Average Error: 0.0 → 0.0
Time: 14.0s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + \sqrt[3]{{\left(e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}\right)}^{3}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
\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}{1 + \sqrt[3]{{\left(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 r208293 = NdChar;
        double r208294 = 1.0;
        double r208295 = Ec;
        double r208296 = Vef;
        double r208297 = r208295 - r208296;
        double r208298 = EDonor;
        double r208299 = r208297 - r208298;
        double r208300 = mu;
        double r208301 = r208299 - r208300;
        double r208302 = -r208301;
        double r208303 = KbT;
        double r208304 = r208302 / r208303;
        double r208305 = exp(r208304);
        double r208306 = r208294 + r208305;
        double r208307 = r208293 / r208306;
        double r208308 = NaChar;
        double r208309 = Ev;
        double r208310 = r208309 + r208296;
        double r208311 = EAccept;
        double r208312 = r208310 + r208311;
        double r208313 = -r208300;
        double r208314 = r208312 + r208313;
        double r208315 = r208314 / r208303;
        double r208316 = exp(r208315);
        double r208317 = r208294 + r208316;
        double r208318 = r208308 / r208317;
        double r208319 = r208307 + r208318;
        return r208319;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r208320 = NdChar;
        double r208321 = 1.0;
        double r208322 = Ec;
        double r208323 = Vef;
        double r208324 = r208322 - r208323;
        double r208325 = EDonor;
        double r208326 = r208324 - r208325;
        double r208327 = mu;
        double r208328 = r208326 - r208327;
        double r208329 = -r208328;
        double r208330 = KbT;
        double r208331 = r208329 / r208330;
        double r208332 = exp(r208331);
        double r208333 = 3.0;
        double r208334 = pow(r208332, r208333);
        double r208335 = cbrt(r208334);
        double r208336 = r208321 + r208335;
        double r208337 = r208320 / r208336;
        double r208338 = NaChar;
        double r208339 = Ev;
        double r208340 = r208339 + r208323;
        double r208341 = EAccept;
        double r208342 = r208340 + r208341;
        double r208343 = -r208327;
        double r208344 = r208342 + r208343;
        double r208345 = r208344 / r208330;
        double r208346 = exp(r208345);
        double r208347 = r208321 + r208346;
        double r208348 = r208338 / r208347;
        double r208349 = r208337 + r208348;
        return r208349;
}

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

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(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))))))