Average Error: 0.0 → 0.0
Time: 12.1s
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 r11093008 = x;
        double r11093009 = 2.0;
        double r11093010 = r11093008 / r11093009;
        double r11093011 = y;
        double r11093012 = r11093011 * r11093008;
        double r11093013 = r11093010 + r11093012;
        double r11093014 = z;
        double r11093015 = r11093013 + r11093014;
        return r11093015;
}
↓
double f(double x, double y, double z) {
        double r11093016 = z;
        double r11093017 = 0.5;
        double r11093018 = y;
        double r11093019 = r11093017 + r11093018;
        double r11093020 = x;
        double r11093021 = r11093019 * r11093020;
        double r11093022 = r11093016 + r11093021;
        return r11093022;
}

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))