Average Error: 0.0 → 0.0
Time: 2.5s
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 r361745 = x;
        double r361746 = 2.0;
        double r361747 = r361745 / r361746;
        double r361748 = y;
        double r361749 = r361748 * r361745;
        double r361750 = r361747 + r361749;
        double r361751 = z;
        double r361752 = r361750 + r361751;
        return r361752;
}
↓
double f(double x, double y, double z) {
        double r361753 = x;
        double r361754 = y;
        double r361755 = 0.5;
        double r361756 = r361754 + r361755;
        double r361757 = r361753 * r361756;
        double r361758 = z;
        double r361759 = r361757 + r361758;
        return r361759;
}

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 2020065 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))