Average Error: 0.0 → 0.0
Time: 976.0ms
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 r232560 = x;
        double r232561 = 2.0;
        double r232562 = r232560 / r232561;
        double r232563 = y;
        double r232564 = r232563 * r232560;
        double r232565 = r232562 + r232564;
        double r232566 = z;
        double r232567 = r232565 + r232566;
        return r232567;
}
↓
double f(double x, double y, double z) {
        double r232568 = x;
        double r232569 = y;
        double r232570 = 0.5;
        double r232571 = r232569 + r232570;
        double r232572 = r232568 * r232571;
        double r232573 = z;
        double r232574 = r232572 + r232573;
        return r232574;
}

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 2020083 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))