Average Error: 0.0 → 0.0
Time: 1.9s
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 r218013 = x;
        double r218014 = 2.0;
        double r218015 = r218013 / r218014;
        double r218016 = y;
        double r218017 = r218016 * r218013;
        double r218018 = r218015 + r218017;
        double r218019 = z;
        double r218020 = r218018 + r218019;
        return r218020;
}
↓
double f(double x, double y, double z) {
        double r218021 = x;
        double r218022 = y;
        double r218023 = 0.5;
        double r218024 = r218022 + r218023;
        double r218025 = r218021 * r218024;
        double r218026 = z;
        double r218027 = r218025 + r218026;
        return r218027;
}

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 2020034 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))