Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[z + \left(0.5 + y\right) \cdot x\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
z + \left(0.5 + y\right) \cdot x
double f(double x, double y, double z) {
        double r195645 = x;
        double r195646 = 2.0;
        double r195647 = r195645 / r195646;
        double r195648 = y;
        double r195649 = r195648 * r195645;
        double r195650 = r195647 + r195649;
        double r195651 = z;
        double r195652 = r195650 + r195651;
        return r195652;
}
↓
double f(double x, double y, double z) {
        double r195653 = z;
        double r195654 = 0.5;
        double r195655 = y;
        double r195656 = r195654 + r195655;
        double r195657 = x;
        double r195658 = r195656 * r195657;
        double r195659 = r195653 + r195658;
        return r195659;
}

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

    \[\leadsto \color{blue}{\left(y + 0.5\right) \cdot x} + z\]

  4. Final simplification0.0

    \[\leadsto z + \left(0.5 + y\right) \cdot x\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))