Average Error: 0.0 → 0.0
Time: 2.7m
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{-\frac{Ec - \left(EDonor + \left(mu + Vef\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}} \cdot \sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}}\right) \cdot \sqrt[3]{\sqrt{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}} \cdot \sqrt{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}}}}\]
\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{Ec - \left(EDonor + \left(mu + Vef\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}} \cdot \sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}}\right) \cdot \sqrt[3]{\sqrt{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}} \cdot \sqrt{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r84279127 = NdChar;
        double r84279128 = 1.0;
        double r84279129 = Ec;
        double r84279130 = Vef;
        double r84279131 = r84279129 - r84279130;
        double r84279132 = EDonor;
        double r84279133 = r84279131 - r84279132;
        double r84279134 = mu;
        double r84279135 = r84279133 - r84279134;
        double r84279136 = -r84279135;
        double r84279137 = KbT;
        double r84279138 = r84279136 / r84279137;
        double r84279139 = exp(r84279138);
        double r84279140 = r84279128 + r84279139;
        double r84279141 = r84279127 / r84279140;
        double r84279142 = NaChar;
        double r84279143 = Ev;
        double r84279144 = r84279143 + r84279130;
        double r84279145 = EAccept;
        double r84279146 = r84279144 + r84279145;
        double r84279147 = -r84279134;
        double r84279148 = r84279146 + r84279147;
        double r84279149 = r84279148 / r84279137;
        double r84279150 = exp(r84279149);
        double r84279151 = r84279128 + r84279150;
        double r84279152 = r84279142 / r84279151;
        double r84279153 = r84279141 + r84279152;
        return r84279153;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r84279154 = NdChar;
        double r84279155 = 1.0;
        double r84279156 = Ec;
        double r84279157 = EDonor;
        double r84279158 = mu;
        double r84279159 = Vef;
        double r84279160 = r84279158 + r84279159;
        double r84279161 = r84279157 + r84279160;
        double r84279162 = r84279156 - r84279161;
        double r84279163 = KbT;
        double r84279164 = r84279162 / r84279163;
        double r84279165 = -r84279164;
        double r84279166 = exp(r84279165);
        double r84279167 = r84279155 + r84279166;
        double r84279168 = r84279154 / r84279167;
        double r84279169 = NaChar;
        double r84279170 = Ev;
        double r84279171 = r84279170 + r84279159;
        double r84279172 = r84279171 - r84279158;
        double r84279173 = EAccept;
        double r84279174 = r84279172 + r84279173;
        double r84279175 = r84279174 / r84279163;
        double r84279176 = exp(r84279175);
        double r84279177 = cbrt(r84279176);
        double r84279178 = r84279177 * r84279177;
        double r84279179 = sqrt(r84279176);
        double r84279180 = r84279179 * r84279179;
        double r84279181 = cbrt(r84279180);
        double r84279182 = r84279178 * r84279181;
        double r84279183 = r84279155 + r84279182;
        double r84279184 = r84279169 / r84279183;
        double r84279185 = r84279168 + r84279184;
        return r84279185;
}

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

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

  4. Applied add-cube-cbrt0.0

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

  6. Applied add-sqr-sqrt0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  (+ (/ NdChar (+ 1 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))