Average Error: 0.0 → 0.0
Time: 29.3s
Precision: 64
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NdChar}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1} + \frac{NaChar}{1 + \sqrt{e^{\frac{\left(Vef - mu\right) + \left(Ev + EAccept\right)}{KbT}}} \cdot \sqrt{\left(\sqrt[3]{\sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}}} \cdot \sqrt[3]{\sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}}}\right)\right) \cdot \left(\sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}} \cdot \sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}}\right)}}\]
\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}{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} + 1} + \frac{NaChar}{1 + \sqrt{e^{\frac{\left(Vef - mu\right) + \left(Ev + EAccept\right)}{KbT}}} \cdot \sqrt{\left(\sqrt[3]{\sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}}} \cdot \sqrt[3]{\sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}}}\right)\right) \cdot \left(\sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}} \cdot \sqrt[3]{e^{\frac{1}{\frac{KbT}{\left(Vef - mu\right) + \left(Ev + EAccept\right)}}}}\right)}}
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r5714727 = NdChar;
        double r5714728 = 1.0;
        double r5714729 = Ec;
        double r5714730 = Vef;
        double r5714731 = r5714729 - r5714730;
        double r5714732 = EDonor;
        double r5714733 = r5714731 - r5714732;
        double r5714734 = mu;
        double r5714735 = r5714733 - r5714734;
        double r5714736 = -r5714735;
        double r5714737 = KbT;
        double r5714738 = r5714736 / r5714737;
        double r5714739 = exp(r5714738);
        double r5714740 = r5714728 + r5714739;
        double r5714741 = r5714727 / r5714740;
        double r5714742 = NaChar;
        double r5714743 = Ev;
        double r5714744 = r5714743 + r5714730;
        double r5714745 = EAccept;
        double r5714746 = r5714744 + r5714745;
        double r5714747 = -r5714734;
        double r5714748 = r5714746 + r5714747;
        double r5714749 = r5714748 / r5714737;
        double r5714750 = exp(r5714749);
        double r5714751 = r5714728 + r5714750;
        double r5714752 = r5714742 / r5714751;
        double r5714753 = r5714741 + r5714752;
        return r5714753;
}
↓
double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r5714754 = NdChar;
        double r5714755 = mu;
        double r5714756 = Ec;
        double r5714757 = Vef;
        double r5714758 = r5714756 - r5714757;
        double r5714759 = EDonor;
        double r5714760 = r5714758 - r5714759;
        double r5714761 = r5714755 - r5714760;
        double r5714762 = KbT;
        double r5714763 = r5714761 / r5714762;
        double r5714764 = exp(r5714763);
        double r5714765 = 1.0;
        double r5714766 = r5714764 + r5714765;
        double r5714767 = r5714754 / r5714766;
        double r5714768 = NaChar;
        double r5714769 = r5714757 - r5714755;
        double r5714770 = Ev;
        double r5714771 = EAccept;
        double r5714772 = r5714770 + r5714771;
        double r5714773 = r5714769 + r5714772;
        double r5714774 = r5714773 / r5714762;
        double r5714775 = exp(r5714774);
        double r5714776 = sqrt(r5714775);
        double r5714777 = r5714762 / r5714773;
        double r5714778 = r5714765 / r5714777;
        double r5714779 = exp(r5714778);
        double r5714780 = cbrt(r5714779);
        double r5714781 = cbrt(r5714780);
        double r5714782 = r5714781 * r5714781;
        double r5714783 = r5714781 * r5714782;
        double r5714784 = r5714780 * r5714780;
        double r5714785 = r5714783 * r5714784;
        double r5714786 = sqrt(r5714785);
        double r5714787 = r5714776 * r5714786;
        double r5714788 = r5714765 + r5714787;
        double r5714789 = r5714768 / r5714788;
        double r5714790 = r5714767 + r5714789;
        return r5714790;
}

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

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

  4. Applied add-sqr-sqrt0.0

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

  6. Applied clear-num0.0

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

  8. Applied add-cube-cbrt0.0

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

  10. Applied add-cube-cbrt0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019152 
(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))))))