Average Error: 0.0 → 0.0
Time: 883.0ms
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 r238046 = x;
        double r238047 = 2.0;
        double r238048 = r238046 / r238047;
        double r238049 = y;
        double r238050 = r238049 * r238046;
        double r238051 = r238048 + r238050;
        double r238052 = z;
        double r238053 = r238051 + r238052;
        return r238053;
}
↓
double f(double x, double y, double z) {
        double r238054 = x;
        double r238055 = y;
        double r238056 = 0.5;
        double r238057 = r238055 + r238056;
        double r238058 = r238054 * r238057;
        double r238059 = z;
        double r238060 = r238058 + r238059;
        return r238060;
}

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 2020062 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))