Average Error: 0.0 → 0
Time: 892.0ms
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 r153825 = x;
        double r153826 = y;
        double r153827 = r153825 * r153826;
        double r153828 = 2.0;
        double r153829 = r153827 / r153828;
        double r153830 = z;
        double r153831 = 8.0;
        double r153832 = r153830 / r153831;
        double r153833 = r153829 - r153832;
        return r153833;
}
↓
double f(double x, double y, double z) {
        double r153834 = x;
        double r153835 = 1.0;
        double r153836 = r153834 / r153835;
        double r153837 = y;
        double r153838 = 2.0;
        double r153839 = r153837 / r153838;
        double r153840 = z;
        double r153841 = 8.0;
        double r153842 = r153840 / r153841;
        double r153843 = -r153842;
        double r153844 = fma(r153836, r153839, r153843);
        return r153844;
}

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 2020027 +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)))