Average Error: 0.0 → 0
Time: 5.7s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)
double f(double x, double y, double z) {
        double r130152 = x;
        double r130153 = y;
        double r130154 = r130152 * r130153;
        double r130155 = 2.0;
        double r130156 = r130154 / r130155;
        double r130157 = z;
        double r130158 = 8.0;
        double r130159 = r130157 / r130158;
        double r130160 = r130156 - r130159;
        return r130160;
}
↓
double f(double x, double y, double z) {
        double r130161 = x;
        double r130162 = y;
        double r130163 = 2.0;
        double r130164 = r130162 / r130163;
        double r130165 = z;
        double r130166 = 8.0;
        double r130167 = r130165 / r130166;
        double r130168 = -r130167;
        double r130169 = fma(r130161, r130164, r130168);
        return r130169;
}

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

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

Reproduce

herbie shell --seed 2019323 +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)))