Average Error: 0.0 → 0.0
Time: 6.8s
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 r140961 = x;
        double r140962 = 2.0;
        double r140963 = r140961 / r140962;
        double r140964 = y;
        double r140965 = r140964 * r140961;
        double r140966 = r140963 + r140965;
        double r140967 = z;
        double r140968 = r140966 + r140967;
        return r140968;
}
↓
double f(double x, double y, double z) {
        double r140969 = x;
        double r140970 = 2.0;
        double r140971 = r140969 / r140970;
        double r140972 = z;
        double r140973 = y;
        double r140974 = r140969 * r140973;
        double r140975 = r140972 + r140974;
        double r140976 = r140971 + r140975;
        return r140976;
}

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))