Average Error: 0.0 → 0.0
Time: 855.0ms
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 r175311 = x;
        double r175312 = y;
        double r175313 = r175311 * r175312;
        double r175314 = 2.0;
        double r175315 = r175313 / r175314;
        double r175316 = z;
        double r175317 = 8.0;
        double r175318 = r175316 / r175317;
        double r175319 = r175315 - r175318;
        return r175319;
}
↓
double f(double x, double y, double z) {
        double r175320 = x;
        double r175321 = 1.0;
        double r175322 = r175320 / r175321;
        double r175323 = y;
        double r175324 = 2.0;
        double r175325 = r175323 / r175324;
        double r175326 = z;
        double r175327 = 8.0;
        double r175328 = r175326 / r175327;
        double r175329 = -r175328;
        double r175330 = fma(r175322, r175325, r175329);
        return r175330;
}

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 2020060 +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)))