Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[x \cdot \left(y + 0.5\right) + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
x \cdot \left(y + 0.5\right) + z
double f(double x, double y, double z) {
        double r284698 = x;
        double r284699 = 2.0;
        double r284700 = r284698 / r284699;
        double r284701 = y;
        double r284702 = r284701 * r284698;
        double r284703 = r284700 + r284702;
        double r284704 = z;
        double r284705 = r284703 + r284704;
        return r284705;
}
↓
double f(double x, double y, double z) {
        double r284706 = x;
        double r284707 = y;
        double r284708 = 0.5;
        double r284709 = r284707 + r284708;
        double r284710 = r284706 * r284709;
        double r284711 = z;
        double r284712 = r284710 + r284711;
        return r284712;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot x + x \cdot y\right)} + z\]

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(y + 0.5\right)} + z\]

  4. Final simplification0.0

    \[\leadsto x \cdot \left(y + 0.5\right) + z\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))