Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[x + \frac{y - x}{z}\]
↓
\[x + \left(\frac{y}{z} - \frac{x}{z}\right)\]
x + \frac{y - x}{z}
↓
x + \left(\frac{y}{z} - \frac{x}{z}\right)
double f(double x, double y, double z) {
        double r17895 = x;
        double r17896 = y;
        double r17897 = r17896 - r17895;
        double r17898 = z;
        double r17899 = r17897 / r17898;
        double r17900 = r17895 + r17899;
        return r17900;
}
↓
double f(double x, double y, double z) {
        double r17901 = x;
        double r17902 = y;
        double r17903 = z;
        double r17904 = r17902 / r17903;
        double r17905 = r17901 / r17903;
        double r17906 = r17904 - r17905;
        double r17907 = r17901 + r17906;
        return r17907;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))