Average Error: 0.0 → 0.0
Time: 14.2s
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 r17874 = x;
        double r17875 = y;
        double r17876 = r17875 - r17874;
        double r17877 = z;
        double r17878 = r17876 / r17877;
        double r17879 = r17874 + r17878;
        return r17879;
}
↓
double f(double x, double y, double z) {
        double r17880 = x;
        double r17881 = y;
        double r17882 = z;
        double r17883 = r17881 / r17882;
        double r17884 = r17880 / r17882;
        double r17885 = r17883 - r17884;
        double r17886 = r17880 + r17885;
        return r17886;
}

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)))