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 r13388848 = x;
        double r13388849 = y;
        double r13388850 = r13388848 * r13388849;
        double r13388851 = 2.0;
        double r13388852 = r13388850 / r13388851;
        double r13388853 = z;
        double r13388854 = 8.0;
        double r13388855 = r13388853 / r13388854;
        double r13388856 = r13388852 - r13388855;
        return r13388856;
}
↓
double f(double x, double y, double z) {
        double r13388857 = x;
        double r13388858 = y;
        double r13388859 = 2.0;
        double r13388860 = r13388858 / r13388859;
        double r13388861 = z;
        double r13388862 = 8.0;
        double r13388863 = r13388861 / r13388862;
        double r13388864 = -r13388863;
        double r13388865 = fma(r13388857, r13388860, r13388864);
        return r13388865;
}

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 2019170 +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)))