r201137;
        double r201139 = KbT;
        double r201140 = r201138 / r201139;
        double r201141 = exp(r201140);
        double r201142 = r201130 + r201141;
        double r201143 = r201129 / r201142;
        double r201144 = NaChar;
        double r201145 = Ev;
        double r201146 = r201145 + r201132;
        double r201147 = EAccept;
        double r201148 = r201146 + r201147;
        double r201149 = -r201136;
        double r201150 = r201148 + r201149;
        double r201151 = r201150 / r201139;
        double r201152 = exp(r201151);
        double r201153 = r201130 + r201152;
        double r201154 = r201144 / r201153;
        double r201155 = r201143 + r201154;
        return r201155;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r201156 = NdChar;
        double r201157 = 1.0;
        double r201158 = Ec;
        double r201159 = Vef;
        double r201160 = r201158 - r201159;
        double r201161 = EDonor;
        double r201162 = r201160 - r201161;
        double r201163 = mu;
        double r201164 = r201162 - r201163;
        double r201165 = -r201164;
        double r201166 = KbT;
        double r201167 = r201165 / r201166;
        double r201168 = exp(r201167);
        double r201169 = r201157 + r201168;
        double r201170 = r201156 / r201169;
        double r201171 = NaChar;
        double r201172 = Ev;
        double r201173 = r201172 + r201159;
        double r201174 = EAccept;
        double r201175 = r201173 + r201174;
        double r201176 = r201175 - r201163;
        double r201177 = r201176 / r201166;
        double r201178 = cbrt(r201177);
        double r201179 = exp(r201178);
        double r201180 = pow(r201179, r201178);
        double r201181 = -r201163;
        double r201182 = r201175 + r201181;
        double r201183 = r201182 / r201166;
        double r201184 = cbrt(r201183);
        double r201185 = pow(r201180, r201184);
        double r201186 = r201157 + r201185;
        double r201187 = r201171 / r201186;
        double r201188 = r201170 + r201187;
        return r201188;
}

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 add-cube-cbrt0.0

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

  4. Applied exp-prod0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

    \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + {\left({\left(e^{\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\right)}^{\left(\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}\right)}^{\left(\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}\right)}}\]

Reproduce

herbie shell --seed 2019303 
(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))))))