Average Error: 0.0 → 0.0
Time: 1.1s
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 r178240 = x;
        double r178241 = y;
        double r178242 = r178240 * r178241;
        double r178243 = 2.0;
        double r178244 = r178242 / r178243;
        double r178245 = z;
        double r178246 = 8.0;
        double r178247 = r178245 / r178246;
        double r178248 = r178244 - r178247;
        return r178248;
}
↓
double f(double x, double y, double z) {
        double r178249 = x;
        double r178250 = 1.0;
        double r178251 = r178249 / r178250;
        double r178252 = y;
        double r178253 = 2.0;
        double r178254 = r178252 / r178253;
        double r178255 = z;
        double r178256 = 8.0;
        double r178257 = r178255 / r178256;
        double r178258 = -r178257;
        double r178259 = fma(r178251, r178254, r178258);
        return r178259;
}

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 2020089 +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)))