Average Error: 0.0 → 0.0
Time: 12.3s
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 r11222730 = x;
        double r11222731 = 2.0;
        double r11222732 = r11222730 / r11222731;
        double r11222733 = y;
        double r11222734 = r11222733 * r11222730;
        double r11222735 = r11222732 + r11222734;
        double r11222736 = z;
        double r11222737 = r11222735 + r11222736;
        return r11222737;
}
↓
double f(double x, double y, double z) {
        double r11222738 = z;
        double r11222739 = 0.5;
        double r11222740 = y;
        double r11222741 = r11222739 + r11222740;
        double r11222742 = x;
        double r11222743 = r11222741 * r11222742;
        double r11222744 = r11222738 + r11222743;
        return r11222744;
}

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

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

  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))