Average Error: 0.0 → 0.0
Time: 926.0ms
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 r214242 = x;
        double r214243 = y;
        double r214244 = r214242 * r214243;
        double r214245 = 2.0;
        double r214246 = r214244 / r214245;
        double r214247 = z;
        double r214248 = 8.0;
        double r214249 = r214247 / r214248;
        double r214250 = r214246 - r214249;
        return r214250;
}
↓
double f(double x, double y, double z) {
        double r214251 = x;
        double r214252 = 1.0;
        double r214253 = r214251 / r214252;
        double r214254 = y;
        double r214255 = 2.0;
        double r214256 = r214254 / r214255;
        double r214257 = z;
        double r214258 = 8.0;
        double r214259 = r214257 / r214258;
        double r214260 = -r214259;
        double r214261 = fma(r214253, r214256, r214260);
        return r214261;
}

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-neg0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 +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)))