Average Error: 0.0 → 0.0
Time: 5.4s
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 r148124 = x;
        double r148125 = 2.0;
        double r148126 = r148124 / r148125;
        double r148127 = y;
        double r148128 = r148127 * r148124;
        double r148129 = r148126 + r148128;
        double r148130 = z;
        double r148131 = r148129 + r148130;
        return r148131;
}
↓
double f(double x, double y, double z) {
        double r148132 = x;
        double r148133 = y;
        double r148134 = 2.0;
        double r148135 = r148132 / r148134;
        double r148136 = fma(r148132, r148133, r148135);
        double r148137 = z;
        double r148138 = r148136 + r148137;
        return r148138;
}

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 2019323 +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))