Average Error: 0.0 → 0
Time: 1.1s
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 r234272 = x;
        double r234273 = y;
        double r234274 = r234272 * r234273;
        double r234275 = 2.0;
        double r234276 = r234274 / r234275;
        double r234277 = z;
        double r234278 = 8.0;
        double r234279 = r234277 / r234278;
        double r234280 = r234276 - r234279;
        return r234280;
}
↓
double f(double x, double y, double z) {
        double r234281 = x;
        double r234282 = 1.0;
        double r234283 = r234281 / r234282;
        double r234284 = y;
        double r234285 = 2.0;
        double r234286 = r234284 / r234285;
        double r234287 = z;
        double r234288 = 8.0;
        double r234289 = r234287 / r234288;
        double r234290 = -r234289;
        double r234291 = fma(r234283, r234286, r234290);
        return r234291;
}

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 2020035 +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)))