Average Error: 0.0 → 0.0
Time: 934.0ms
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 r236843 = x;
        double r236844 = y;
        double r236845 = r236843 * r236844;
        double r236846 = 2.0;
        double r236847 = r236845 / r236846;
        double r236848 = z;
        double r236849 = 8.0;
        double r236850 = r236848 / r236849;
        double r236851 = r236847 - r236850;
        return r236851;
}
↓
double f(double x, double y, double z) {
        double r236852 = x;
        double r236853 = 1.0;
        double r236854 = r236852 / r236853;
        double r236855 = y;
        double r236856 = 2.0;
        double r236857 = r236855 / r236856;
        double r236858 = z;
        double r236859 = 8.0;
        double r236860 = r236858 / r236859;
        double r236861 = -r236860;
        double r236862 = fma(r236854, r236857, r236861);
        return r236862;
}

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 2020002 +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)))