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

Average Error: 0.1 → 0.1

Time: 4.5s

Precision: 64

Math

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

↓

\[\left(\left(\left(x \cdot \log \left(\sqrt{\left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt{\sqrt[3]{y}}\right)\right) + x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{\sqrt{y}}\right)\right)\right) - z\right) - y\]

C

double f(double x, double y, double z) {
        double r32128 = x;
        double r32129 = y;
        double r32130 = log(r32129);
        double r32131 = r32128 * r32130;
        double r32132 = z;
        double r32133 = r32131 - r32132;
        double r32134 = r32133 - r32129;
        return r32134;
}

↓

double f(double x, double y, double z) {
        double r32135 = x;
        double r32136 = 1.0;
        double r32137 = y;
        double r32138 = 0.3333333333333333;
        double r32139 = pow(r32137, r32138);
        double r32140 = r32136 * r32139;
        double r32141 = cbrt(r32137);
        double r32142 = r32140 * r32141;
        double r32143 = sqrt(r32142);
        double r32144 = log(r32143);
        double r32145 = r32135 * r32144;
        double r32146 = sqrt(r32141);
        double r32147 = log(r32146);
        double r32148 = r32135 * r32147;
        double r32149 = r32145 + r32148;
        double r32150 = sqrt(r32137);
        double r32151 = sqrt(r32150);
        double r32152 = log(r32151);
        double r32153 = r32152 + r32152;
        double r32154 = r32135 * r32153;
        double r32155 = r32149 + r32154;
        double r32156 = z;
        double r32157 = r32155 - r32156;
        double r32158 = r32157 - r32137;
        return r32158;
}

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. Using strategy rm

7. Applied add-sqr-sqrt 0.1

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

8. Applied sqrt-prod 0.1

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

9. Applied log-prod 0.1

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

11. Applied add-cube-cbrt 0.1

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

12. Applied sqrt-prod 0.1

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

13. Applied log-prod 0.1

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

14. Applied distribute-lft-in 0.1

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

16. Applied *-un-lft-identity 0.1

    \[\leadsto \left(\left(\left(x \cdot \log \left(\sqrt{\sqrt[3]{\color{blue}{1 \cdot y}} \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt{\sqrt[3]{y}}\right)\right) + x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{\sqrt{y}}\right)\right)\right) - z\right) - y\]

17. Applied cbrt-prod 0.1

    \[\leadsto \left(\left(\left(x \cdot \log \left(\sqrt{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt{\sqrt[3]{y}}\right)\right) + x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{\sqrt{y}}\right)\right)\right) - z\right) - y\]

18. Simplified 0.1

    \[\leadsto \left(\left(\left(x \cdot \log \left(\sqrt{\left(\color{blue}{1} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt{\sqrt[3]{y}}\right)\right) + x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{\sqrt{y}}\right)\right)\right) - z\right) - y\]

19. Simplified 0.1

    \[\leadsto \left(\left(\left(x \cdot \log \left(\sqrt{\left(1 \cdot \color{blue}{{y}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt{\sqrt[3]{y}}\right)\right) + x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{\sqrt{y}}\right)\right)\right) - z\right) - y\]

20. Final simplification 0.1

    \[\leadsto \left(\left(\left(x \cdot \log \left(\sqrt{\left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt{\sqrt[3]{y}}\right)\right) + x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{\sqrt{y}}\right)\right)\right) - z\right) - y\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))