Average Error: 0.0 → 0.0
Time: 1.7s
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 r318323 = x;
        double r318324 = 2.0;
        double r318325 = r318323 / r318324;
        double r318326 = y;
        double r318327 = r318326 * r318323;
        double r318328 = r318325 + r318327;
        double r318329 = z;
        double r318330 = r318328 + r318329;
        return r318330;
}
↓
double f(double x, double y, double z) {
        double r318331 = x;
        double r318332 = y;
        double r318333 = 0.5;
        double r318334 = r318332 + r318333;
        double r318335 = r318331 * r318334;
        double r318336 = z;
        double r318337 = r318335 + r318336;
        return r318337;
}

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 2019362 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))