Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\frac{x}{2} + \left(z + x \cdot y\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\frac{x}{2} + \left(z + x \cdot y\right)
double f(double x, double y, double z) {
        double r139006 = x;
        double r139007 = 2.0;
        double r139008 = r139006 / r139007;
        double r139009 = y;
        double r139010 = r139009 * r139006;
        double r139011 = r139008 + r139010;
        double r139012 = z;
        double r139013 = r139011 + r139012;
        return r139013;
}
↓
double f(double x, double y, double z) {
        double r139014 = x;
        double r139015 = 2.0;
        double r139016 = r139014 / r139015;
        double r139017 = z;
        double r139018 = y;
        double r139019 = r139014 * r139018;
        double r139020 = r139017 + r139019;
        double r139021 = r139016 + r139020;
        return r139021;
}

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. Using strategy rm

  3. Applied associate-+l+0.0

    \[\leadsto \color{blue}{\frac{x}{2} + \left(y \cdot x + z\right)}\]

  4. Simplified0.0

    \[\leadsto \frac{x}{2} + \color{blue}{\left(z + x \cdot y\right)}\]

  5. Final simplification0.0

    \[\leadsto \frac{x}{2} + \left(z + x \cdot y\right)\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))