Average Error: 0.0 → 0.0
Time: 2.5m
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + e^{-\frac{Ec - \left(EDonor + \left(mu + Vef\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}} \cdot \sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}}\right) \cdot \sqrt[3]{\sqrt{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}} \cdot \sqrt{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}}}}\]
\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{Ec - \left(EDonor + \left(mu + Vef\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}} \cdot \sqrt[3]{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}}\right) \cdot \sqrt[3]{\sqrt{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}} \cdot \sqrt{e^{\frac{\left(\left(Ev + Vef\right) - mu\right) + EAccept}{KbT}}}}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r26222318 = NdChar;
        double r26222319 = 1.0;
        double r26222320 = Ec;
        double r26222321 = Vef;
        double r26222322 = r26222320 - r26222321;
        double r26222323 = EDonor;
        double r26222324 = r26222322 - r26222323;
        double r26222325 = mu;
        double r26222326 = r26222324 - r26222325;
        double r26222327 = -r26222326;
        double r26222328 = KbT;
        double r26222329 = r26222327 / r26222328;
        double r26222330 = exp(r26222329);
        double r26222331 = r26222319 + r26222330;
        double r26222332 = r26222318 / r26222331;
        double r26222333 = NaChar;
        double r26222334 = Ev;
        double r26222335 = r26222334 + r26222321;
        double r26222336 = EAccept;
        double r26222337 = r26222335 + r26222336;
        double r26222338 = -r26222325;
        double r26222339 = r26222337 + r26222338;
        double r26222340 = r26222339 / r26222328;
        double r26222341 = exp(r26222340);
        double r26222342 = r26222319 + r26222341;
        double r26222343 = r26222333 / r26222342;
        double r26222344 = r26222332 + r26222343;
        return r26222344;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r26222345 = NdChar;
        double r26222346 = 1.0;
        double r26222347 = Ec;
        double r26222348 = EDonor;
        double r26222349 = mu;
        double r26222350 = Vef;
        double r26222351 = r26222349 + r26222350;
        double r26222352 = r26222348 + r26222351;
        double r26222353 = r26222347 - r26222352;
        double r26222354 = KbT;
        double r26222355 = r26222353 / r26222354;
        double r26222356 = -r26222355;
        double r26222357 = exp(r26222356);
        double r26222358 = r26222346 + r26222357;
        double r26222359 = r26222345 / r26222358;
        double r26222360 = NaChar;
        double r26222361 = Ev;
        double r26222362 = r26222361 + r26222350;
        double r26222363 = r26222362 - r26222349;
        double r26222364 = EAccept;
        double r26222365 = r26222363 + r26222364;
        double r26222366 = r26222365 / r26222354;
        double r26222367 = exp(r26222366);
        double r26222368 = cbrt(r26222367);
        double r26222369 = r26222368 * r26222368;
        double r26222370 = sqrt(r26222367);
        double r26222371 = r26222370 * r26222370;
        double r26222372 = cbrt(r26222371);
        double r26222373 = r26222369 * r26222372;
        double r26222374 = r26222346 + r26222373;
        double r26222375 = r26222360 / r26222374;
        double r26222376 = r26222359 + r26222375;
        return r26222376;
}

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

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

  4. Applied add-cube-cbrt0.0

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

  6. Applied add-sqr-sqrt0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(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))))))