Average Error: 0.0 → 0.0
Time: 5.3s
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 r309597 = x;
        double r309598 = 2.0;
        double r309599 = r309597 / r309598;
        double r309600 = y;
        double r309601 = r309600 * r309597;
        double r309602 = r309599 + r309601;
        double r309603 = z;
        double r309604 = r309602 + r309603;
        return r309604;
}
↓
double f(double x, double y, double z) {
        double r309605 = x;
        double r309606 = y;
        double r309607 = 0.5;
        double r309608 = r309606 + r309607;
        double r309609 = r309605 * r309608;
        double r309610 = z;
        double r309611 = r309609 + r309610;
        return r309611;
}

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 2020047 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))