Average Error: 0.1 → 0.1
Time: 5.5s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\log \left(\left({\left({\left({y}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\log \left(\left({\left({\left({y}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(1 \cdot {y}^{\frac{1}{3}}\right) \cdot x - z\right)\right) - y
double f(double x, double y, double z) {
        double r27842 = x;
        double r27843 = y;
        double r27844 = log(r27843);
        double r27845 = r27842 * r27844;
        double r27846 = z;
        double r27847 = r27845 - r27846;
        double r27848 = r27847 - r27843;
        return r27848;
}
↓
double f(double x, double y, double z) {
        double r27849 = y;
        double r27850 = 0.3333333333333333;
        double r27851 = pow(r27849, r27850);
        double r27852 = 0.6666666666666666;
        double r27853 = cbrt(r27852);
        double r27854 = r27853 * r27853;
        double r27855 = pow(r27851, r27854);
        double r27856 = pow(r27855, r27853);
        double r27857 = cbrt(r27849);
        double r27858 = pow(r27857, r27850);
        double r27859 = r27856 * r27858;
        double r27860 = r27859 * r27857;
        double r27861 = log(r27860);
        double r27862 = x;
        double r27863 = r27861 * r27862;
        double r27864 = 1.0;
        double r27865 = r27864 * r27851;
        double r27866 = log(r27865);
        double r27867 = r27866 * r27862;
        double r27868 = z;
        double r27869 = r27867 - r27868;
        double r27870 = r27863 + r27869;
        double r27871 = r27870 - r27849;
        return r27871;
}

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-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  8. Applied *-un-lft-identity0.1

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

  9. Applied cbrt-prod0.1

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

  10. Simplified0.1

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

  11. Simplified0.1

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

  13. Applied add-cube-cbrt0.1

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

  14. Simplified0.1

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

  15. Simplified0.2

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

  17. Applied add-cube-cbrt0.1

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

  18. Applied pow-unpow0.1

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

  19. Final simplification0.1

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

Reproduce

herbie shell --seed 2020057 +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))