Average Error: 0.0 → 0.0
Time: 538.0ms
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\mathsf{fma}\left(x, y, \frac{x}{2}\right) + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\mathsf{fma}\left(x, y, \frac{x}{2}\right) + z
double f(double x, double y, double z) {
        double r29990 = x;
        double r29991 = 2.0;
        double r29992 = r29990 / r29991;
        double r29993 = y;
        double r29994 = r29993 * r29990;
        double r29995 = r29992 + r29994;
        double r29996 = z;
        double r29997 = r29995 + r29996;
        return r29997;
}
↓
double f(double x, double y, double z) {
        double r29998 = x;
        double r29999 = y;
        double r30000 = 2.0;
        double r30001 = r29998 / r30000;
        double r30002 = fma(r29998, r29999, r30001);
        double r30003 = z;
        double r30004 = r30002 + r30003;
        return r30004;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +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))