Average Error: 0.0 → 0.0
Time: 7.3s
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 r224092 = x;
        double r224093 = 2.0;
        double r224094 = r224092 / r224093;
        double r224095 = y;
        double r224096 = r224095 * r224092;
        double r224097 = r224094 + r224096;
        double r224098 = z;
        double r224099 = r224097 + r224098;
        return r224099;
}
↓
double f(double x, double y, double z) {
        double r224100 = x;
        double r224101 = y;
        double r224102 = 0.5;
        double r224103 = r224101 + r224102;
        double r224104 = r224100 * r224103;
        double r224105 = z;
        double r224106 = r224104 + r224105;
        return r224106;
}

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 2019303 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))