Average Error: 0.0 → 0.0
Time: 35.8s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NaChar}{e^{\frac{\left(Vef - mu\right) + \left(Ev + EAccept\right)}{KbT}} + 1} + \frac{NdChar}{1 + {\left(\sqrt{e^{\sqrt[3]{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT} \cdot \frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}}\right)}^{\left(\sqrt[3]{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}\right)} \cdot {\left(\sqrt{e^{\sqrt[3]{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT} \cdot \frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}}\right)}^{\left(\sqrt[3]{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}\right)}}\]
\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{NaChar}{e^{\frac{\left(Vef - mu\right) + \left(Ev + EAccept\right)}{KbT}} + 1} + \frac{NdChar}{1 + {\left(\sqrt{e^{\sqrt[3]{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT} \cdot \frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}}\right)}^{\left(\sqrt[3]{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}\right)} \cdot {\left(\sqrt{e^{\sqrt[3]{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT} \cdot \frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}}\right)}^{\left(\sqrt[3]{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}\right)}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r5831598 = NdChar;
        double r5831599 = 1.0;
        double r5831600 = Ec;
        double r5831601 = Vef;
        double r5831602 = r5831600 - r5831601;
        double r5831603 = EDonor;
        double r5831604 = r5831602 - r5831603;
        double r5831605 = mu;
        double r5831606 = r5831604 - r5831605;
        double r5831607 = -r5831606;
        double r5831608 = KbT;
        double r5831609 = r5831607 / r5831608;
        double r5831610 = exp(r5831609);
        double r5831611 = r5831599 + r5831610;
        double r5831612 = r5831598 / r5831611;
        double r5831613 = NaChar;
        double r5831614 = Ev;
        double r5831615 = r5831614 + r5831601;
        double r5831616 = EAccept;
        double r5831617 = r5831615 + r5831616;
        double r5831618 = -r5831605;
        double r5831619 = r5831617 + r5831618;
        double r5831620 = r5831619 / r5831608;
        double r5831621 = exp(r5831620);
        double r5831622 = r5831599 + r5831621;
        double r5831623 = r5831613 / r5831622;
        double r5831624 = r5831612 + r5831623;
        return r5831624;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r5831625 = NaChar;
        double r5831626 = Vef;
        double r5831627 = mu;
        double r5831628 = r5831626 - r5831627;
        double r5831629 = Ev;
        double r5831630 = EAccept;
        double r5831631 = r5831629 + r5831630;
        double r5831632 = r5831628 + r5831631;
        double r5831633 = KbT;
        double r5831634 = r5831632 / r5831633;
        double r5831635 = exp(r5831634);
        double r5831636 = 1.0;
        double r5831637 = r5831635 + r5831636;
        double r5831638 = r5831625 / r5831637;
        double r5831639 = NdChar;
        double r5831640 = Ec;
        double r5831641 = r5831640 - r5831626;
        double r5831642 = EDonor;
        double r5831643 = r5831641 - r5831642;
        double r5831644 = r5831627 - r5831643;
        double r5831645 = r5831644 / r5831633;
        double r5831646 = r5831645 * r5831645;
        double r5831647 = cbrt(r5831646);
        double r5831648 = exp(r5831647);
        double r5831649 = sqrt(r5831648);
        double r5831650 = cbrt(r5831645);
        double r5831651 = pow(r5831649, r5831650);
        double r5831652 = r5831651 * r5831651;
        double r5831653 = r5831636 + r5831652;
        double r5831654 = r5831639 / r5831653;
        double r5831655 = r5831638 + r5831654;
        return r5831655;
}

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

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

  4. Applied add-cube-cbrt0.0

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

  5. Applied exp-prod0.0

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

  7. Applied cbrt-unprod0.0

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

  9. Applied add-sqr-sqrt0.0

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

  10. Applied unpow-prod-down0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019146 
(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))))))