Average Error: 0.0 → 0.0
Time: 3.3s
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 r245073 = x;
        double r245074 = 2.0;
        double r245075 = r245073 / r245074;
        double r245076 = y;
        double r245077 = r245076 * r245073;
        double r245078 = r245075 + r245077;
        double r245079 = z;
        double r245080 = r245078 + r245079;
        return r245080;
}
↓
double f(double x, double y, double z) {
        double r245081 = x;
        double r245082 = y;
        double r245083 = 0.5;
        double r245084 = r245082 + r245083;
        double r245085 = r245081 * r245084;
        double r245086 = z;
        double r245087 = r245085 + r245086;
        return r245087;
}

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 2020018 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))