Average Error: 0.0 → 0.0
Time: 2.0s
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 r271181 = x;
        double r271182 = 2.0;
        double r271183 = r271181 / r271182;
        double r271184 = y;
        double r271185 = r271184 * r271181;
        double r271186 = r271183 + r271185;
        double r271187 = z;
        double r271188 = r271186 + r271187;
        return r271188;
}
↓
double f(double x, double y, double z) {
        double r271189 = x;
        double r271190 = y;
        double r271191 = 0.5;
        double r271192 = r271190 + r271191;
        double r271193 = r271189 * r271192;
        double r271194 = z;
        double r271195 = r271193 + r271194;
        return r271195;
}

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 2020046 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))