Average Error: 0.0 → 0.0
Time: 868.0ms
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 r191197 = x;
        double r191198 = y;
        double r191199 = r191197 * r191198;
        double r191200 = 2.0;
        double r191201 = r191199 / r191200;
        double r191202 = z;
        double r191203 = 8.0;
        double r191204 = r191202 / r191203;
        double r191205 = r191201 - r191204;
        return r191205;
}
↓
double f(double x, double y, double z) {
        double r191206 = x;
        double r191207 = 1.0;
        double r191208 = r191206 / r191207;
        double r191209 = y;
        double r191210 = 2.0;
        double r191211 = r191209 / r191210;
        double r191212 = z;
        double r191213 = 8.0;
        double r191214 = r191212 / r191213;
        double r191215 = -r191214;
        double r191216 = fma(r191208, r191211, r191215);
        return r191216;
}

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 2020064 +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)))