Average Error: 0.0 → 0.0
Time: 22.6s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + \left(\sqrt[3]{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} \cdot \sqrt[3]{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\right) \cdot \sqrt[3]{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
\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 + \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}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r320529 = NdChar;
        double r320530 = 1.0;
        double r320531 = Ec;
        double r320532 = Vef;
        double r320533 = r320531 - r320532;
        double r320534 = EDonor;
        double r320535 = r320533 - r320534;
        double r320536 = mu;
        double r320537 = r320535 - r320536;
        double r320538 = -r320537;
        double r320539 = KbT;
        double r320540 = r320538 / r320539;
        double r320541 = exp(r320540);
        double r320542 = r320530 + r320541;
        double r320543 = r320529 / r320542;
        double r320544 = NaChar;
        double r320545 = Ev;
        double r320546 = r320545 + r320532;
        double r320547 = EAccept;
        double r320548 = r320546 + r320547;
        double r320549 = -r320536;
        double r320550 = r320548 + r320549;
        double r320551 = r320550 / r320539;
        double r320552 = exp(r320551);
        double r320553 = r320530 + r320552;
        double r320554 = r320544 / r320553;
        double r320555 = r320543 + r320554;
        return r320555;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r320556 = NdChar;
        double r320557 = 1.0;
        double r320558 = Ec;
        double r320559 = Vef;
        double r320560 = r320558 - r320559;
        double r320561 = EDonor;
        double r320562 = r320560 - r320561;
        double r320563 = mu;
        double r320564 = r320562 - r320563;
        double r320565 = -r320564;
        double r320566 = KbT;
        double r320567 = r320565 / r320566;
        double r320568 = exp(r320567);
        double r320569 = cbrt(r320568);
        double r320570 = r320569 * r320569;
        double r320571 = r320570 * r320569;
        double r320572 = r320557 + r320571;
        double r320573 = r320556 / r320572;
        double r320574 = NaChar;
        double r320575 = Ev;
        double r320576 = r320575 + r320559;
        double r320577 = EAccept;
        double r320578 = r320576 + r320577;
        double r320579 = -r320563;
        double r320580 = r320578 + r320579;
        double r320581 = r320580 / r320566;
        double r320582 = exp(r320581);
        double r320583 = r320557 + r320582;
        double r320584 = r320574 / r320583;
        double r320585 = r320573 + r320584;
        return r320585;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019351 
(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))))))