Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\mathsf{fma}\left(x, y, z\right) + \frac{x}{2}\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\mathsf{fma}\left(x, y, z\right) + \frac{x}{2}
double f(double x, double y, double z) {
        double r236205 = x;
        double r236206 = 2.0;
        double r236207 = r236205 / r236206;
        double r236208 = y;
        double r236209 = r236208 * r236205;
        double r236210 = r236207 + r236209;
        double r236211 = z;
        double r236212 = r236210 + r236211;
        return r236212;
}
↓
double f(double x, double y, double z) {
        double r236213 = x;
        double r236214 = y;
        double r236215 = z;
        double r236216 = fma(r236213, r236214, r236215);
        double r236217 = 2.0;
        double r236218 = r236213 / r236217;
        double r236219 = r236216 + r236218;
        return r236219;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(\frac{x}{2} + y \cdot x\right) + z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z\right) + \frac{x}{2}}\]

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))