Average Error: 0.0 → 0.0
Time: 4.3s
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 r328582 = x;
        double r328583 = 2.0;
        double r328584 = r328582 / r328583;
        double r328585 = y;
        double r328586 = r328585 * r328582;
        double r328587 = r328584 + r328586;
        double r328588 = z;
        double r328589 = r328587 + r328588;
        return r328589;
}
↓
double f(double x, double y, double z) {
        double r328590 = x;
        double r328591 = y;
        double r328592 = 0.5;
        double r328593 = r328591 + r328592;
        double r328594 = r328590 * r328593;
        double r328595 = z;
        double r328596 = r328594 + r328595;
        return r328596;
}

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 2020046 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))