Average Error: 0.0 → 0.0
Time: 845.0ms
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)
double f(double x, double y, double z) {
        double r214898 = x;
        double r214899 = y;
        double r214900 = r214898 * r214899;
        double r214901 = 2.0;
        double r214902 = r214900 / r214901;
        double r214903 = z;
        double r214904 = 8.0;
        double r214905 = r214903 / r214904;
        double r214906 = r214902 - r214905;
        return r214906;
}
↓
double f(double x, double y, double z) {
        double r214907 = x;
        double r214908 = 1.0;
        double r214909 = r214907 / r214908;
        double r214910 = y;
        double r214911 = 2.0;
        double r214912 = r214910 / r214911;
        double r214913 = z;
        double r214914 = 8.0;
        double r214915 = r214913 / r214914;
        double r214916 = -r214915;
        double r214917 = fma(r214909, r214912, r214916);
        return r214917;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\frac{x \cdot y}{2} - \frac{z}{8}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2}} - \frac{z}{8}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2}} - \frac{z}{8}\]

  5. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)}\]

  6. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2) (/ z 8)))