Average Error: 0.0 → 0.0
Time: 3.7s
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 r8135248 = x;
        double r8135249 = y;
        double r8135250 = r8135248 * r8135249;
        double r8135251 = 2.0;
        double r8135252 = r8135250 / r8135251;
        double r8135253 = z;
        double r8135254 = 8.0;
        double r8135255 = r8135253 / r8135254;
        double r8135256 = r8135252 - r8135255;
        return r8135256;
}
↓
double f(double x, double y, double z) {
        double r8135257 = x;
        double r8135258 = y;
        double r8135259 = 2.0;
        double r8135260 = r8135258 / r8135259;
        double r8135261 = z;
        double r8135262 = 8.0;
        double r8135263 = r8135261 / r8135262;
        double r8135264 = -r8135263;
        double r8135265 = fma(r8135257, r8135260, r8135264);
        return r8135265;
}

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

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  (- (/ (* x y) 2.0) (/ z 8.0)))