Average Error: 0.0 → 0.0
Time: 19.1s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + \left(\sqrt[3]{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} \cdot \sqrt[3]{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\right) \cdot \sqrt[3]{{\left(e^{\frac{-\sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu} \cdot \sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}}}\right)}^{\left(\frac{\sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu}}{\sqrt[3]{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
\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 + \left(\sqrt[3]{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} \cdot \sqrt[3]{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\right) \cdot \sqrt[3]{{\left(e^{\frac{-\sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu} \cdot \sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}}}\right)}^{\left(\frac{\sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu}}{\sqrt[3]{KbT}}\right)}}} + \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 r330617 = NdChar;
        double r330618 = 1.0;
        double r330619 = Ec;
        double r330620 = Vef;
        double r330621 = r330619 - r330620;
        double r330622 = EDonor;
        double r330623 = r330621 - r330622;
        double r330624 = mu;
        double r330625 = r330623 - r330624;
        double r330626 = -r330625;
        double r330627 = KbT;
        double r330628 = r330626 / r330627;
        double r330629 = exp(r330628);
        double r330630 = r330618 + r330629;
        double r330631 = r330617 / r330630;
        double r330632 = NaChar;
        double r330633 = Ev;
        double r330634 = r330633 + r330620;
        double r330635 = EAccept;
        double r330636 = r330634 + r330635;
        double r330637 = -r330624;
        double r330638 = r330636 + r330637;
        double r330639 = r330638 / r330627;
        double r330640 = exp(r330639);
        double r330641 = r330618 + r330640;
        double r330642 = r330632 / r330641;
        double r330643 = r330631 + r330642;
        return r330643;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r330644 = NdChar;
        double r330645 = 1.0;
        double r330646 = Ec;
        double r330647 = Vef;
        double r330648 = r330646 - r330647;
        double r330649 = EDonor;
        double r330650 = r330648 - r330649;
        double r330651 = mu;
        double r330652 = r330650 - r330651;
        double r330653 = -r330652;
        double r330654 = KbT;
        double r330655 = r330653 / r330654;
        double r330656 = exp(r330655);
        double r330657 = cbrt(r330656);
        double r330658 = r330657 * r330657;
        double r330659 = cbrt(r330652);
        double r330660 = r330659 * r330659;
        double r330661 = -r330660;
        double r330662 = cbrt(r330654);
        double r330663 = r330662 * r330662;
        double r330664 = r330661 / r330663;
        double r330665 = exp(r330664);
        double r330666 = r330659 / r330662;
        double r330667 = pow(r330665, r330666);
        double r330668 = cbrt(r330667);
        double r330669 = r330658 * r330668;
        double r330670 = r330645 + r330669;
        double r330671 = r330644 / r330670;
        double r330672 = NaChar;
        double r330673 = Ev;
        double r330674 = r330673 + r330647;
        double r330675 = EAccept;
        double r330676 = r330674 + r330675;
        double r330677 = -r330651;
        double r330678 = r330676 + r330677;
        double r330679 = r330678 / r330654;
        double r330680 = exp(r330679);
        double r330681 = r330645 + r330680;
        double r330682 = r330672 / r330681;
        double r330683 = r330671 + r330682;
        return r330683;
}

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

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

  5. Applied add-cube-cbrt0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied distribute-lft-neg-in0.0

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

  8. Applied times-frac0.0

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

  9. Applied exp-prod0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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))))))