Average Error: 0.0 → 0.0
Time: 1.0s
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 r268381 = x;
        double r268382 = y;
        double r268383 = r268381 * r268382;
        double r268384 = 2.0;
        double r268385 = r268383 / r268384;
        double r268386 = z;
        double r268387 = 8.0;
        double r268388 = r268386 / r268387;
        double r268389 = r268385 - r268388;
        return r268389;
}
↓
double f(double x, double y, double z) {
        double r268390 = x;
        double r268391 = 1.0;
        double r268392 = r268390 / r268391;
        double r268393 = y;
        double r268394 = 2.0;
        double r268395 = r268393 / r268394;
        double r268396 = z;
        double r268397 = 8.0;
        double r268398 = r268396 / r268397;
        double r268399 = -r268398;
        double r268400 = fma(r268392, r268395, r268399);
        return r268400;
}

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 2020034 +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)))