Average Error: 0.0 → 0.0
Time: 14.9s
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 r17876 = x;
        double r17877 = y;
        double r17878 = r17877 - r17876;
        double r17879 = z;
        double r17880 = r17878 / r17879;
        double r17881 = r17876 + r17880;
        return r17881;
}
↓
double f(double x, double y, double z) {
        double r17882 = x;
        double r17883 = y;
        double r17884 = z;
        double r17885 = r17883 / r17884;
        double r17886 = r17882 / r17884;
        double r17887 = r17885 - r17886;
        double r17888 = r17882 + r17887;
        return r17888;
}

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