Average Error: 0.0 → 0.0
Time: 987.0ms
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 r216162 = x;
        double r216163 = y;
        double r216164 = r216162 * r216163;
        double r216165 = 2.0;
        double r216166 = r216164 / r216165;
        double r216167 = z;
        double r216168 = 8.0;
        double r216169 = r216167 / r216168;
        double r216170 = r216166 - r216169;
        return r216170;
}
↓
double f(double x, double y, double z) {
        double r216171 = x;
        double r216172 = 1.0;
        double r216173 = r216171 / r216172;
        double r216174 = y;
        double r216175 = 2.0;
        double r216176 = r216174 / r216175;
        double r216177 = z;
        double r216178 = 8.0;
        double r216179 = r216177 / r216178;
        double r216180 = -r216179;
        double r216181 = fma(r216173, r216176, r216180);
        return r216181;
}

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 2019362 +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)))