Average Error: 0.0 → 0.0
Time: 9.0s
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 r18756 = x;
        double r18757 = 2.0;
        double r18758 = r18756 / r18757;
        double r18759 = y;
        double r18760 = r18759 * r18756;
        double r18761 = r18758 + r18760;
        double r18762 = z;
        double r18763 = r18761 + r18762;
        return r18763;
}
↓
double f(double x, double y, double z) {
        double r18764 = x;
        double r18765 = y;
        double r18766 = 0.5;
        double r18767 = r18765 + r18766;
        double r18768 = r18764 * r18767;
        double r18769 = z;
        double r18770 = r18768 + r18769;
        return r18770;
}

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 2019310 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))