Average Error: 0.0 → 0.0
Time: 3.7m
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + \frac{1}{e^{\frac{Ec - \left(EDonor + \left(mu + Vef\right)\right)}{KbT}}}} + \frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}} + 1}\]
\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 + \frac{1}{e^{\frac{Ec - \left(EDonor + \left(mu + Vef\right)\right)}{KbT}}}} + \frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}} + 1}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r50368728 = NdChar;
        double r50368729 = 1.0;
        double r50368730 = Ec;
        double r50368731 = Vef;
        double r50368732 = r50368730 - r50368731;
        double r50368733 = EDonor;
        double r50368734 = r50368732 - r50368733;
        double r50368735 = mu;
        double r50368736 = r50368734 - r50368735;
        double r50368737 = -r50368736;
        double r50368738 = KbT;
        double r50368739 = r50368737 / r50368738;
        double r50368740 = exp(r50368739);
        double r50368741 = r50368729 + r50368740;
        double r50368742 = r50368728 / r50368741;
        double r50368743 = NaChar;
        double r50368744 = Ev;
        double r50368745 = r50368744 + r50368731;
        double r50368746 = EAccept;
        double r50368747 = r50368745 + r50368746;
        double r50368748 = -r50368735;
        double r50368749 = r50368747 + r50368748;
        double r50368750 = r50368749 / r50368738;
        double r50368751 = exp(r50368750);
        double r50368752 = r50368729 + r50368751;
        double r50368753 = r50368743 / r50368752;
        double r50368754 = r50368742 + r50368753;
        return r50368754;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r50368755 = NdChar;
        double r50368756 = 1.0;
        double r50368757 = Ec;
        double r50368758 = EDonor;
        double r50368759 = mu;
        double r50368760 = Vef;
        double r50368761 = r50368759 + r50368760;
        double r50368762 = r50368758 + r50368761;
        double r50368763 = r50368757 - r50368762;
        double r50368764 = KbT;
        double r50368765 = r50368763 / r50368764;
        double r50368766 = exp(r50368765);
        double r50368767 = r50368756 / r50368766;
        double r50368768 = r50368756 + r50368767;
        double r50368769 = r50368755 / r50368768;
        double r50368770 = NaChar;
        double r50368771 = Ev;
        double r50368772 = r50368771 + r50368760;
        double r50368773 = r50368772 - r50368759;
        double r50368774 = EAccept;
        double r50368775 = r50368773 + r50368774;
        double r50368776 = r50368775 / r50368764;
        double r50368777 = exp(r50368776);
        double r50368778 = r50368777 + r50368756;
        double r50368779 = r50368770 / r50368778;
        double r50368780 = r50368769 + r50368779;
        return r50368780;
}

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 neg-sub00.0

    \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}}} + \frac{NdChar}{e^{\frac{\color{blue}{0 - \left(Ec - \left(\left(Vef + mu\right) + EDonor\right)\right)}}{KbT}} + 1}\]

  5. Applied div-sub0.0

    \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}}} + \frac{NdChar}{e^{\color{blue}{\frac{0}{KbT} - \frac{Ec - \left(\left(Vef + mu\right) + EDonor\right)}{KbT}}} + 1}\]

  6. Applied exp-diff0.0

    \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept + \left(\left(Ev + Vef\right) - mu\right)}{KbT}}} + \frac{NdChar}{\color{blue}{\frac{e^{\frac{0}{KbT}}}{e^{\frac{Ec - \left(\left(Vef + mu\right) + EDonor\right)}{KbT}}}} + 1}\]

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019119 
(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))))))