Average Error: 0.0 → 0.0
Time: 11.7s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(\sqrt[3]{e^{\left(\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)\right) \cdot \frac{1}{KbT}}} \cdot \sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\right) \cdot \sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}}\]
\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{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \left(\sqrt[3]{e^{\left(\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)\right) \cdot \frac{1}{KbT}}} \cdot \sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\right) \cdot \sqrt[3]{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 r279502 = NdChar;
        double r279503 = 1.0;
        double r279504 = Ec;
        double r279505 = Vef;
        double r279506 = r279504 - r279505;
        double r279507 = EDonor;
        double r279508 = r279506 - r279507;
        double r279509 = mu;
        double r279510 = r279508 - r279509;
        double r279511 = -r279510;
        double r279512 = KbT;
        double r279513 = r279511 / r279512;
        double r279514 = exp(r279513);
        double r279515 = r279503 + r279514;
        double r279516 = r279502 / r279515;
        double r279517 = NaChar;
        double r279518 = Ev;
        double r279519 = r279518 + r279505;
        double r279520 = EAccept;
        double r279521 = r279519 + r279520;
        double r279522 = -r279509;
        double r279523 = r279521 + r279522;
        double r279524 = r279523 / r279512;
        double r279525 = exp(r279524);
        double r279526 = r279503 + r279525;
        double r279527 = r279517 / r279526;
        double r279528 = r279516 + r279527;
        return r279528;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r279529 = NdChar;
        double r279530 = 1.0;
        double r279531 = Ec;
        double r279532 = Vef;
        double r279533 = r279531 - r279532;
        double r279534 = EDonor;
        double r279535 = r279533 - r279534;
        double r279536 = mu;
        double r279537 = r279535 - r279536;
        double r279538 = -r279537;
        double r279539 = KbT;
        double r279540 = r279538 / r279539;
        double r279541 = exp(r279540);
        double r279542 = r279530 + r279541;
        double r279543 = r279529 / r279542;
        double r279544 = NaChar;
        double r279545 = Ev;
        double r279546 = r279545 + r279532;
        double r279547 = EAccept;
        double r279548 = r279546 + r279547;
        double r279549 = -r279536;
        double r279550 = r279548 + r279549;
        double r279551 = 1.0;
        double r279552 = r279551 / r279539;
        double r279553 = r279550 * r279552;
        double r279554 = exp(r279553);
        double r279555 = cbrt(r279554);
        double r279556 = r279550 / r279539;
        double r279557 = exp(r279556);
        double r279558 = cbrt(r279557);
        double r279559 = r279555 * r279558;
        double r279560 = r279559 * r279558;
        double r279561 = r279530 + r279560;
        double r279562 = r279544 / r279561;
        double r279563 = r279543 + r279562;
        return r279563;
}

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

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

  5. Applied div-inv0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020024 
(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))))))