Average Error: 0.0 → 0.0
Time: 3.9s
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 r8420835 = x;
        double r8420836 = y;
        double r8420837 = r8420835 * r8420836;
        double r8420838 = 2.0;
        double r8420839 = r8420837 / r8420838;
        double r8420840 = z;
        double r8420841 = 8.0;
        double r8420842 = r8420840 / r8420841;
        double r8420843 = r8420839 - r8420842;
        return r8420843;
}
↓
double f(double x, double y, double z) {
        double r8420844 = x;
        double r8420845 = y;
        double r8420846 = 2.0;
        double r8420847 = r8420845 / r8420846;
        double r8420848 = z;
        double r8420849 = 8.0;
        double r8420850 = r8420848 / r8420849;
        double r8420851 = -r8420850;
        double r8420852 = fma(r8420844, r8420847, r8420851);
        return r8420852;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  (- (/ (* x y) 2.0) (/ z 8.0)))