Average Error: 0.0 → 0.0
Time: 928.0ms
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 r200123 = x;
        double r200124 = y;
        double r200125 = r200123 * r200124;
        double r200126 = 2.0;
        double r200127 = r200125 / r200126;
        double r200128 = z;
        double r200129 = 8.0;
        double r200130 = r200128 / r200129;
        double r200131 = r200127 - r200130;
        return r200131;
}
↓
double f(double x, double y, double z) {
        double r200132 = x;
        double r200133 = 1.0;
        double r200134 = r200132 / r200133;
        double r200135 = y;
        double r200136 = 2.0;
        double r200137 = r200135 / r200136;
        double r200138 = z;
        double r200139 = 8.0;
        double r200140 = r200138 / r200139;
        double r200141 = -r200140;
        double r200142 = fma(r200134, r200137, r200141);
        return r200142;
}

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 2020018 +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)))