Average Error: 0.0 → 0.0
Time: 20.7s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{e^{\frac{mu + \left(EDonor - \left(Ec - Vef\right)\right)}{KbT}} + 1} + \frac{NaChar}{1 + \sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{3}}}\]
\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}{e^{\frac{mu + \left(EDonor - \left(Ec - Vef\right)\right)}{KbT}} + 1} + \frac{NaChar}{1 + \sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{3}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r313962 = NdChar;
        double r313963 = 1.0;
        double r313964 = Ec;
        double r313965 = Vef;
        double r313966 = r313964 - r313965;
        double r313967 = EDonor;
        double r313968 = r313966 - r313967;
        double r313969 = mu;
        double r313970 = r313968 - r313969;
        double r313971 = -r313970;
        double r313972 = KbT;
        double r313973 = r313971 / r313972;
        double r313974 = exp(r313973);
        double r313975 = r313963 + r313974;
        double r313976 = r313962 / r313975;
        double r313977 = NaChar;
        double r313978 = Ev;
        double r313979 = r313978 + r313965;
        double r313980 = EAccept;
        double r313981 = r313979 + r313980;
        double r313982 = -r313969;
        double r313983 = r313981 + r313982;
        double r313984 = r313983 / r313972;
        double r313985 = exp(r313984);
        double r313986 = r313963 + r313985;
        double r313987 = r313977 / r313986;
        double r313988 = r313976 + r313987;
        return r313988;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r313989 = NdChar;
        double r313990 = mu;
        double r313991 = EDonor;
        double r313992 = Ec;
        double r313993 = Vef;
        double r313994 = r313992 - r313993;
        double r313995 = r313991 - r313994;
        double r313996 = r313990 + r313995;
        double r313997 = KbT;
        double r313998 = r313996 / r313997;
        double r313999 = exp(r313998);
        double r314000 = 1.0;
        double r314001 = r313999 + r314000;
        double r314002 = r313989 / r314001;
        double r314003 = NaChar;
        double r314004 = Ev;
        double r314005 = r314004 + r313993;
        double r314006 = EAccept;
        double r314007 = r314005 + r314006;
        double r314008 = r314007 - r313990;
        double r314009 = r314008 / r313997;
        double r314010 = exp(r314009);
        double r314011 = 3.0;
        double r314012 = pow(r314010, r314011);
        double r314013 = cbrt(r314012);
        double r314014 = r314000 + r314013;
        double r314015 = r314003 / r314014;
        double r314016 = r314002 + r314015;
        return r314016;
}

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

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  (+ (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))