Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{1 + {\left(e^{\frac{-\sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu} \cdot \sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}}}\right)}^{\left(\frac{\sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu}}{\sqrt[3]{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
\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 + {\left(e^{\frac{-\sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu} \cdot \sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}}}\right)}^{\left(\frac{\sqrt[3]{\left(\left(Ec - Vef\right) - EDonor\right) - mu}}{\sqrt[3]{KbT}}\right)}} + \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 r312107 = NdChar;
        double r312108 = 1.0;
        double r312109 = Ec;
        double r312110 = Vef;
        double r312111 = r312109 - r312110;
        double r312112 = EDonor;
        double r312113 = r312111 - r312112;
        double r312114 = mu;
        double r312115 = r312113 - r312114;
        double r312116 = -r312115;
        double r312117 = KbT;
        double r312118 = r312116 / r312117;
        double r312119 = exp(r312118);
        double r312120 = r312108 + r312119;
        double r312121 = r312107 / r312120;
        double r312122 = NaChar;
        double r312123 = Ev;
        double r312124 = r312123 + r312110;
        double r312125 = EAccept;
        double r312126 = r312124 + r312125;
        double r312127 = -r312114;
        double r312128 = r312126 + r312127;
        double r312129 = r312128 / r312117;
        double r312130 = exp(r312129);
        double r312131 = r312108 + r312130;
        double r312132 = r312122 / r312131;
        double r312133 = r312121 + r312132;
        return r312133;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r312134 = NdChar;
        double r312135 = 1.0;
        double r312136 = Ec;
        double r312137 = Vef;
        double r312138 = r312136 - r312137;
        double r312139 = EDonor;
        double r312140 = r312138 - r312139;
        double r312141 = mu;
        double r312142 = r312140 - r312141;
        double r312143 = cbrt(r312142);
        double r312144 = r312143 * r312143;
        double r312145 = -r312144;
        double r312146 = KbT;
        double r312147 = cbrt(r312146);
        double r312148 = r312147 * r312147;
        double r312149 = r312145 / r312148;
        double r312150 = exp(r312149);
        double r312151 = r312143 / r312147;
        double r312152 = pow(r312150, r312151);
        double r312153 = r312135 + r312152;
        double r312154 = r312134 / r312153;
        double r312155 = NaChar;
        double r312156 = Ev;
        double r312157 = r312156 + r312137;
        double r312158 = EAccept;
        double r312159 = r312157 + r312158;
        double r312160 = -r312141;
        double r312161 = r312159 + r312160;
        double r312162 = r312161 / r312146;
        double r312163 = exp(r312162);
        double r312164 = r312135 + r312163;
        double r312165 = r312155 / r312164;
        double r312166 = r312154 + r312165;
        return r312166;
}

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

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

  4. Applied add-cube-cbrt0.0

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

  5. Applied distribute-lft-neg-in0.0

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

  6. Applied times-frac0.0

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

  7. Applied exp-prod0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020039 
(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))))))