Average Error: 0.1 → 0.1
Time: 21.3s
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 r831829 = x;
        double r831830 = y;
        double r831831 = log(r831830);
        double r831832 = r831829 * r831831;
        double r831833 = z;
        double r831834 = r831832 - r831833;
        double r831835 = r831834 - r831830;
        return r831835;
}
↓
double f(double x, double y, double z) {
        double r831836 = y;
        double r831837 = cbrt(r831836);
        double r831838 = r831837 * r831837;
        double r831839 = log(r831838);
        double r831840 = x;
        double r831841 = r831839 * r831840;
        double r831842 = 1.0;
        double r831843 = r831842 / r831836;
        double r831844 = -0.3333333333333333;
        double r831845 = pow(r831843, r831844);
        double r831846 = log(r831845);
        double r831847 = r831840 * r831846;
        double r831848 = r831841 + r831847;
        double r831849 = z;
        double r831850 = r831848 - r831849;
        double r831851 = r831850 - r831836;
        return r831851;
}

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 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  (- (- (* x (log y)) z) y))