Average Error: 0.1 → 0.1
Time: 12.1s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\mathsf{fma}\left(x, \log y, -y\right) - z\right) + \left(y - y\right)\]
\left(x \cdot \log y - z\right) - y
↓
\left(\mathsf{fma}\left(x, \log y, -y\right) - z\right) + \left(y - y\right)
double f(double x, double y, double z) {
        double r22049 = x;
        double r22050 = y;
        double r22051 = log(r22050);
        double r22052 = r22049 * r22051;
        double r22053 = z;
        double r22054 = r22052 - r22053;
        double r22055 = r22054 - r22050;
        return r22055;
}
↓
double f(double x, double y, double z) {
        double r22056 = x;
        double r22057 = y;
        double r22058 = log(r22057);
        double r22059 = -r22057;
        double r22060 = fma(r22056, r22058, r22059);
        double r22061 = z;
        double r22062 = r22060 - r22061;
        double r22063 = r22057 - r22057;
        double r22064 = r22062 + r22063;
        return r22064;
}

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-cbrt0.5

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

  4. Applied add-sqr-sqrt32.3

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

  5. Applied prod-diff32.3

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

    \[\leadsto \left(\mathsf{fma}\left(x, \log y, -y\right) - z\right) + \left(y - y\right)\]

Reproduce

herbie shell --seed 2020043 +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))