Bulmash initializePoisson

Average Error: 0.0 → 0.0

Time: 25.5s

Precision: 64

• could not determine a ground truth for program body

  1. NdChar = 5.765096427492256e-291
  2. Ec = 1.586496827119884e+120
  3. Vef = -4.115349544704707e+184
  4. EDonor = 1.7751445845594604e+29
  5. mu = 9.52208805545793e-166
  6. KbT = 1.4966316402072362e+49
  7. NaChar = -2.2557235851799486e-290
  8. Ev = -3.567767816900689e+54
  9. EAccept = -3.485210428198179e+64

Math

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

↓

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

C

double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r219760 = NdChar;
        double r219761 = 1.0;
        double r219762 = Ec;
        double r219763 = Vef;
        double r219764 = r219762 - r219763;
        double r219765 = EDonor;
        double r219766 = r219764 - r219765;
        double r219767 = mu;
        double r219768 = r219766 - r219767;
        double r219769 = -r219768;
        double r219770 = KbT;
        double r219771 = r219769 / r219770;
        double r219772 = exp(r219771);
        double r219773 = r219761 + r219772;
        double r219774 = r219760 / r219773;
        double r219775 = NaChar;
        double r219776 = Ev;
        double r219777 = r219776 + r219763;
        double r219778 = EAccept;
        double r219779 = r219777 + r219778;
        double r219780 = -r219767;
        double r219781 = r219779 + r219780;
        double r219782 = r219781 / r219770;
        double r219783 = exp(r219782);
        double r219784 = r219761 + r219783;
        double r219785 = r219775 / r219784;
        double r219786 = r219774 + r219785;
        return r219786;
}

↓

double f(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
        double r219787 = NdChar;
        double r219788 = 1.0;
        double r219789 = Ec;
        double r219790 = Vef;
        double r219791 = r219789 - r219790;
        double r219792 = EDonor;
        double r219793 = r219791 - r219792;
        double r219794 = mu;
        double r219795 = r219793 - r219794;
        double r219796 = -r219795;
        double r219797 = KbT;
        double r219798 = r219796 / r219797;
        double r219799 = exp(r219798);
        double r219800 = sqrt(r219799);
        double r219801 = r219800 * r219800;
        double r219802 = r219788 + r219801;
        double r219803 = r219787 / r219802;
        double r219804 = NaChar;
        double r219805 = Ev;
        double r219806 = r219805 + r219790;
        double r219807 = EAccept;
        double r219808 = r219806 + r219807;
        double r219809 = -r219794;
        double r219810 = r219808 + r219809;
        double r219811 = r219810 / r219797;
        double r219812 = exp(r219811);
        double r219813 = cbrt(r219812);
        double r219814 = r219813 * r219813;
        double r219815 = r219814 * r219813;
        double r219816 = r219788 + r219815;
        double r219817 = r219804 / r219816;
        double r219818 = r219803 + r219817;
        return r219818;
}

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-cube-cbrt 0.0

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

5. Applied add-sqr-sqrt 0.0

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

6. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019298 
(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))))))