Average Error: 0.1 → 0
Time: 1.3s
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 r184298 = x;
        double r184299 = y;
        double r184300 = r184298 * r184299;
        double r184301 = 2.0;
        double r184302 = r184300 / r184301;
        double r184303 = z;
        double r184304 = 8.0;
        double r184305 = r184303 / r184304;
        double r184306 = r184302 - r184305;
        return r184306;
}
↓
double f(double x, double y, double z) {
        double r184307 = x;
        double r184308 = 1.0;
        double r184309 = r184307 / r184308;
        double r184310 = y;
        double r184311 = 2.0;
        double r184312 = r184310 / r184311;
        double r184313 = z;
        double r184314 = 8.0;
        double r184315 = r184313 / r184314;
        double r184316 = -r184315;
        double r184317 = fma(r184309, r184312, r184316);
        return r184317;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[\frac{x \cdot y}{2} - \frac{z}{8}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.1

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

  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 2020036 +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)))