Average Error: 0.1 → 0.1
Time: 14.6s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \frac{1}{3} \cdot \left(\log y \cdot x\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \frac{1}{3} \cdot \left(\log y \cdot x\right)\right) - z\right) - y
double f(double x, double y, double z) {
        double r29850 = x;
        double r29851 = y;
        double r29852 = log(r29851);
        double r29853 = r29850 * r29852;
        double r29854 = z;
        double r29855 = r29853 - r29854;
        double r29856 = r29855 - r29851;
        return r29856;
}
↓
double f(double x, double y, double z) {
        double r29857 = 2.0;
        double r29858 = y;
        double r29859 = cbrt(r29858);
        double r29860 = log(r29859);
        double r29861 = r29857 * r29860;
        double r29862 = x;
        double r29863 = r29861 * r29862;
        double r29864 = 0.3333333333333333;
        double r29865 = log(r29858);
        double r29866 = r29865 * r29862;
        double r29867 = r29864 * r29866;
        double r29868 = r29863 + r29867;
        double r29869 = z;
        double r29870 = r29868 - r29869;
        double r29871 = r29870 - r29858;
        return r29871;
}

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

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Applied log-pow0.1

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

  11. Applied associate-*l*0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))