Average Error: 0.0 → 0.0
Time: 7.4s
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 r830642 = x;
        double r830643 = 2.0;
        double r830644 = r830642 / r830643;
        double r830645 = y;
        double r830646 = r830645 * r830642;
        double r830647 = r830644 + r830646;
        double r830648 = z;
        double r830649 = r830647 + r830648;
        return r830649;
}
↓
double f(double x, double y, double z) {
        double r830650 = x;
        double r830651 = y;
        double r830652 = 0.5;
        double r830653 = r830651 + r830652;
        double r830654 = r830650 * r830653;
        double r830655 = z;
        double r830656 = r830654 + r830655;
        return r830656;
}

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 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))