Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[x \cdot \left(y + \frac{1}{2}\right) + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
x \cdot \left(y + \frac{1}{2}\right) + z
double f(double x, double y, double z) {
        double r206607 = x;
        double r206608 = 2.0;
        double r206609 = r206607 / r206608;
        double r206610 = y;
        double r206611 = r206610 * r206607;
        double r206612 = r206609 + r206611;
        double r206613 = z;
        double r206614 = r206612 + r206613;
        return r206614;
}
↓
double f(double x, double y, double z) {
        double r206615 = x;
        double r206616 = y;
        double r206617 = 1.0;
        double r206618 = 2.0;
        double r206619 = r206617 / r206618;
        double r206620 = r206616 + r206619;
        double r206621 = r206615 * r206620;
        double r206622 = z;
        double r206623 = r206621 + r206622;
        return r206623;
}

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

    \[\leadsto \color{blue}{x \cdot \left(y + \frac{1}{2}\right)} + z\]

  4. Final simplification0.0

    \[\leadsto x \cdot \left(y + \frac{1}{2}\right) + z\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))