Average Error: 0.0 → 0.0
Time: 5.7s
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 r114593 = x;
        double r114594 = y;
        double r114595 = r114593 * r114594;
        double r114596 = 2.0;
        double r114597 = r114595 / r114596;
        double r114598 = z;
        double r114599 = 8.0;
        double r114600 = r114598 / r114599;
        double r114601 = r114597 - r114600;
        return r114601;
}
↓
double f(double x, double y, double z) {
        double r114602 = x;
        double r114603 = y;
        double r114604 = 2.0;
        double r114605 = r114603 / r114604;
        double r114606 = z;
        double r114607 = 8.0;
        double r114608 = r114606 / r114607;
        double r114609 = -r114608;
        double r114610 = fma(r114602, r114605, r114609);
        return r114610;
}

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)))