Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[x \cdot \left(0.5 + y\right) + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
x \cdot \left(0.5 + y\right) + z
double f(double x, double y, double z) {
        double r187021 = x;
        double r187022 = 2.0;
        double r187023 = r187021 / r187022;
        double r187024 = y;
        double r187025 = r187024 * r187021;
        double r187026 = r187023 + r187025;
        double r187027 = z;
        double r187028 = r187026 + r187027;
        return r187028;
}
↓
double f(double x, double y, double z) {
        double r187029 = x;
        double r187030 = 0.5;
        double r187031 = y;
        double r187032 = r187030 + r187031;
        double r187033 = r187029 * r187032;
        double r187034 = z;
        double r187035 = r187033 + r187034;
        return r187035;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))