Average Error: 0.0 → 0.0
Time: 8.6s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\left(\sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}} \cdot \sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}\right) \cdot \sqrt[3]{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}}\]
\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 + e^{\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}}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r272182 = NdChar;
        double r272183 = 1.0;
        double r272184 = Ec;
        double r272185 = Vef;
        double r272186 = r272184 - r272185;
        double r272187 = EDonor;
        double r272188 = r272186 - r272187;
        double r272189 = mu;
        double r272190 = r272188 - r272189;
        double r272191 = -r272190;
        double r272192 = KbT;
        double r272193 = r272191 / r272192;
        double r272194 = exp(r272193);
        double r272195 = r272183 + r272194;
        double r272196 = r272182 / r272195;
        double r272197 = NaChar;
        double r272198 = Ev;
        double r272199 = r272198 + r272185;
        double r272200 = EAccept;
        double r272201 = r272199 + r272200;
        double r272202 = -r272189;
        double r272203 = r272201 + r272202;
        double r272204 = r272203 / r272192;
        double r272205 = exp(r272204);
        double r272206 = r272183 + r272205;
        double r272207 = r272197 / r272206;
        double r272208 = r272196 + r272207;
        return r272208;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r272209 = NdChar;
        double r272210 = 1.0;
        double r272211 = Ec;
        double r272212 = Vef;
        double r272213 = r272211 - r272212;
        double r272214 = EDonor;
        double r272215 = r272213 - r272214;
        double r272216 = mu;
        double r272217 = r272215 - r272216;
        double r272218 = -r272217;
        double r272219 = KbT;
        double r272220 = r272218 / r272219;
        double r272221 = exp(r272220);
        double r272222 = r272210 + r272221;
        double r272223 = r272209 / r272222;
        double r272224 = NaChar;
        double r272225 = Ev;
        double r272226 = r272225 + r272212;
        double r272227 = EAccept;
        double r272228 = r272226 + r272227;
        double r272229 = -r272216;
        double r272230 = r272228 + r272229;
        double r272231 = r272230 / r272219;
        double r272232 = cbrt(r272231);
        double r272233 = r272232 * r272232;
        double r272234 = r272233 * r272232;
        double r272235 = exp(r272234);
        double r272236 = r272210 + r272235;
        double r272237 = r272224 / r272236;
        double r272238 = r272223 + r272237;
        return r272238;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020064 
(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))))))