Average Error: 0.0 → 0.0
Time: 7.2s
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 r300971 = x;
        double r300972 = 2.0;
        double r300973 = r300971 / r300972;
        double r300974 = y;
        double r300975 = r300974 * r300971;
        double r300976 = r300973 + r300975;
        double r300977 = z;
        double r300978 = r300976 + r300977;
        return r300978;
}
↓
double f(double x, double y, double z) {
        double r300979 = x;
        double r300980 = y;
        double r300981 = 0.5;
        double r300982 = r300980 + r300981;
        double r300983 = r300979 * r300982;
        double r300984 = z;
        double r300985 = r300983 + r300984;
        return r300985;
}

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))