Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[x + \frac{y - x}{z}\]
↓
\[\left(x + \frac{y}{z}\right) - \frac{x}{z}\]
x + \frac{y - x}{z}
↓
\left(x + \frac{y}{z}\right) - \frac{x}{z}
double f(double x, double y, double z) {
        double r14794 = x;
        double r14795 = y;
        double r14796 = r14795 - r14794;
        double r14797 = z;
        double r14798 = r14796 / r14797;
        double r14799 = r14794 + r14798;
        return r14799;
}
↓
double f(double x, double y, double z) {
        double r14800 = x;
        double r14801 = y;
        double r14802 = z;
        double r14803 = r14801 / r14802;
        double r14804 = r14800 + r14803;
        double r14805 = r14800 / r14802;
        double r14806 = r14804 - r14805;
        return r14806;
}

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

    \[x + \frac{y - x}{z}\]
  2. Using strategy rm

  3. Applied div-sub0.0

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

  4. Applied associate-+r-0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))