Average Error: 0.0 → 0.0
Time: 4.8s
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 r265155 = x;
        double r265156 = 2.0;
        double r265157 = r265155 / r265156;
        double r265158 = y;
        double r265159 = r265158 * r265155;
        double r265160 = r265157 + r265159;
        double r265161 = z;
        double r265162 = r265160 + r265161;
        return r265162;
}
↓
double f(double x, double y, double z) {
        double r265163 = x;
        double r265164 = y;
        double r265165 = 0.5;
        double r265166 = r265164 + r265165;
        double r265167 = r265163 * r265166;
        double r265168 = z;
        double r265169 = r265167 + r265168;
        return r265169;
}

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 2020045 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))