Average Error: 0.0 → 0.0
Time: 1.8m
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}} + 1} + \frac{NdChar}{1 + e^{\frac{\sqrt[3]{-\left(Ec - \left(EDonor + \left(mu + Vef\right)\right)\right)} \cdot \sqrt[3]{-\left(Ec - \left(EDonor + \left(mu + Vef\right)\right)\right)}}{\frac{KbT}{\sqrt[3]{-\left(Ec - \left(EDonor + \left(mu + Vef\right)\right)\right)}}}}}\]
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r46394917 = NdChar;
        double r46394918 = 1.0;
        double r46394919 = Ec;
        double r46394920 = Vef;
        double r46394921 = r46394919 - r46394920;
        double r46394922 = EDonor;
        double r46394923 = r46394921 - r46394922;
        double r46394924 = mu;
        double r46394925 = r46394923 - r46394924;
        double r46394926 = -r46394925;
        double r46394927 = KbT;
        double r46394928 = r46394926 / r46394927;
        double r46394929 = exp(r46394928);
        double r46394930 = r46394918 + r46394929;
        double r46394931 = r46394917 / r46394930;
        double r46394932 = NaChar;
        double r46394933 = Ev;
        double r46394934 = r46394933 + r46394920;
        double r46394935 = EAccept;
        double r46394936 = r46394934 + r46394935;
        double r46394937 = -r46394924;
        double r46394938 = r46394936 + r46394937;
        double r46394939 = r46394938 / r46394927;
        double r46394940 = exp(r46394939);
        double r46394941 = r46394918 + r46394940;
        double r46394942 = r46394932 / r46394941;
        double r46394943 = r46394931 + r46394942;
        return r46394943;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r46394944 = NaChar;
        double r46394945 = Ev;
        double r46394946 = Vef;
        double r46394947 = r46394945 + r46394946;
        double r46394948 = mu;
        double r46394949 = r46394947 - r46394948;
        double r46394950 = EAccept;
        double r46394951 = r46394949 + r46394950;
        double r46394952 = KbT;
        double r46394953 = r46394951 / r46394952;
        double r46394954 = exp(r46394953);
        double r46394955 = 1.0;
        double r46394956 = r46394954 + r46394955;
        double r46394957 = r46394944 / r46394956;
        double r46394958 = NdChar;
        double r46394959 = Ec;
        double r46394960 = EDonor;
        double r46394961 = r46394948 + r46394946;
        double r46394962 = r46394960 + r46394961;
        double r46394963 = r46394959 - r46394962;
        double r46394964 = -r46394963;
        double r46394965 = cbrt(r46394964);
        double r46394966 = r46394965 * r46394965;
        double r46394967 = r46394952 / r46394965;
        double r46394968 = r46394966 / r46394967;
        double r46394969 = exp(r46394968);
        double r46394970 = r46394955 + r46394969;
        double r46394971 = r46394958 / r46394970;
        double r46394972 = r46394957 + r46394971;
        return r46394972;
}


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

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

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

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

  5. Applied associate-/l*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019101 
(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))))))