Average Error: 0.0 → 0.0
Time: 26.9s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + \sqrt{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} \cdot \sqrt{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
\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 + \sqrt{e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} \cdot \sqrt{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 r211244 = NdChar;
        double r211245 = 1.0;
        double r211246 = Ec;
        double r211247 = Vef;
        double r211248 = r211246 - r211247;
        double r211249 = EDonor;
        double r211250 = r211248 - r211249;
        double r211251 = mu;
        double r211252 = r211250 - r211251;
        double r211253 = -r211252;
        double r211254 = KbT;
        double r211255 = r211253 / r211254;
        double r211256 = exp(r211255);
        double r211257 = r211245 + r211256;
        double r211258 = r211244 / r211257;
        double r211259 = NaChar;
        double r211260 = Ev;
        double r211261 = r211260 + r211247;
        double r211262 = EAccept;
        double r211263 = r211261 + r211262;
        double r211264 = -r211251;
        double r211265 = r211263 + r211264;
        double r211266 = r211265 / r211254;
        double r211267 = exp(r211266);
        double r211268 = r211245 + r211267;
        double r211269 = r211259 / r211268;
        double r211270 = r211258 + r211269;
        return r211270;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r211271 = NdChar;
        double r211272 = 1.0;
        double r211273 = Ec;
        double r211274 = Vef;
        double r211275 = r211273 - r211274;
        double r211276 = EDonor;
        double r211277 = r211275 - r211276;
        double r211278 = mu;
        double r211279 = r211277 - r211278;
        double r211280 = -r211279;
        double r211281 = KbT;
        double r211282 = r211280 / r211281;
        double r211283 = exp(r211282);
        double r211284 = sqrt(r211283);
        double r211285 = r211284 * r211284;
        double r211286 = r211272 + r211285;
        double r211287 = r211271 / r211286;
        double r211288 = NaChar;
        double r211289 = Ev;
        double r211290 = r211289 + r211274;
        double r211291 = EAccept;
        double r211292 = r211290 + r211291;
        double r211293 = -r211278;
        double r211294 = r211292 + r211293;
        double r211295 = r211294 / r211281;
        double r211296 = exp(r211295);
        double r211297 = r211272 + r211296;
        double r211298 = r211288 / r211297;
        double r211299 = r211287 + r211298;
        return r211299;
}

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-sqr-sqrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019294 
(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))))))