Average Error: 0.0 → 0
Time: 5.4s
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 r145711 = x;
        double r145712 = y;
        double r145713 = r145711 * r145712;
        double r145714 = 2.0;
        double r145715 = r145713 / r145714;
        double r145716 = z;
        double r145717 = 8.0;
        double r145718 = r145716 / r145717;
        double r145719 = r145715 - r145718;
        return r145719;
}
↓
double f(double x, double y, double z) {
        double r145720 = x;
        double r145721 = y;
        double r145722 = 2.0;
        double r145723 = r145721 / r145722;
        double r145724 = z;
        double r145725 = 8.0;
        double r145726 = r145724 / r145725;
        double r145727 = -r145726;
        double r145728 = fma(r145720, r145723, r145727);
        return r145728;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)}\]

  6. Final simplification0

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

Reproduce

herbie shell --seed 2019323 +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)))