Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\left(0.5 + y\right) \cdot x + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\left(0.5 + y\right) \cdot x + z
double f(double x, double y, double z) {
        double r793758 = x;
        double r793759 = 2.0;
        double r793760 = r793758 / r793759;
        double r793761 = y;
        double r793762 = r793761 * r793758;
        double r793763 = r793760 + r793762;
        double r793764 = z;
        double r793765 = r793763 + r793764;
        return r793765;
}
↓
double f(double x, double y, double z) {
        double r793766 = 0.5;
        double r793767 = y;
        double r793768 = r793766 + r793767;
        double r793769 = x;
        double r793770 = r793768 * r793769;
        double r793771 = z;
        double r793772 = r793770 + r793771;
        return r793772;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))