Average Error: 0.0 → 0.0
Time: 2.0s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(\frac{x}{2}, y, -\frac{z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(\frac{x}{2}, y, -\frac{z}{8}\right)
double f(double x, double y, double z) {
        double r248211 = x;
        double r248212 = y;
        double r248213 = r248211 * r248212;
        double r248214 = 2.0;
        double r248215 = r248213 / r248214;
        double r248216 = z;
        double r248217 = 8.0;
        double r248218 = r248216 / r248217;
        double r248219 = r248215 - r248218;
        return r248219;
}
↓
double f(double x, double y, double z) {
        double r248220 = x;
        double r248221 = 2.0;
        double r248222 = r248220 / r248221;
        double r248223 = y;
        double r248224 = z;
        double r248225 = 8.0;
        double r248226 = r248224 / r248225;
        double r248227 = -r248226;
        double r248228 = fma(r248222, r248223, r248227);
        return r248228;
}

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

    \[\leadsto \frac{x \cdot y}{2} - \color{blue}{1 \cdot \frac{z}{8}}\]

  4. Applied *-un-lft-identity0.0

    \[\leadsto \color{blue}{1 \cdot \frac{x \cdot y}{2}} - 1 \cdot \frac{z}{8}\]

  5. Applied distribute-lft-out--0.0

    \[\leadsto \color{blue}{1 \cdot \left(\frac{x \cdot y}{2} - \frac{z}{8}\right)}\]

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 +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)))