Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)
double f(double x, double y, double z) {
        double r96162 = x;
        double r96163 = y;
        double r96164 = r96162 * r96163;
        double r96165 = 2.0;
        double r96166 = r96164 / r96165;
        double r96167 = z;
        double r96168 = 8.0;
        double r96169 = r96167 / r96168;
        double r96170 = r96166 - r96169;
        return r96170;
}
↓
double f(double x, double y, double z) {
        double r96171 = x;
        double r96172 = y;
        double r96173 = 2.0;
        double r96174 = r96172 / r96173;
        double r96175 = z;
        double r96176 = 8.0;
        double r96177 = r96175 / r96176;
        double r96178 = -r96177;
        double r96179 = fma(r96171, r96174, r96178);
        return r96179;
}

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

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

Reproduce

herbie shell --seed 2019326 +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)))