Average Error: 0.0 → 0.0
Time: 31.5s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{\sqrt{e^{\frac{mu + \left(EDonor - \left(Ec - Vef\right)\right)}{KbT}}} \cdot \sqrt{e^{\frac{mu + \left(EDonor - \left(Ec - Vef\right)\right)}{KbT}}} + 1} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\]
\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}{\sqrt{e^{\frac{mu + \left(EDonor - \left(Ec - Vef\right)\right)}{KbT}}} \cdot \sqrt{e^{\frac{mu + \left(EDonor - \left(Ec - Vef\right)\right)}{KbT}}} + 1} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r125338 = NdChar;
        double r125339 = 1.0;
        double r125340 = Ec;
        double r125341 = Vef;
        double r125342 = r125340 - r125341;
        double r125343 = EDonor;
        double r125344 = r125342 - r125343;
        double r125345 = mu;
        double r125346 = r125344 - r125345;
        double r125347 = -r125346;
        double r125348 = KbT;
        double r125349 = r125347 / r125348;
        double r125350 = exp(r125349);
        double r125351 = r125339 + r125350;
        double r125352 = r125338 / r125351;
        double r125353 = NaChar;
        double r125354 = Ev;
        double r125355 = r125354 + r125341;
        double r125356 = EAccept;
        double r125357 = r125355 + r125356;
        double r125358 = -r125345;
        double r125359 = r125357 + r125358;
        double r125360 = r125359 / r125348;
        double r125361 = exp(r125360);
        double r125362 = r125339 + r125361;
        double r125363 = r125353 / r125362;
        double r125364 = r125352 + r125363;
        return r125364;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r125365 = NdChar;
        double r125366 = mu;
        double r125367 = EDonor;
        double r125368 = Ec;
        double r125369 = Vef;
        double r125370 = r125368 - r125369;
        double r125371 = r125367 - r125370;
        double r125372 = r125366 + r125371;
        double r125373 = KbT;
        double r125374 = r125372 / r125373;
        double r125375 = exp(r125374);
        double r125376 = sqrt(r125375);
        double r125377 = r125376 * r125376;
        double r125378 = 1.0;
        double r125379 = r125377 + r125378;
        double r125380 = r125365 / r125379;
        double r125381 = NaChar;
        double r125382 = Ev;
        double r125383 = r125382 + r125369;
        double r125384 = EAccept;
        double r125385 = r125383 + r125384;
        double r125386 = r125385 - r125366;
        double r125387 = r125386 / r125373;
        double r125388 = exp(r125387);
        double r125389 = r125378 + r125388;
        double r125390 = r125381 / r125389;
        double r125391 = r125380 + r125390;
        return r125391;
}

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

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

  4. Applied add-sqr-sqrt0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(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))))))