Average Error: 0.0 → 0
Time: 990.0ms
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 r162125 = x;
        double r162126 = y;
        double r162127 = r162125 * r162126;
        double r162128 = 2.0;
        double r162129 = r162127 / r162128;
        double r162130 = z;
        double r162131 = 8.0;
        double r162132 = r162130 / r162131;
        double r162133 = r162129 - r162132;
        return r162133;
}
↓
double f(double x, double y, double z) {
        double r162134 = x;
        double r162135 = 1.0;
        double r162136 = r162134 / r162135;
        double r162137 = y;
        double r162138 = 2.0;
        double r162139 = r162137 / r162138;
        double r162140 = z;
        double r162141 = 8.0;
        double r162142 = r162140 / r162141;
        double r162143 = -r162142;
        double r162144 = fma(r162136, r162139, r162143);
        return r162144;
}

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

    \[\leadsto \mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)\]

Reproduce

herbie shell --seed 2020062 +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)))