Average Error: 0.0 → 0.0
Time: 5.9s
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 r211246 = x;
        double r211247 = 2.0;
        double r211248 = r211246 / r211247;
        double r211249 = y;
        double r211250 = r211249 * r211246;
        double r211251 = r211248 + r211250;
        double r211252 = z;
        double r211253 = r211251 + r211252;
        return r211253;
}
↓
double f(double x, double y, double z) {
        double r211254 = x;
        double r211255 = y;
        double r211256 = 0.5;
        double r211257 = r211255 + r211256;
        double r211258 = r211254 * r211257;
        double r211259 = z;
        double r211260 = r211258 + r211259;
        return r211260;
}

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 2019208 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))