Average Error: 0.0 → 0.0
Time: 1.1s
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 r302171 = x;
        double r302172 = 2.0;
        double r302173 = r302171 / r302172;
        double r302174 = y;
        double r302175 = r302174 * r302171;
        double r302176 = r302173 + r302175;
        double r302177 = z;
        double r302178 = r302176 + r302177;
        return r302178;
}
↓
double f(double x, double y, double z) {
        double r302179 = x;
        double r302180 = y;
        double r302181 = 0.5;
        double r302182 = r302180 + r302181;
        double r302183 = r302179 * r302182;
        double r302184 = z;
        double r302185 = r302183 + r302184;
        return r302185;
}

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 2020035 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))