Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[y \cdot x + \left(0.5 \cdot x + z\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
y \cdot x + \left(0.5 \cdot x + z\right)
double f(double x, double y, double z) {
        double r243887 = x;
        double r243888 = 2.0;
        double r243889 = r243887 / r243888;
        double r243890 = y;
        double r243891 = r243890 * r243887;
        double r243892 = r243889 + r243891;
        double r243893 = z;
        double r243894 = r243892 + r243893;
        return r243894;
}
↓
double f(double x, double y, double z) {
        double r243895 = y;
        double r243896 = x;
        double r243897 = r243895 * r243896;
        double r243898 = 0.5;
        double r243899 = r243898 * r243896;
        double r243900 = z;
        double r243901 = r243899 + r243900;
        double r243902 = r243897 + r243901;
        return r243902;
}

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. Using strategy rm

  5. Applied distribute-rgt-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))