Average Error: 0.0 → 0
Time: 956.0ms
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 r170221 = x;
        double r170222 = y;
        double r170223 = r170221 * r170222;
        double r170224 = 2.0;
        double r170225 = r170223 / r170224;
        double r170226 = z;
        double r170227 = 8.0;
        double r170228 = r170226 / r170227;
        double r170229 = r170225 - r170228;
        return r170229;
}
↓
double f(double x, double y, double z) {
        double r170230 = x;
        double r170231 = 1.0;
        double r170232 = r170230 / r170231;
        double r170233 = y;
        double r170234 = 2.0;
        double r170235 = r170233 / r170234;
        double r170236 = z;
        double r170237 = 8.0;
        double r170238 = r170236 / r170237;
        double r170239 = -r170238;
        double r170240 = fma(r170232, r170235, r170239);
        return r170240;
}

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

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

Reproduce

herbie shell --seed 2020001 +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)))