Average Error: 0.0 → 0.0
Time: 819.0ms
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 r270576 = x;
        double r270577 = 2.0;
        double r270578 = r270576 / r270577;
        double r270579 = y;
        double r270580 = r270579 * r270576;
        double r270581 = r270578 + r270580;
        double r270582 = z;
        double r270583 = r270581 + r270582;
        return r270583;
}
↓
double f(double x, double y, double z) {
        double r270584 = x;
        double r270585 = y;
        double r270586 = 0.5;
        double r270587 = r270585 + r270586;
        double r270588 = r270584 * r270587;
        double r270589 = z;
        double r270590 = r270588 + r270589;
        return r270590;
}

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

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

  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 2020057 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))