Bulmash initializePoisson

Average Error: 0.0 → 0.0

Time: 18.9s

Precision: 64

• could not determine a ground truth for program body

  1. NdChar = -6.930036466083977e-51
  2. Ec = -4.364035695974269e-98
  3. Vef = -1.7942673936242644e-209
  4. EDonor = -3.826380113265966e+42
  5. mu = 1.4571914105267237e+45
  6. KbT = -1.5704121987480476e-139
  7. NaChar = 2.7235040088843226e-50
  8. Ev = -3.0663383388816752e-183
  9. EAccept = 8.493972672517434e+189

Math

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

↓

\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\frac{3}{2}}} \cdot \sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\frac{3}{2}}}}\]

C

double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r155757 = NdChar;
        double r155758 = 1.0;
        double r155759 = Ec;
        double r155760 = Vef;
        double r155761 = r155759 - r155760;
        double r155762 = EDonor;
        double r155763 = r155761 - r155762;
        double r155764 = mu;
        double r155765 = r155763 - r155764;
        double r155766 = -r155765;
        double r155767 = KbT;
        double r155768 = r155766 / r155767;
        double r155769 = exp(r155768);
        double r155770 = r155758 + r155769;
        double r155771 = r155757 / r155770;
        double r155772 = NaChar;
        double r155773 = Ev;
        double r155774 = r155773 + r155760;
        double r155775 = EAccept;
        double r155776 = r155774 + r155775;
        double r155777 = -r155764;
        double r155778 = r155776 + r155777;
        double r155779 = r155778 / r155767;
        double r155780 = exp(r155779);
        double r155781 = r155758 + r155780;
        double r155782 = r155772 / r155781;
        double r155783 = r155771 + r155782;
        return r155783;
}

↓

double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r155784 = NdChar;
        double r155785 = 1.0;
        double r155786 = Ec;
        double r155787 = Vef;
        double r155788 = r155786 - r155787;
        double r155789 = EDonor;
        double r155790 = r155788 - r155789;
        double r155791 = mu;
        double r155792 = r155790 - r155791;
        double r155793 = -r155792;
        double r155794 = KbT;
        double r155795 = r155793 / r155794;
        double r155796 = exp(r155795);
        double r155797 = r155785 + r155796;
        double r155798 = r155784 / r155797;
        double r155799 = NaChar;
        double r155800 = Ev;
        double r155801 = r155800 + r155787;
        double r155802 = EAccept;
        double r155803 = r155801 + r155802;
        double r155804 = r155803 - r155791;
        double r155805 = r155804 / r155794;
        double r155806 = exp(r155805);
        double r155807 = 1.5;
        double r155808 = pow(r155806, r155807);
        double r155809 = cbrt(r155808);
        double r155810 = r155809 * r155809;
        double r155811 = r155785 + r155810;
        double r155812 = r155799 / r155811;
        double r155813 = r155798 + r155812;
        return r155813;
}

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

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-cbrt-cube 0.0

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

4. Simplified 0.0

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

6. Applied sqr-pow 0.0

   \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \sqrt[3]{\color{blue}{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\left(\frac{3}{2}\right)}}}}\]

7. Applied cbrt-prod 0.0

   \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{\sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\left(\frac{3}{2}\right)}} \cdot \sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\left(\frac{3}{2}\right)}}}}\]

8. Simplified 0.0

   \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{\sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\frac{3}{2}}}} \cdot \sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\left(\frac{3}{2}\right)}}}\]

9. Simplified 0.0

   \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\frac{3}{2}}} \cdot \color{blue}{\sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\frac{3}{2}}}}}\]

10. Final simplification 0.0

    \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + \sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\frac{3}{2}}} \cdot \sqrt[3]{{\left(e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\right)}^{\frac{3}{2}}}}\]

Reproduce

herbie shell --seed 2019212 
(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))))))