Average Error: 0.0 → 0.0
Time: 7.5s
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 r160336 = x;
        double r160337 = 2.0;
        double r160338 = r160336 / r160337;
        double r160339 = y;
        double r160340 = r160339 * r160336;
        double r160341 = r160338 + r160340;
        double r160342 = z;
        double r160343 = r160341 + r160342;
        return r160343;
}
↓
double f(double x, double y, double z) {
        double r160344 = z;
        double r160345 = x;
        double r160346 = y;
        double r160347 = 0.5;
        double r160348 = r160346 + r160347;
        double r160349 = r160345 * r160348;
        double r160350 = r160344 + r160349;
        return r160350;
}

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 2019323 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))