Average Error: 0.0 → 0.0
Time: 43.0s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + {\left(e^{\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} \cdot \sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\right)}^{\left(\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}\right)}}\]
\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{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + {\left(e^{\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} \cdot \sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\right)}^{\left(\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}\right)}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r278274 = NdChar;
        double r278275 = 1.0;
        double r278276 = Ec;
        double r278277 = Vef;
        double r278278 = r278276 - r278277;
        double r278279 = EDonor;
        double r278280 = r278278 - r278279;
        double r278281 = mu;
        double r278282 = r278280 - r278281;
        double r278283 = -r278282;
        double r278284 = KbT;
        double r278285 = r278283 / r278284;
        double r278286 = exp(r278285);
        double r278287 = r278275 + r278286;
        double r278288 = r278274 / r278287;
        double r278289 = NaChar;
        double r278290 = Ev;
        double r278291 = r278290 + r278277;
        double r278292 = EAccept;
        double r278293 = r278291 + r278292;
        double r278294 = -r278281;
        double r278295 = r278293 + r278294;
        double r278296 = r278295 / r278284;
        double r278297 = exp(r278296);
        double r278298 = r278275 + r278297;
        double r278299 = r278289 / r278298;
        double r278300 = r278288 + r278299;
        return r278300;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r278301 = NdChar;
        double r278302 = 1.0;
        double r278303 = Ec;
        double r278304 = Vef;
        double r278305 = r278303 - r278304;
        double r278306 = EDonor;
        double r278307 = r278305 - r278306;
        double r278308 = mu;
        double r278309 = r278307 - r278308;
        double r278310 = -r278309;
        double r278311 = KbT;
        double r278312 = r278310 / r278311;
        double r278313 = exp(r278312);
        double r278314 = r278302 + r278313;
        double r278315 = r278301 / r278314;
        double r278316 = NaChar;
        double r278317 = Ev;
        double r278318 = r278317 + r278304;
        double r278319 = EAccept;
        double r278320 = r278318 + r278319;
        double r278321 = r278320 - r278308;
        double r278322 = r278321 / r278311;
        double r278323 = cbrt(r278322);
        double r278324 = r278323 * r278323;
        double r278325 = exp(r278324);
        double r278326 = -r278308;
        double r278327 = r278320 + r278326;
        double r278328 = r278327 / r278311;
        double r278329 = cbrt(r278328);
        double r278330 = pow(r278325, r278329);
        double r278331 = r278302 + r278330;
        double r278332 = r278316 / r278331;
        double r278333 = r278315 + r278332;
        return r278333;
}

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

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

  4. Applied exp-prod0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(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))))))