Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[y \cdot x + \left(0.5 \cdot x + z\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
y \cdot x + \left(0.5 \cdot x + z\right)
double f(double x, double y, double z) {
        double r336283 = x;
        double r336284 = 2.0;
        double r336285 = r336283 / r336284;
        double r336286 = y;
        double r336287 = r336286 * r336283;
        double r336288 = r336285 + r336287;
        double r336289 = z;
        double r336290 = r336288 + r336289;
        return r336290;
}
↓
double f(double x, double y, double z) {
        double r336291 = y;
        double r336292 = x;
        double r336293 = r336291 * r336292;
        double r336294 = 0.5;
        double r336295 = r336294 * r336292;
        double r336296 = z;
        double r336297 = r336295 + r336296;
        double r336298 = r336293 + r336297;
        return r336298;
}

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

    \[\leadsto \color{blue}{x \cdot \left(y + 0.5\right) + z}\]
  4. Using strategy rm

  5. Applied distribute-rgt-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))