Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{1}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}} \cdot \frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{\sqrt[3]{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}
↓
\frac{NdChar}{1 + e^{\frac{1}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}} \cdot \frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{\sqrt[3]{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r287651 = NdChar;
        double r287652 = 1.0;
        double r287653 = Ec;
        double r287654 = Vef;
        double r287655 = r287653 - r287654;
        double r287656 = EDonor;
        double r287657 = r287655 - r287656;
        double r287658 = mu;
        double r287659 = r287657 - r287658;
        double r287660 = -r287659;
        double r287661 = KbT;
        double r287662 = r287660 / r287661;
        double r287663 = exp(r287662);
        double r287664 = r287652 + r287663;
        double r287665 = r287651 / r287664;
        double r287666 = NaChar;
        double r287667 = Ev;
        double r287668 = r287667 + r287654;
        double r287669 = EAccept;
        double r287670 = r287668 + r287669;
        double r287671 = -r287658;
        double r287672 = r287670 + r287671;
        double r287673 = r287672 / r287661;
        double r287674 = exp(r287673);
        double r287675 = r287652 + r287674;
        double r287676 = r287666 / r287675;
        double r287677 = r287665 + r287676;
        return r287677;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r287678 = NdChar;
        double r287679 = 1.0;
        double r287680 = 1.0;
        double r287681 = KbT;
        double r287682 = cbrt(r287681);
        double r287683 = r287682 * r287682;
        double r287684 = r287680 / r287683;
        double r287685 = Ec;
        double r287686 = Vef;
        double r287687 = r287685 - r287686;
        double r287688 = EDonor;
        double r287689 = r287687 - r287688;
        double r287690 = mu;
        double r287691 = r287689 - r287690;
        double r287692 = -r287691;
        double r287693 = r287692 / r287682;
        double r287694 = r287684 * r287693;
        double r287695 = exp(r287694);
        double r287696 = r287679 + r287695;
        double r287697 = r287678 / r287696;
        double r287698 = NaChar;
        double r287699 = Ev;
        double r287700 = r287699 + r287686;
        double r287701 = EAccept;
        double r287702 = r287700 + r287701;
        double r287703 = -r287690;
        double r287704 = r287702 + r287703;
        double r287705 = r287704 / r287681;
        double r287706 = exp(r287705);
        double r287707 = r287679 + r287706;
        double r287708 = r287698 / r287707;
        double r287709 = r287697 + r287708;
        return r287709;
}

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-cube-cbrt0.0

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

  4. Applied *-un-lft-identity0.0

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

  5. Applied times-frac0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020089 
(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))))))