Average Error: 0.0 → 0.0
Time: 520.0ms
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 r208119 = x;
        double r208120 = 2.0;
        double r208121 = r208119 / r208120;
        double r208122 = y;
        double r208123 = r208122 * r208119;
        double r208124 = r208121 + r208123;
        double r208125 = z;
        double r208126 = r208124 + r208125;
        return r208126;
}
↓
double f(double x, double y, double z) {
        double r208127 = x;
        double r208128 = y;
        double r208129 = 2.0;
        double r208130 = r208127 / r208129;
        double r208131 = fma(r208127, r208128, r208130);
        double r208132 = z;
        double r208133 = r208131 + r208132;
        return r208133;
}

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))