Average Error: 0.0 → 0.0
Time: 4.8s
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 r184079 = x;
        double r184080 = 2.0;
        double r184081 = r184079 / r184080;
        double r184082 = y;
        double r184083 = r184082 * r184079;
        double r184084 = r184081 + r184083;
        double r184085 = z;
        double r184086 = r184084 + r184085;
        return r184086;
}
↓
double f(double x, double y, double z) {
        double r184087 = x;
        double r184088 = y;
        double r184089 = 0.5;
        double r184090 = r184088 + r184089;
        double r184091 = r184087 * r184090;
        double r184092 = z;
        double r184093 = r184091 + r184092;
        return r184093;
}

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 2019297 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))