Average Error: 0.1 → 0.1
Time: 5.4s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[x \cdot \log \left({y}^{\frac{1}{3}} \cdot {y}^{\frac{1}{3}}\right) + \left(\left(\log \left({\left({\left({y}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)}\right)}^{\frac{1}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right) - y\right)\]
\left(x \cdot \log y - z\right) - y
↓
x \cdot \log \left({y}^{\frac{1}{3}} \cdot {y}^{\frac{1}{3}}\right) + \left(\left(\log \left({\left({\left({y}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)}\right)}^{\frac{1}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right) - y\right)
double f(double x, double y, double z) {
        double r30750 = x;
        double r30751 = y;
        double r30752 = log(r30751);
        double r30753 = r30750 * r30752;
        double r30754 = z;
        double r30755 = r30753 - r30754;
        double r30756 = r30755 - r30751;
        return r30756;
}
↓
double f(double x, double y, double z) {
        double r30757 = x;
        double r30758 = y;
        double r30759 = 0.3333333333333333;
        double r30760 = pow(r30758, r30759);
        double r30761 = r30760 * r30760;
        double r30762 = log(r30761);
        double r30763 = r30757 * r30762;
        double r30764 = 0.6666666666666666;
        double r30765 = cbrt(r30764);
        double r30766 = r30765 * r30765;
        double r30767 = pow(r30758, r30766);
        double r30768 = pow(r30767, r30765);
        double r30769 = pow(r30768, r30759);
        double r30770 = cbrt(r30758);
        double r30771 = pow(r30770, r30759);
        double r30772 = r30769 * r30771;
        double r30773 = log(r30772);
        double r30774 = r30773 * r30757;
        double r30775 = z;
        double r30776 = r30774 - r30775;
        double r30777 = r30776 - r30758;
        double r30778 = r30763 + r30777;
        return r30778;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Simplified0.1

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

  10. Applied add-sqr-sqrt0.1

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

  11. Applied add-sqr-sqrt0.1

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

  12. Applied swap-sqr0.1

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

  13. Simplified0.1

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

  14. Simplified0.1

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

  16. Applied add-cube-cbrt0.1

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

  17. Applied cbrt-prod0.1

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

  18. Simplified0.2

    \[\leadsto x \cdot \log \left({y}^{\frac{1}{3}} \cdot {y}^{\frac{1}{3}}\right) + \left(\left(\log \left(\color{blue}{{\left({y}^{\frac{2}{3}}\right)}^{\frac{1}{3}}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x - z\right) - y\right)\]

  19. Simplified0.2

    \[\leadsto x \cdot \log \left({y}^{\frac{1}{3}} \cdot {y}^{\frac{1}{3}}\right) + \left(\left(\log \left({\left({y}^{\frac{2}{3}}\right)}^{\frac{1}{3}} \cdot \color{blue}{{\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}}\right) \cdot x - z\right) - y\right)\]
  20. Using strategy rm

  21. Applied add-cube-cbrt0.1

    \[\leadsto x \cdot \log \left({y}^{\frac{1}{3}} \cdot {y}^{\frac{1}{3}}\right) + \left(\left(\log \left({\left({y}^{\color{blue}{\left(\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right) \cdot \sqrt[3]{\frac{2}{3}}\right)}}\right)}^{\frac{1}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right) - y\right)\]

  22. Applied pow-unpow0.1

    \[\leadsto x \cdot \log \left({y}^{\frac{1}{3}} \cdot {y}^{\frac{1}{3}}\right) + \left(\left(\log \left({\color{blue}{\left({\left({y}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)}\right)}}^{\frac{1}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right) - y\right)\]

  23. Final simplification0.1

    \[\leadsto x \cdot \log \left({y}^{\frac{1}{3}} \cdot {y}^{\frac{1}{3}}\right) + \left(\left(\log \left({\left({\left({y}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)}\right)}^{\frac{1}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - z\right) - y\right)\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))