Average Error: 0.0 → 0
Time: 907.0ms
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 r161561 = x;
        double r161562 = y;
        double r161563 = r161561 * r161562;
        double r161564 = 2.0;
        double r161565 = r161563 / r161564;
        double r161566 = z;
        double r161567 = 8.0;
        double r161568 = r161566 / r161567;
        double r161569 = r161565 - r161568;
        return r161569;
}
↓
double f(double x, double y, double z) {
        double r161570 = x;
        double r161571 = 1.0;
        double r161572 = r161570 / r161571;
        double r161573 = y;
        double r161574 = 2.0;
        double r161575 = r161573 / r161574;
        double r161576 = z;
        double r161577 = 8.0;
        double r161578 = r161576 / r161577;
        double r161579 = -r161578;
        double r161580 = fma(r161572, r161575, r161579);
        return r161580;
}

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

    \[\leadsto \mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)\]

Reproduce

herbie shell --seed 2020001 +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)))