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 r10540181 = x;
        double r10540182 = y;
        double r10540183 = r10540181 * r10540182;
        double r10540184 = 2.0;
        double r10540185 = r10540183 / r10540184;
        double r10540186 = z;
        double r10540187 = 8.0;
        double r10540188 = r10540186 / r10540187;
        double r10540189 = r10540185 - r10540188;
        return r10540189;
}
↓
double f(double x, double y, double z) {
        double r10540190 = x;
        double r10540191 = y;
        double r10540192 = 2.0;
        double r10540193 = r10540191 / r10540192;
        double r10540194 = z;
        double r10540195 = 8.0;
        double r10540196 = r10540194 / r10540195;
        double r10540197 = -r10540196;
        double r10540198 = fma(r10540190, r10540193, r10540197);
        return r10540198;
}

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 2019163 +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)))