Average Error: 0.0 → 0.0
Time: 2.8s
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 r236464 = x;
        double r236465 = 2.0;
        double r236466 = r236464 / r236465;
        double r236467 = y;
        double r236468 = r236467 * r236464;
        double r236469 = r236466 + r236468;
        double r236470 = z;
        double r236471 = r236469 + r236470;
        return r236471;
}
↓
double f(double x, double y, double z) {
        double r236472 = x;
        double r236473 = y;
        double r236474 = 0.5;
        double r236475 = r236473 + r236474;
        double r236476 = r236472 * r236475;
        double r236477 = z;
        double r236478 = r236476 + r236477;
        return r236478;
}

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 2020060 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))