Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\left(0.5 + y\right) \cdot x + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\left(0.5 + y\right) \cdot x + z
double f(double x, double y, double z) {
        double r14042263 = x;
        double r14042264 = 2.0;
        double r14042265 = r14042263 / r14042264;
        double r14042266 = y;
        double r14042267 = r14042266 * r14042263;
        double r14042268 = r14042265 + r14042267;
        double r14042269 = z;
        double r14042270 = r14042268 + r14042269;
        return r14042270;
}
↓
double f(double x, double y, double z) {
        double r14042271 = 0.5;
        double r14042272 = y;
        double r14042273 = r14042271 + r14042272;
        double r14042274 = x;
        double r14042275 = r14042273 * r14042274;
        double r14042276 = z;
        double r14042277 = r14042275 + r14042276;
        return r14042277;
}

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

    \[\leadsto \color{blue}{0.5 \cdot x + \left(z + x \cdot y\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{z + \left(0.5 + y\right) \cdot x}\]

  4. Final simplification0.0

    \[\leadsto \left(0.5 + y\right) \cdot x + z\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))