Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 23.3s

Precision: 64

Math

\[\left(x \cdot \log y - z\right) - y\]

↓

\[\left(\left(x \cdot \log \left(\sqrt{\sqrt[3]{y}}\right) - z\right) + \left(\log \left(\sqrt{y}\right) + \log \left(\left|\sqrt[3]{y}\right|\right)\right) \cdot x\right) - y\]

C

double f(double x, double y, double z) {
        double r1030804 = x;
        double r1030805 = y;
        double r1030806 = log(r1030805);
        double r1030807 = r1030804 * r1030806;
        double r1030808 = z;
        double r1030809 = r1030807 - r1030808;
        double r1030810 = r1030809 - r1030805;
        return r1030810;
}

↓

double f(double x, double y, double z) {
        double r1030811 = x;
        double r1030812 = y;
        double r1030813 = cbrt(r1030812);
        double r1030814 = sqrt(r1030813);
        double r1030815 = log(r1030814);
        double r1030816 = r1030811 * r1030815;
        double r1030817 = z;
        double r1030818 = r1030816 - r1030817;
        double r1030819 = sqrt(r1030812);
        double r1030820 = log(r1030819);
        double r1030821 = fabs(r1030813);
        double r1030822 = log(r1030821);
        double r1030823 = r1030820 + r1030822;
        double r1030824 = r1030823 * r1030811;
        double r1030825 = r1030818 + r1030824;
        double r1030826 = r1030825 - r1030812;
        return r1030826;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.1

   \[\left(x \cdot \log y - z\right) - y\]
2. Using strategy rm

3. Applied add-sqr-sqrt 0.1

   \[\leadsto \left(x \cdot \log \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} - z\right) - y\]

4. Applied log-prod 0.1

   \[\leadsto \left(x \cdot \color{blue}{\left(\log \left(\sqrt{y}\right) + \log \left(\sqrt{y}\right)\right)} - z\right) - y\]

5. Applied distribute-lft-in 0.1

   \[\leadsto \left(\color{blue}{\left(x \cdot \log \left(\sqrt{y}\right) + x \cdot \log \left(\sqrt{y}\right)\right)} - z\right) - y\]

6. Applied associate--l+ 0.1

   \[\leadsto \color{blue}{\left(x \cdot \log \left(\sqrt{y}\right) + \left(x \cdot \log \left(\sqrt{y}\right) - z\right)\right)} - y\]
7. Using strategy rm

8. Applied add-cube-cbrt 0.1

   \[\leadsto \left(x \cdot \log \left(\sqrt{y}\right) + \left(x \cdot \log \left(\sqrt{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\right) - z\right)\right) - y\]

9. Applied sqrt-prod 0.1

   \[\leadsto \left(x \cdot \log \left(\sqrt{y}\right) + \left(x \cdot \log \color{blue}{\left(\sqrt{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \sqrt{\sqrt[3]{y}}\right)} - z\right)\right) - y\]

10. Applied log-prod 0.1

    \[\leadsto \left(x \cdot \log \left(\sqrt{y}\right) + \left(x \cdot \color{blue}{\left(\log \left(\sqrt{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + \log \left(\sqrt{\sqrt[3]{y}}\right)\right)} - z\right)\right) - y\]

11. Applied distribute-rgt-in 0.1

    \[\leadsto \left(x \cdot \log \left(\sqrt{y}\right) + \left(\color{blue}{\left(\log \left(\sqrt{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot x + \log \left(\sqrt{\sqrt[3]{y}}\right) \cdot x\right)} - z\right)\right) - y\]

12. Applied associate--l+ 0.1

    \[\leadsto \left(x \cdot \log \left(\sqrt{y}\right) + \color{blue}{\left(\log \left(\sqrt{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot x + \left(\log \left(\sqrt{\sqrt[3]{y}}\right) \cdot x - z\right)\right)}\right) - y\]

13. Applied associate-+r+ 0.1

    \[\leadsto \color{blue}{\left(\left(x \cdot \log \left(\sqrt{y}\right) + \log \left(\sqrt{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot x\right) + \left(\log \left(\sqrt{\sqrt[3]{y}}\right) \cdot x - z\right)\right)} - y\]

14. Simplified 0.1

    \[\leadsto \left(\color{blue}{x \cdot \left(\log \left(\sqrt{y}\right) + \log \left(\left|\sqrt[3]{y}\right|\right)\right)} + \left(\log \left(\sqrt{\sqrt[3]{y}}\right) \cdot x - z\right)\right) - y\]

15. Final simplification 0.1

    \[\leadsto \left(\left(x \cdot \log \left(\sqrt{\sqrt[3]{y}}\right) - z\right) + \left(\log \left(\sqrt{y}\right) + \log \left(\left|\sqrt[3]{y}\right|\right)\right) \cdot x\right) - y\]

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  (- (- (* x (log y)) z) y))