Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\frac{x \cdot y}{2.0} - \frac{z}{8.0}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)\]
\frac{x \cdot y}{2.0} - \frac{z}{8.0}
↓
\mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)
double f(double x, double y, double z) {
        double r11092769 = x;
        double r11092770 = y;
        double r11092771 = r11092769 * r11092770;
        double r11092772 = 2.0;
        double r11092773 = r11092771 / r11092772;
        double r11092774 = z;
        double r11092775 = 8.0;
        double r11092776 = r11092774 / r11092775;
        double r11092777 = r11092773 - r11092776;
        return r11092777;
}
↓
double f(double x, double y, double z) {
        double r11092778 = x;
        double r11092779 = y;
        double r11092780 = 2.0;
        double r11092781 = r11092779 / r11092780;
        double r11092782 = z;
        double r11092783 = 8.0;
        double r11092784 = r11092782 / r11092783;
        double r11092785 = -r11092784;
        double r11092786 = fma(r11092778, r11092781, r11092785);
        return r11092786;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\frac{x \cdot y}{2.0} - \frac{z}{8.0}\]
  2. Using strategy rm

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

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2.0}} - \frac{z}{8.0}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2.0}} - \frac{z}{8.0}\]

  5. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2.0}, -\frac{z}{8.0}\right)}\]

  6. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  (- (/ (* x y) 2.0) (/ z 8.0)))