Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[\frac{x \cdot y}{2.0} - \frac{z}{8.0}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)\]
\frac{x \cdot y}{2.0} - \frac{z}{8.0}
↓
\mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)
double f(double x, double y, double z) {
        double r9517134 = x;
        double r9517135 = y;
        double r9517136 = r9517134 * r9517135;
        double r9517137 = 2.0;
        double r9517138 = r9517136 / r9517137;
        double r9517139 = z;
        double r9517140 = 8.0;
        double r9517141 = r9517139 / r9517140;
        double r9517142 = r9517138 - r9517141;
        return r9517142;
}
↓
double f(double x, double y, double z) {
        double r9517143 = x;
        double r9517144 = y;
        double r9517145 = 2.0;
        double r9517146 = r9517144 / r9517145;
        double r9517147 = z;
        double r9517148 = 8.0;
        double r9517149 = r9517147 / r9517148;
        double r9517150 = -r9517149;
        double r9517151 = fma(r9517143, r9517146, r9517150);
        return r9517151;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\frac{x \cdot y}{2.0} - \frac{z}{8.0}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2.0}} - \frac{z}{8.0}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2.0}} - \frac{z}{8.0}\]

  5. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2.0}, -\frac{z}{8.0}\right)}\]

  6. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)\]

Reproduce

herbie shell --seed 2019158 +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)))