Average Error: 0.0 → 0.0
Time: 3.9m
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NaChar}{\sqrt[3]{\left(\left(e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}} + 1\right) \cdot \left(e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}} + 1\right)\right) \cdot \left(e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}} + 1\right)}} + \frac{NdChar}{1 + e^{\frac{-\left(Ec - \left(EDonor + \left(mu + Vef\right)\right)\right)}{KbT}}}\]
\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{NaChar}{\sqrt[3]{\left(\left(e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}} + 1\right) \cdot \left(e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}} + 1\right)\right) \cdot \left(e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}} + 1\right)}} + \frac{NdChar}{1 + e^{\frac{-\left(Ec - \left(EDonor + \left(mu + Vef\right)\right)\right)}{KbT}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r52160992 = NdChar;
        double r52160993 = 1.0;
        double r52160994 = Ec;
        double r52160995 = Vef;
        double r52160996 = r52160994 - r52160995;
        double r52160997 = EDonor;
        double r52160998 = r52160996 - r52160997;
        double r52160999 = mu;
        double r52161000 = r52160998 - r52160999;
        double r52161001 = -r52161000;
        double r52161002 = KbT;
        double r52161003 = r52161001 / r52161002;
        double r52161004 = exp(r52161003);
        double r52161005 = r52160993 + r52161004;
        double r52161006 = r52160992 / r52161005;
        double r52161007 = NaChar;
        double r52161008 = Ev;
        double r52161009 = r52161008 + r52160995;
        double r52161010 = EAccept;
        double r52161011 = r52161009 + r52161010;
        double r52161012 = -r52160999;
        double r52161013 = r52161011 + r52161012;
        double r52161014 = r52161013 / r52161002;
        double r52161015 = exp(r52161014);
        double r52161016 = r52160993 + r52161015;
        double r52161017 = r52161007 / r52161016;
        double r52161018 = r52161006 + r52161017;
        return r52161018;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r52161019 = NaChar;
        double r52161020 = Ev;
        double r52161021 = Vef;
        double r52161022 = r52161020 + r52161021;
        double r52161023 = mu;
        double r52161024 = r52161022 - r52161023;
        double r52161025 = EAccept;
        double r52161026 = r52161024 + r52161025;
        double r52161027 = KbT;
        double r52161028 = r52161026 / r52161027;
        double r52161029 = exp(r52161028);
        double r52161030 = 1.0;
        double r52161031 = r52161029 + r52161030;
        double r52161032 = r52161031 * r52161031;
        double r52161033 = r52161032 * r52161031;
        double r52161034 = cbrt(r52161033);
        double r52161035 = r52161019 / r52161034;
        double r52161036 = NdChar;
        double r52161037 = Ec;
        double r52161038 = EDonor;
        double r52161039 = r52161023 + r52161021;
        double r52161040 = r52161038 + r52161039;
        double r52161041 = r52161037 - r52161040;
        double r52161042 = -r52161041;
        double r52161043 = r52161042 / r52161027;
        double r52161044 = exp(r52161043);
        double r52161045 = r52161030 + r52161044;
        double r52161046 = r52161036 / r52161045;
        double r52161047 = r52161035 + r52161046;
        return r52161047;
}

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-cbrt-cube0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019124 
(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))))))