Average Error: 0.0 → 0.0
Time: 20.6s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{\sqrt[3]{{\left(e^{\frac{mu + \left(EDonor - \left(Ec - Vef\right)\right)}{KbT}} + 1\right)}^{3}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\]
\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 r254663 = NdChar;
        double r254664 = 1.0;
        double r254665 = Ec;
        double r254666 = Vef;
        double r254667 = r254665 - r254666;
        double r254668 = EDonor;
        double r254669 = r254667 - r254668;
        double r254670 = mu;
        double r254671 = r254669 - r254670;
        double r254672 = -r254671;
        double r254673 = KbT;
        double r254674 = r254672 / r254673;
        double r254675 = exp(r254674);
        double r254676 = r254664 + r254675;
        double r254677 = r254663 / r254676;
        double r254678 = NaChar;
        double r254679 = Ev;
        double r254680 = r254679 + r254666;
        double r254681 = EAccept;
        double r254682 = r254680 + r254681;
        double r254683 = -r254670;
        double r254684 = r254682 + r254683;
        double r254685 = r254684 / r254673;
        double r254686 = exp(r254685);
        double r254687 = r254664 + r254686;
        double r254688 = r254678 / r254687;
        double r254689 = r254677 + r254688;
        return r254689;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r254690 = NdChar;
        double r254691 = mu;
        double r254692 = EDonor;
        double r254693 = Ec;
        double r254694 = Vef;
        double r254695 = r254693 - r254694;
        double r254696 = r254692 - r254695;
        double r254697 = r254691 + r254696;
        double r254698 = KbT;
        double r254699 = r254697 / r254698;
        double r254700 = exp(r254699);
        double r254701 = 1.0;
        double r254702 = r254700 + r254701;
        double r254703 = 3.0;
        double r254704 = pow(r254702, r254703);
        double r254705 = cbrt(r254704);
        double r254706 = r254690 / r254705;
        double r254707 = NaChar;
        double r254708 = Ev;
        double r254709 = r254708 + r254694;
        double r254710 = EAccept;
        double r254711 = r254709 + r254710;
        double r254712 = r254711 - r254691;
        double r254713 = r254712 / r254698;
        double r254714 = exp(r254713);
        double r254715 = r254701 + r254714;
        double r254716 = r254707 / r254715;
        double r254717 = r254706 + r254716;
        return r254717;
}

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 2020045 
(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))))))