Average Error: 0.0 → 0.0
Time: 13.7s
Precision: binary64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)} \cdot \sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}} \cdot \frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
\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{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)} \cdot \sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}} \cdot \frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}
(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
 (+
  (/
   NdChar
   (+
    1.0
    (exp
     (*
      (/
       (*
        (cbrt (- mu (- (- Ec Vef) EDonor)))
        (cbrt (- mu (- (- Ec Vef) EDonor))))
       (* (cbrt KbT) (cbrt KbT)))
      (/ (cbrt (- mu (- (- Ec Vef) EDonor))) (cbrt 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) {
	return (NdChar / (1.0 + exp(((cbrt(mu - ((Ec - Vef) - EDonor)) * cbrt(mu - ((Ec - Vef) - EDonor))) / (cbrt(KbT) * cbrt(KbT))) * (cbrt(mu - ((Ec - Vef) - EDonor)) / cbrt(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. Using strategy rm

  4. Applied add-cube-cbrt_binary640.0

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

  5. Applied add-cube-cbrt_binary640.0

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

  6. Applied times-frac_binary640.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021173 
(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))))))