Average Error: 0.1 → 0.1
Time: 14.8s
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 r31974 = x;
        double r31975 = y;
        double r31976 = log(r31975);
        double r31977 = r31974 * r31976;
        double r31978 = z;
        double r31979 = r31977 - r31978;
        double r31980 = r31979 - r31975;
        return r31980;
}
↓
double f(double x, double y, double z) {
        double r31981 = 2.0;
        double r31982 = y;
        double r31983 = cbrt(r31982);
        double r31984 = log(r31983);
        double r31985 = r31981 * r31984;
        double r31986 = x;
        double r31987 = r31985 * r31986;
        double r31988 = 0.3333333333333333;
        double r31989 = log(r31982);
        double r31990 = r31989 * r31986;
        double r31991 = r31988 * r31990;
        double r31992 = r31987 + r31991;
        double r31993 = z;
        double r31994 = r31992 - r31993;
        double r31995 = r31994 - r31982;
        return r31995;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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))