Average Error: 0.1 → 0.1
Time: 20.4s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(x \cdot \log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(x \cdot \log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right)\right) - z\right) - y
double f(double x, double y, double z) {
        double r25778 = x;
        double r25779 = y;
        double r25780 = log(r25779);
        double r25781 = r25778 * r25780;
        double r25782 = z;
        double r25783 = r25781 - r25782;
        double r25784 = r25783 - r25779;
        return r25784;
}
↓
double f(double x, double y, double z) {
        double r25785 = x;
        double r25786 = 2.0;
        double r25787 = y;
        double r25788 = cbrt(r25787);
        double r25789 = log(r25788);
        double r25790 = r25786 * r25789;
        double r25791 = r25785 * r25790;
        double r25792 = 0.6666666666666666;
        double r25793 = pow(r25787, r25792);
        double r25794 = cbrt(r25793);
        double r25795 = log(r25794);
        double r25796 = r25785 * r25795;
        double r25797 = cbrt(r25788);
        double r25798 = log(r25797);
        double r25799 = r25798 * r25785;
        double r25800 = r25796 + r25799;
        double r25801 = r25791 + r25800;
        double r25802 = z;
        double r25803 = r25801 - r25802;
        double r25804 = r25803 - r25787;
        return r25804;
}

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. Simplified0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Simplified0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019209 +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))