Average Error: 0.0 → 0.0
Time: 940.0ms
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 r225024 = x;
        double r225025 = 2.0;
        double r225026 = r225024 / r225025;
        double r225027 = y;
        double r225028 = r225027 * r225024;
        double r225029 = r225026 + r225028;
        double r225030 = z;
        double r225031 = r225029 + r225030;
        return r225031;
}
↓
double f(double x, double y, double z) {
        double r225032 = x;
        double r225033 = y;
        double r225034 = 0.5;
        double r225035 = r225033 + r225034;
        double r225036 = r225032 * r225035;
        double r225037 = z;
        double r225038 = r225036 + r225037;
        return r225038;
}

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 2019353 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))