Average Error: 0.0 → 0.0
Time: 1.7s
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 r815 = x;
        double r816 = y;
        double r817 = r815 * r816;
        double r818 = 2.0;
        double r819 = r817 / r818;
        double r820 = z;
        double r821 = 8.0;
        double r822 = r820 / r821;
        double r823 = r819 - r822;
        return r823;
}
↓
double f(double x, double y, double z) {
        double r824 = x;
        double r825 = 1.0;
        double r826 = r824 / r825;
        double r827 = y;
        double r828 = 2.0;
        double r829 = r827 / r828;
        double r830 = z;
        double r831 = 8.0;
        double r832 = r830 / r831;
        double r833 = -r832;
        double r834 = fma(r826, r829, r833);
        return r834;
}

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 2020025 +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)))