Average Error: 0.0 → 0.0
Time: 14.7s
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 r18581 = x;
        double r18582 = y;
        double r18583 = r18582 - r18581;
        double r18584 = z;
        double r18585 = r18583 / r18584;
        double r18586 = r18581 + r18585;
        return r18586;
}
↓
double f(double x, double y, double z) {
        double r18587 = x;
        double r18588 = y;
        double r18589 = z;
        double r18590 = r18588 / r18589;
        double r18591 = r18587 / r18589;
        double r18592 = r18590 - r18591;
        double r18593 = r18587 + r18592;
        return r18593;
}

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 2019199 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))