Average Error: 0.0 → 0.0
Time: 4.7s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[z + x \cdot \left(y + 0.5\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
z + x \cdot \left(y + 0.5\right)
double f(double x, double y, double z) {
        double r317752 = x;
        double r317753 = 2.0;
        double r317754 = r317752 / r317753;
        double r317755 = y;
        double r317756 = r317755 * r317752;
        double r317757 = r317754 + r317756;
        double r317758 = z;
        double r317759 = r317757 + r317758;
        return r317759;
}
↓
double f(double x, double y, double z) {
        double r317760 = z;
        double r317761 = x;
        double r317762 = y;
        double r317763 = 0.5;
        double r317764 = r317762 + r317763;
        double r317765 = r317761 * r317764;
        double r317766 = r317760 + r317765;
        return r317766;
}

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

    \[\leadsto \color{blue}{0.5 \cdot x + \left(z + x \cdot y\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{z + x \cdot \left(y + 0.5\right)}\]

  4. Final simplification0.0

    \[\leadsto z + x \cdot \left(y + 0.5\right)\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))