Average Error: 0.0 → 0.0
Time: 1.1s
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 r265363 = x;
        double r265364 = 2.0;
        double r265365 = r265363 / r265364;
        double r265366 = y;
        double r265367 = r265366 * r265363;
        double r265368 = r265365 + r265367;
        double r265369 = z;
        double r265370 = r265368 + r265369;
        return r265370;
}
↓
double f(double x, double y, double z) {
        double r265371 = x;
        double r265372 = y;
        double r265373 = 0.5;
        double r265374 = r265372 + r265373;
        double r265375 = r265371 * r265374;
        double r265376 = z;
        double r265377 = r265375 + r265376;
        return r265377;
}

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 2020036 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))