Average Error: 0.0 → 0.0
Time: 2.3s
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 r17786353 = x;
        double r17786354 = 2.0;
        double r17786355 = r17786353 / r17786354;
        double r17786356 = y;
        double r17786357 = r17786356 * r17786353;
        double r17786358 = r17786355 + r17786357;
        double r17786359 = z;
        double r17786360 = r17786358 + r17786359;
        return r17786360;
}
↓
double f(double x, double y, double z) {
        double r17786361 = x;
        double r17786362 = y;
        double r17786363 = 0.5;
        double r17786364 = r17786362 + r17786363;
        double r17786365 = r17786361 * r17786364;
        double r17786366 = z;
        double r17786367 = r17786365 + r17786366;
        return r17786367;
}

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 2019174 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))