Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{\sqrt[3]{{\left(e^{\frac{mu + \left(EDonor - \left(Ec - Vef\right)\right)}{KbT}} + 1\right)}^{3}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\]
\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}{\sqrt[3]{{\left(e^{\frac{mu + \left(EDonor - \left(Ec - Vef\right)\right)}{KbT}} + 1\right)}^{3}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r182999 = NdChar;
        double r183000 = 1.0;
        double r183001 = Ec;
        double r183002 = Vef;
        double r183003 = r183001 - r183002;
        double r183004 = EDonor;
        double r183005 = r183003 - r183004;
        double r183006 = mu;
        double r183007 = r183005 - r183006;
        double r183008 = -r183007;
        double r183009 = KbT;
        double r183010 = r183008 / r183009;
        double r183011 = exp(r183010);
        double r183012 = r183000 + r183011;
        double r183013 = r182999 / r183012;
        double r183014 = NaChar;
        double r183015 = Ev;
        double r183016 = r183015 + r183002;
        double r183017 = EAccept;
        double r183018 = r183016 + r183017;
        double r183019 = -r183006;
        double r183020 = r183018 + r183019;
        double r183021 = r183020 / r183009;
        double r183022 = exp(r183021);
        double r183023 = r183000 + r183022;
        double r183024 = r183014 / r183023;
        double r183025 = r183013 + r183024;
        return r183025;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r183026 = NdChar;
        double r183027 = mu;
        double r183028 = EDonor;
        double r183029 = Ec;
        double r183030 = Vef;
        double r183031 = r183029 - r183030;
        double r183032 = r183028 - r183031;
        double r183033 = r183027 + r183032;
        double r183034 = KbT;
        double r183035 = r183033 / r183034;
        double r183036 = exp(r183035);
        double r183037 = 1.0;
        double r183038 = r183036 + r183037;
        double r183039 = 3.0;
        double r183040 = pow(r183038, r183039);
        double r183041 = cbrt(r183040);
        double r183042 = r183026 / r183041;
        double r183043 = NaChar;
        double r183044 = Ev;
        double r183045 = r183044 + r183030;
        double r183046 = EAccept;
        double r183047 = r183045 + r183046;
        double r183048 = r183047 - r183027;
        double r183049 = r183048 / r183034;
        double r183050 = exp(r183049);
        double r183051 = r183037 + r183050;
        double r183052 = r183043 / r183051;
        double r183053 = r183042 + r183052;
        return r183053;
}

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

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

  4. Applied add-cbrt-cube0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019305 
(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))))))