Average Error: 0.0 → 0
Time: 899.0ms
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 r167812 = x;
        double r167813 = y;
        double r167814 = r167812 * r167813;
        double r167815 = 2.0;
        double r167816 = r167814 / r167815;
        double r167817 = z;
        double r167818 = 8.0;
        double r167819 = r167817 / r167818;
        double r167820 = r167816 - r167819;
        return r167820;
}
↓
double f(double x, double y, double z) {
        double r167821 = x;
        double r167822 = 1.0;
        double r167823 = r167821 / r167822;
        double r167824 = y;
        double r167825 = 2.0;
        double r167826 = r167824 / r167825;
        double r167827 = z;
        double r167828 = 8.0;
        double r167829 = r167827 / r167828;
        double r167830 = -r167829;
        double r167831 = fma(r167823, r167826, r167830);
        return r167831;
}

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 2020039 +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)))