Average Error: 0.0 → 0
Time: 796.0ms
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 r172828 = x;
        double r172829 = y;
        double r172830 = r172828 * r172829;
        double r172831 = 2.0;
        double r172832 = r172830 / r172831;
        double r172833 = z;
        double r172834 = 8.0;
        double r172835 = r172833 / r172834;
        double r172836 = r172832 - r172835;
        return r172836;
}
↓
double f(double x, double y, double z) {
        double r172837 = x;
        double r172838 = 1.0;
        double r172839 = r172837 / r172838;
        double r172840 = y;
        double r172841 = 2.0;
        double r172842 = r172840 / r172841;
        double r172843 = z;
        double r172844 = 8.0;
        double r172845 = r172843 / r172844;
        double r172846 = -r172845;
        double r172847 = fma(r172839, r172842, r172846);
        return r172847;
}

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 2020065 +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)))