Average Error: 0.0 → 0.0
Time: 1.8s
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 r251904 = x;
        double r251905 = 2.0;
        double r251906 = r251904 / r251905;
        double r251907 = y;
        double r251908 = r251907 * r251904;
        double r251909 = r251906 + r251908;
        double r251910 = z;
        double r251911 = r251909 + r251910;
        return r251911;
}
↓
double f(double x, double y, double z) {
        double r251912 = x;
        double r251913 = y;
        double r251914 = 0.5;
        double r251915 = r251913 + r251914;
        double r251916 = r251912 * r251915;
        double r251917 = z;
        double r251918 = r251916 + r251917;
        return r251918;
}

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

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

  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 2020024 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))