Average Error: 0.0 → 0
Time: 831.0ms
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 r194265 = x;
        double r194266 = y;
        double r194267 = r194265 * r194266;
        double r194268 = 2.0;
        double r194269 = r194267 / r194268;
        double r194270 = z;
        double r194271 = 8.0;
        double r194272 = r194270 / r194271;
        double r194273 = r194269 - r194272;
        return r194273;
}
↓
double f(double x, double y, double z) {
        double r194274 = x;
        double r194275 = 1.0;
        double r194276 = r194274 / r194275;
        double r194277 = y;
        double r194278 = 2.0;
        double r194279 = r194277 / r194278;
        double r194280 = z;
        double r194281 = 8.0;
        double r194282 = r194280 / r194281;
        double r194283 = -r194282;
        double r194284 = fma(r194276, r194279, r194283);
        return r194284;
}

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 2020057 +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)))