Average Error: 0.0 → 0
Time: 10.0s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)
double f(double x, double y, double z) {
        double r11324426 = x;
        double r11324427 = y;
        double r11324428 = r11324426 * r11324427;
        double r11324429 = 2.0;
        double r11324430 = r11324428 / r11324429;
        double r11324431 = z;
        double r11324432 = 8.0;
        double r11324433 = r11324431 / r11324432;
        double r11324434 = r11324430 - r11324433;
        return r11324434;
}
↓
double f(double x, double y, double z) {
        double r11324435 = x;
        double r11324436 = y;
        double r11324437 = 2.0;
        double r11324438 = r11324436 / r11324437;
        double r11324439 = z;
        double r11324440 = 8.0;
        double r11324441 = r11324439 / r11324440;
        double r11324442 = -r11324441;
        double r11324443 = fma(r11324435, r11324438, r11324442);
        return r11324443;
}

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

    \[\leadsto \mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  (- (/ (* x y) 2.0) (/ z 8.0)))