Average Error: 0.0 → 0.0
Time: 888.0ms
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 r216176 = x;
        double r216177 = 2.0;
        double r216178 = r216176 / r216177;
        double r216179 = y;
        double r216180 = r216179 * r216176;
        double r216181 = r216178 + r216180;
        double r216182 = z;
        double r216183 = r216181 + r216182;
        return r216183;
}
↓
double f(double x, double y, double z) {
        double r216184 = x;
        double r216185 = y;
        double r216186 = 0.5;
        double r216187 = r216185 + r216186;
        double r216188 = r216184 * r216187;
        double r216189 = z;
        double r216190 = r216188 + r216189;
        return r216190;
}

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 2020062 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))