Average Error: 0.0 → 0.0
Time: 16.8s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{\sqrt[3]{{\left(1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}\right)}^{3}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
\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}{\sqrt[3]{{\left(1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}\right)}^{3}}} + \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 r331271 = NdChar;
        double r331272 = 1.0;
        double r331273 = Ec;
        double r331274 = Vef;
        double r331275 = r331273 - r331274;
        double r331276 = EDonor;
        double r331277 = r331275 - r331276;
        double r331278 = mu;
        double r331279 = r331277 - r331278;
        double r331280 = -r331279;
        double r331281 = KbT;
        double r331282 = r331280 / r331281;
        double r331283 = exp(r331282);
        double r331284 = r331272 + r331283;
        double r331285 = r331271 / r331284;
        double r331286 = NaChar;
        double r331287 = Ev;
        double r331288 = r331287 + r331274;
        double r331289 = EAccept;
        double r331290 = r331288 + r331289;
        double r331291 = -r331278;
        double r331292 = r331290 + r331291;
        double r331293 = r331292 / r331281;
        double r331294 = exp(r331293);
        double r331295 = r331272 + r331294;
        double r331296 = r331286 / r331295;
        double r331297 = r331285 + r331296;
        return r331297;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r331298 = NdChar;
        double r331299 = 1.0;
        double r331300 = Ec;
        double r331301 = Vef;
        double r331302 = r331300 - r331301;
        double r331303 = EDonor;
        double r331304 = r331302 - r331303;
        double r331305 = mu;
        double r331306 = r331304 - r331305;
        double r331307 = -r331306;
        double r331308 = KbT;
        double r331309 = r331307 / r331308;
        double r331310 = exp(r331309);
        double r331311 = r331299 + r331310;
        double r331312 = 3.0;
        double r331313 = pow(r331311, r331312);
        double r331314 = cbrt(r331313);
        double r331315 = r331298 / r331314;
        double r331316 = NaChar;
        double r331317 = Ev;
        double r331318 = r331317 + r331301;
        double r331319 = EAccept;
        double r331320 = r331318 + r331319;
        double r331321 = -r331305;
        double r331322 = r331320 + r331321;
        double r331323 = r331322 / r331308;
        double r331324 = exp(r331323);
        double r331325 = r331299 + r331324;
        double r331326 = r331316 / r331325;
        double r331327 = r331315 + r331326;
        return r331327;
}

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-cbrt-cube0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(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))))))