Average Error: 0.1 → 0.1
Time: 23.8s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + x \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + x \cdot \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)\right) - z\right) - y
double f(double x, double y, double z) {
        double r965774 = x;
        double r965775 = y;
        double r965776 = log(r965775);
        double r965777 = r965774 * r965776;
        double r965778 = z;
        double r965779 = r965777 - r965778;
        double r965780 = r965779 - r965775;
        return r965780;
}
↓
double f(double x, double y, double z) {
        double r965781 = y;
        double r965782 = cbrt(r965781);
        double r965783 = r965782 * r965782;
        double r965784 = log(r965783);
        double r965785 = x;
        double r965786 = r965784 * r965785;
        double r965787 = 1.0;
        double r965788 = r965787 / r965781;
        double r965789 = -0.3333333333333333;
        double r965790 = pow(r965788, r965789);
        double r965791 = log(r965790);
        double r965792 = r965785 * r965791;
        double r965793 = r965786 + r965792;
        double r965794 = z;
        double r965795 = r965793 - r965794;
        double r965796 = r965795 - r965781;
        return r965796;
}

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. Using strategy rm

  7. Applied pow1/30.1

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

  9. Applied add-cube-cbrt0.2

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

  10. Applied pow-unpow0.2

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

  11. Taylor expanded around inf 0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  (- (- (* x (log y)) z) y))