Average Error: 0.0 → 0.0
Time: 29.7s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[z + \left(0.5 + y\right) \cdot x\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
z + \left(0.5 + y\right) \cdot x
double f(double x, double y, double z) {
        double r11573959 = x;
        double r11573960 = 2.0;
        double r11573961 = r11573959 / r11573960;
        double r11573962 = y;
        double r11573963 = r11573962 * r11573959;
        double r11573964 = r11573961 + r11573963;
        double r11573965 = z;
        double r11573966 = r11573964 + r11573965;
        return r11573966;
}
↓
double f(double x, double y, double z) {
        double r11573967 = z;
        double r11573968 = 0.5;
        double r11573969 = y;
        double r11573970 = r11573968 + r11573969;
        double r11573971 = x;
        double r11573972 = r11573970 * r11573971;
        double r11573973 = r11573967 + r11573972;
        return r11573973;
}

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

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))