Average Error: 0.0 → 0.0
Time: 894.0ms
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 r179791 = x;
        double r179792 = y;
        double r179793 = r179791 * r179792;
        double r179794 = 2.0;
        double r179795 = r179793 / r179794;
        double r179796 = z;
        double r179797 = 8.0;
        double r179798 = r179796 / r179797;
        double r179799 = r179795 - r179798;
        return r179799;
}
↓
double f(double x, double y, double z) {
        double r179800 = x;
        double r179801 = 1.0;
        double r179802 = r179800 / r179801;
        double r179803 = y;
        double r179804 = 2.0;
        double r179805 = r179803 / r179804;
        double r179806 = z;
        double r179807 = 8.0;
        double r179808 = r179806 / r179807;
        double r179809 = -r179808;
        double r179810 = fma(r179802, r179805, r179809);
        return r179810;
}

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)))