Average Error: 0.0 → 0.0
Time: 3.8s
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 r9014648 = x;
        double r9014649 = y;
        double r9014650 = r9014648 * r9014649;
        double r9014651 = 2.0;
        double r9014652 = r9014650 / r9014651;
        double r9014653 = z;
        double r9014654 = 8.0;
        double r9014655 = r9014653 / r9014654;
        double r9014656 = r9014652 - r9014655;
        return r9014656;
}
↓
double f(double x, double y, double z) {
        double r9014657 = x;
        double r9014658 = y;
        double r9014659 = 2.0;
        double r9014660 = r9014658 / r9014659;
        double r9014661 = z;
        double r9014662 = 8.0;
        double r9014663 = r9014661 / r9014662;
        double r9014664 = -r9014663;
        double r9014665 = fma(r9014657, r9014660, r9014664);
        return r9014665;
}

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 2019171 +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)))