Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[\left(\frac{x}{2.0} + y \cdot x\right) + z\]
↓
\[z + \mathsf{fma}\left(y, x, \frac{x}{2.0}\right)\]
\left(\frac{x}{2.0} + y \cdot x\right) + z
↓
z + \mathsf{fma}\left(y, x, \frac{x}{2.0}\right)
double f(double x, double y, double z) {
        double r3275154 = x;
        double r3275155 = 2.0;
        double r3275156 = r3275154 / r3275155;
        double r3275157 = y;
        double r3275158 = r3275157 * r3275154;
        double r3275159 = r3275156 + r3275158;
        double r3275160 = z;
        double r3275161 = r3275159 + r3275160;
        return r3275161;
}
↓
double f(double x, double y, double z) {
        double r3275162 = z;
        double r3275163 = y;
        double r3275164 = x;
        double r3275165 = 2.0;
        double r3275166 = r3275164 / r3275165;
        double r3275167 = fma(r3275163, r3275164, r3275166);
        double r3275168 = r3275162 + r3275167;
        return r3275168;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(\frac{x}{2.0} + y \cdot x\right) + z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \frac{x}{2.0}\right) + z}\]

  3. Final simplification0.0

    \[\leadsto z + \mathsf{fma}\left(y, x, \frac{x}{2.0}\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))