Average Error: 0.0 → 0.0
Time: 751.0ms
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 r178507 = x;
        double r178508 = y;
        double r178509 = r178507 * r178508;
        double r178510 = 2.0;
        double r178511 = r178509 / r178510;
        double r178512 = z;
        double r178513 = 8.0;
        double r178514 = r178512 / r178513;
        double r178515 = r178511 - r178514;
        return r178515;
}
↓
double f(double x, double y, double z) {
        double r178516 = x;
        double r178517 = 1.0;
        double r178518 = r178516 / r178517;
        double r178519 = y;
        double r178520 = 2.0;
        double r178521 = r178519 / r178520;
        double r178522 = z;
        double r178523 = 8.0;
        double r178524 = r178522 / r178523;
        double r178525 = -r178524;
        double r178526 = fma(r178518, r178521, r178525);
        return r178526;
}

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 2020056 +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)))