Average Error: 0.1 → 0.1
Time: 11.5s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\mathsf{fma}\left(x, 2 \cdot \log \left(\sqrt[3]{y}\right), \log \left(\sqrt[3]{y}\right) \cdot x\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\mathsf{fma}\left(x, 2 \cdot \log \left(\sqrt[3]{y}\right), \log \left(\sqrt[3]{y}\right) \cdot x\right) - z\right) - y
double f(double x, double y, double z) {
        double r29930 = x;
        double r29931 = y;
        double r29932 = log(r29931);
        double r29933 = r29930 * r29932;
        double r29934 = z;
        double r29935 = r29933 - r29934;
        double r29936 = r29935 - r29931;
        return r29936;
}
↓
double f(double x, double y, double z) {
        double r29937 = x;
        double r29938 = 2.0;
        double r29939 = y;
        double r29940 = cbrt(r29939);
        double r29941 = log(r29940);
        double r29942 = r29938 * r29941;
        double r29943 = r29941 * r29937;
        double r29944 = fma(r29937, r29942, r29943);
        double r29945 = z;
        double r29946 = r29944 - r29945;
        double r29947 = r29946 - r29939;
        return r29947;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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. Simplified0.1

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

  9. Applied fma-def0.1

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

  10. Final simplification0.1

    \[\leadsto \left(\mathsf{fma}\left(x, 2 \cdot \log \left(\sqrt[3]{y}\right), \log \left(\sqrt[3]{y}\right) \cdot x\right) - z\right) - y\]

Reproduce

herbie shell --seed 2019351 +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))