Average Error: 0.0 → 0.0
Time: 771.0ms
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 r181361 = x;
        double r181362 = y;
        double r181363 = r181361 * r181362;
        double r181364 = 2.0;
        double r181365 = r181363 / r181364;
        double r181366 = z;
        double r181367 = 8.0;
        double r181368 = r181366 / r181367;
        double r181369 = r181365 - r181368;
        return r181369;
}
↓
double f(double x, double y, double z) {
        double r181370 = x;
        double r181371 = 1.0;
        double r181372 = r181370 / r181371;
        double r181373 = y;
        double r181374 = 2.0;
        double r181375 = r181373 / r181374;
        double r181376 = z;
        double r181377 = 8.0;
        double r181378 = r181376 / r181377;
        double r181379 = -r181378;
        double r181380 = fma(r181372, r181375, r181379);
        return r181380;
}

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 2020046 +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)))