Average Error: 0.0 → 0.0
Time: 23.7s
Precision: binary64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
↓
\[\begin{array}{l} t_0 := \frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\\ t_1 := \sqrt[3]{{\left(e^{2}\right)}^{t_0}}\\ \frac{NdChar}{1 + \sqrt[3]{\left(t_1 \cdot t_1\right) \cdot \sqrt[3]{{\left(e^{\sqrt{2}}\right)}^{\left(t_0 \cdot \sqrt{2}\right)}}} \cdot \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} \end{array} \]
\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}}}
↓
\begin{array}{l}
t_0 := \frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\\
t_1 := \sqrt[3]{{\left(e^{2}\right)}^{t_0}}\\
\frac{NdChar}{1 + \sqrt[3]{\left(t_1 \cdot t_1\right) \cdot \sqrt[3]{{\left(e^{\sqrt{2}}\right)}^{\left(t_0 \cdot \sqrt{2}\right)}}} \cdot \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}
\end{array}

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
  (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
↓
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ (+ EDonor (- (+ Vef mu) Ec)) KbT))
        (t_1 (cbrt (pow (exp 2.0) t_0))))
   (+
    (/
     NdChar
     (+
      1.0
      (*
       (cbrt (* (* t_1 t_1) (cbrt (pow (exp (sqrt 2.0)) (* t_0 (sqrt 2.0))))))
       (cbrt (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT))))))
    (/ NaChar (+ 1.0 (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)))))))
double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp(-(((Ec - Vef) - EDonor) - mu) / KbT))) + (NaChar / (1.0 + exp((((Ev + Vef) + EAccept) + -mu) / KbT)));
}
↓
double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (EDonor + ((Vef + mu) - Ec)) / KbT;
	double t_1 = cbrt(pow(exp(2.0), t_0));
	return (NdChar / (1.0 + (cbrt((t_1 * t_1) * cbrt(pow(exp(sqrt(2.0)), (t_0 * sqrt(2.0))))) * cbrt(exp((mu - ((Ec - Vef) - EDonor)) / KbT))))) + (NaChar / (1.0 + exp((((Vef + Ev) + EAccept) - mu) / KbT)));
}

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

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

  3. Applied add-cube-cbrt_binary640.0

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

  4. Applied add-cbrt-cube_binary640.0

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

  5. Simplified0.0

    \[\leadsto \frac{NdChar}{1 + \sqrt[3]{\color{blue}{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}} \cdot \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} \]

  6. Applied add-cbrt-cube_binary640.0

    \[\leadsto \frac{NdChar}{1 + \color{blue}{\sqrt[3]{\left(\sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}\right) \cdot \sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}}} \cdot \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} \]

  7. Applied add-sqr-sqrt_binary640.0

    \[\leadsto \frac{NdChar}{1 + \sqrt[3]{\left(\sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}\right) \cdot \sqrt[3]{{\left(e^{\color{blue}{\sqrt{2} \cdot \sqrt{2}}}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}} \cdot \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} \]

  8. Applied exp-prod_binary640.0

    \[\leadsto \frac{NdChar}{1 + \sqrt[3]{\left(\sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}\right) \cdot \sqrt[3]{{\color{blue}{\left({\left(e^{\sqrt{2}}\right)}^{\left(\sqrt{2}\right)}\right)}}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}} \cdot \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} \]

  9. Applied pow-pow_binary640.0

    \[\leadsto \frac{NdChar}{1 + \sqrt[3]{\left(\sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}\right) \cdot \sqrt[3]{\color{blue}{{\left(e^{\sqrt{2}}\right)}^{\left(\sqrt{2} \cdot \frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}}} \cdot \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} \]

  10. Simplified0.0

    \[\leadsto \frac{NdChar}{1 + \sqrt[3]{\left(\sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}\right) \cdot \sqrt[3]{{\left(e^{\sqrt{2}}\right)}^{\color{blue}{\left(\frac{\left(\left(Vef + mu\right) - Ec\right) + EDonor}{KbT} \cdot \sqrt{2}\right)}}}} \cdot \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} \]

  11. Final simplification0.0

    \[\leadsto \frac{NdChar}{1 + \sqrt[3]{\left(\sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}} \cdot \sqrt[3]{{\left(e^{2}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT}\right)}}\right) \cdot \sqrt[3]{{\left(e^{\sqrt{2}}\right)}^{\left(\frac{EDonor + \left(\left(Vef + mu\right) - Ec\right)}{KbT} \cdot \sqrt{2}\right)}}} \cdot \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} \]

Reproduce

herbie shell --seed 2021313 
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  :precision binary64
  (+ (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))