Average Error: 0.0 → 0.0
Time: 7.4s
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 r203269 = x;
        double r203270 = 2.0;
        double r203271 = r203269 / r203270;
        double r203272 = y;
        double r203273 = r203272 * r203269;
        double r203274 = r203271 + r203273;
        double r203275 = z;
        double r203276 = r203274 + r203275;
        return r203276;
}
↓
double f(double x, double y, double z) {
        double r203277 = x;
        double r203278 = 2.0;
        double r203279 = r203277 / r203278;
        double r203280 = z;
        double r203281 = y;
        double r203282 = r203277 * r203281;
        double r203283 = r203280 + r203282;
        double r203284 = r203279 + r203283;
        return r203284;
}

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))