Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[\left(\frac{x}{2.0} + y \cdot x\right) + z\]
↓
\[z + \left(0.5 + y\right) \cdot x\]
\left(\frac{x}{2.0} + y \cdot x\right) + z
↓
z + \left(0.5 + y\right) \cdot x
double f(double x, double y, double z) {
        double r13630657 = x;
        double r13630658 = 2.0;
        double r13630659 = r13630657 / r13630658;
        double r13630660 = y;
        double r13630661 = r13630660 * r13630657;
        double r13630662 = r13630659 + r13630661;
        double r13630663 = z;
        double r13630664 = r13630662 + r13630663;
        return r13630664;
}
↓
double f(double x, double y, double z) {
        double r13630665 = z;
        double r13630666 = 0.5;
        double r13630667 = y;
        double r13630668 = r13630666 + r13630667;
        double r13630669 = x;
        double r13630670 = r13630668 * r13630669;
        double r13630671 = r13630665 + r13630670;
        return r13630671;
}

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

    \[\left(\frac{x}{2.0} + y \cdot x\right) + z\]

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))