Average Error: 0.0 → 0.0
Time: 979.0ms
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 r252850 = x;
        double r252851 = 2.0;
        double r252852 = r252850 / r252851;
        double r252853 = y;
        double r252854 = r252853 * r252850;
        double r252855 = r252852 + r252854;
        double r252856 = z;
        double r252857 = r252855 + r252856;
        return r252857;
}
↓
double f(double x, double y, double z) {
        double r252858 = x;
        double r252859 = y;
        double r252860 = 0.5;
        double r252861 = r252859 + r252860;
        double r252862 = r252858 * r252861;
        double r252863 = z;
        double r252864 = r252862 + r252863;
        return r252864;
}

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 2020100 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))