Average Error: 0.0 → 0.1
Time: 43.0s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{1}{\frac{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1}{NdChar}} + \frac{NaChar}{e^{\frac{\left(Ev + \left(Vef + EAccept\right)\right) - mu}{KbT}} + 1}\]
\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{1}{\frac{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1}{NdChar}} + \frac{NaChar}{e^{\frac{\left(Ev + \left(Vef + EAccept\right)\right) - mu}{KbT}} + 1}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r6841170 = NdChar;
        double r6841171 = 1.0;
        double r6841172 = Ec;
        double r6841173 = Vef;
        double r6841174 = r6841172 - r6841173;
        double r6841175 = EDonor;
        double r6841176 = r6841174 - r6841175;
        double r6841177 = mu;
        double r6841178 = r6841176 - r6841177;
        double r6841179 = -r6841178;
        double r6841180 = KbT;
        double r6841181 = r6841179 / r6841180;
        double r6841182 = exp(r6841181);
        double r6841183 = r6841171 + r6841182;
        double r6841184 = r6841170 / r6841183;
        double r6841185 = NaChar;
        double r6841186 = Ev;
        double r6841187 = r6841186 + r6841173;
        double r6841188 = EAccept;
        double r6841189 = r6841187 + r6841188;
        double r6841190 = -r6841177;
        double r6841191 = r6841189 + r6841190;
        double r6841192 = r6841191 / r6841180;
        double r6841193 = exp(r6841192);
        double r6841194 = r6841171 + r6841193;
        double r6841195 = r6841185 / r6841194;
        double r6841196 = r6841184 + r6841195;
        return r6841196;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r6841197 = 1.0;
        double r6841198 = mu;
        double r6841199 = Ec;
        double r6841200 = Vef;
        double r6841201 = r6841199 - r6841200;
        double r6841202 = EDonor;
        double r6841203 = r6841201 - r6841202;
        double r6841204 = r6841198 - r6841203;
        double r6841205 = KbT;
        double r6841206 = r6841204 / r6841205;
        double r6841207 = exp(r6841206);
        double r6841208 = r6841207 + r6841197;
        double r6841209 = NdChar;
        double r6841210 = r6841208 / r6841209;
        double r6841211 = r6841197 / r6841210;
        double r6841212 = NaChar;
        double r6841213 = Ev;
        double r6841214 = EAccept;
        double r6841215 = r6841200 + r6841214;
        double r6841216 = r6841213 + r6841215;
        double r6841217 = r6841216 - r6841198;
        double r6841218 = r6841217 / r6841205;
        double r6841219 = exp(r6841218);
        double r6841220 = r6841219 + r6841197;
        double r6841221 = r6841212 / r6841220;
        double r6841222 = r6841211 + r6841221;
        return r6841222;
}

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

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

  4. Applied *-un-lft-identity0.0

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

  5. Applied associate-/l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019134 
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  (+ (/ NdChar (+ 1 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))