Average Error: 0.0 → 0.0
Time: 12.7s
Precision: 64
\[\left(\frac{x}{2.0} + y \cdot x\right) + z\]
↓
\[z + \left(0.5 + y\right) \cdot x\]
\left(\frac{x}{2.0} + y \cdot x\right) + z
↓
z + \left(0.5 + y\right) \cdot x
double f(double x, double y, double z) {
        double r23646479 = x;
        double r23646480 = 2.0;
        double r23646481 = r23646479 / r23646480;
        double r23646482 = y;
        double r23646483 = r23646482 * r23646479;
        double r23646484 = r23646481 + r23646483;
        double r23646485 = z;
        double r23646486 = r23646484 + r23646485;
        return r23646486;
}
↓
double f(double x, double y, double z) {
        double r23646487 = z;
        double r23646488 = 0.5;
        double r23646489 = y;
        double r23646490 = r23646488 + r23646489;
        double r23646491 = x;
        double r23646492 = r23646490 * r23646491;
        double r23646493 = r23646487 + r23646492;
        return r23646493;
}

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

    \[\left(\frac{x}{2.0} + y \cdot x\right) + z\]

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

    \[\leadsto z + \left(0.5 + y\right) \cdot x\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))