Average Error: 0.0 → 0.0
Time: 905.0ms
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 r213655 = x;
        double r213656 = y;
        double r213657 = r213655 * r213656;
        double r213658 = 2.0;
        double r213659 = r213657 / r213658;
        double r213660 = z;
        double r213661 = 8.0;
        double r213662 = r213660 / r213661;
        double r213663 = r213659 - r213662;
        return r213663;
}
↓
double f(double x, double y, double z) {
        double r213664 = x;
        double r213665 = 1.0;
        double r213666 = r213664 / r213665;
        double r213667 = y;
        double r213668 = 2.0;
        double r213669 = r213667 / r213668;
        double r213670 = z;
        double r213671 = 8.0;
        double r213672 = r213670 / r213671;
        double r213673 = -r213672;
        double r213674 = fma(r213666, r213669, r213673);
        return r213674;
}

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 2019353 +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)))