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 r218137 = x;
        double r218138 = 2.0;
        double r218139 = r218137 / r218138;
        double r218140 = y;
        double r218141 = r218140 * r218137;
        double r218142 = r218139 + r218141;
        double r218143 = z;
        double r218144 = r218142 + r218143;
        return r218144;
}
↓
double f(double x, double y, double z) {
        double r218145 = x;
        double r218146 = y;
        double r218147 = 0.5;
        double r218148 = r218146 + r218147;
        double r218149 = r218145 * r218148;
        double r218150 = z;
        double r218151 = r218149 + r218150;
        return r218151;
}

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 2020081 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))