Average Error: 0.0 → 0.0
Time: 39.6s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \sqrt[3]{\sqrt{{\left(e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}\right)}^{3}}} \cdot \sqrt[3]{\sqrt{{\left(e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}\right)}^{3}}}}\]
\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}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \sqrt[3]{\sqrt{{\left(e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}\right)}^{3}}} \cdot \sqrt[3]{\sqrt{{\left(e^{\frac{\left(EAccept + \left(Ev + Vef\right)\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 r141038 = NdChar;
        double r141039 = 1.0;
        double r141040 = Ec;
        double r141041 = Vef;
        double r141042 = r141040 - r141041;
        double r141043 = EDonor;
        double r141044 = r141042 - r141043;
        double r141045 = mu;
        double r141046 = r141044 - r141045;
        double r141047 = -r141046;
        double r141048 = KbT;
        double r141049 = r141047 / r141048;
        double r141050 = exp(r141049);
        double r141051 = r141039 + r141050;
        double r141052 = r141038 / r141051;
        double r141053 = NaChar;
        double r141054 = Ev;
        double r141055 = r141054 + r141041;
        double r141056 = EAccept;
        double r141057 = r141055 + r141056;
        double r141058 = -r141045;
        double r141059 = r141057 + r141058;
        double r141060 = r141059 / r141048;
        double r141061 = exp(r141060);
        double r141062 = r141039 + r141061;
        double r141063 = r141053 / r141062;
        double r141064 = r141052 + r141063;
        return r141064;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r141065 = NdChar;
        double r141066 = 1.0;
        double r141067 = Ec;
        double r141068 = Vef;
        double r141069 = r141067 - r141068;
        double r141070 = EDonor;
        double r141071 = r141069 - r141070;
        double r141072 = mu;
        double r141073 = r141071 - r141072;
        double r141074 = -r141073;
        double r141075 = KbT;
        double r141076 = r141074 / r141075;
        double r141077 = exp(r141076);
        double r141078 = r141066 + r141077;
        double r141079 = r141065 / r141078;
        double r141080 = NaChar;
        double r141081 = EAccept;
        double r141082 = Ev;
        double r141083 = r141082 + r141068;
        double r141084 = r141081 + r141083;
        double r141085 = r141084 - r141072;
        double r141086 = r141085 / r141075;
        double r141087 = exp(r141086);
        double r141088 = 3.0;
        double r141089 = pow(r141087, r141088);
        double r141090 = sqrt(r141089);
        double r141091 = cbrt(r141090);
        double r141092 = r141091 * r141091;
        double r141093 = r141066 + r141092;
        double r141094 = r141080 / r141093;
        double r141095 = r141079 + r141094;
        return r141095;
}

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. Using strategy rm

  3. Applied add-cbrt-cube0.0

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

  4. Simplified0.0

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

  6. Applied add-sqr-sqrt0.0

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

  7. Applied cbrt-prod0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(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))))))