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

Average Error: 0.1 → 0.1

Time: 17.1s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r28122 = x;
        double r28123 = y;
        double r28124 = log(r28123);
        double r28125 = r28122 * r28124;
        double r28126 = z;
        double r28127 = r28125 - r28126;
        double r28128 = r28127 - r28123;
        return r28128;
}

↓

double f(double x, double y, double z) {
        double r28129 = y;
        double r28130 = sqrt(r28129);
        double r28131 = log(r28130);
        double r28132 = x;
        double r28133 = r28131 * r28132;
        double r28134 = cbrt(r28129);
        double r28135 = fabs(r28134);
        double r28136 = log(r28135);
        double r28137 = r28136 * r28132;
        double r28138 = sqrt(r28134);
        double r28139 = log(r28138);
        double r28140 = r28132 * r28139;
        double r28141 = r28137 + r28140;
        double r28142 = z;
        double r28143 = r28141 - r28142;
        double r28144 = r28133 + r28143;
        double r28145 = r28144 - r28129;
        return r28145;
}

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-rgt-in 0.1

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

6. Applied associate--l+ 0.1

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

7. Simplified 0.1

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

9. Applied add-cube-cbrt 0.1

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

10. Applied sqrt-prod 0.1

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

11. Applied log-prod 0.1

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

12. Applied distribute-lft-in 0.1

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

13. Simplified 0.1

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

14. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))