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 r10826 = x;
        double r10827 = y;
        double r10828 = r10827 - r10826;
        double r10829 = z;
        double r10830 = r10828 / r10829;
        double r10831 = r10826 + r10830;
        return r10831;
}
↓
double f(double x, double y, double z) {
        double r10832 = x;
        double r10833 = y;
        double r10834 = z;
        double r10835 = r10833 / r10834;
        double r10836 = r10832 + r10835;
        double r10837 = r10832 / r10834;
        double r10838 = r10836 - r10837;
        return r10838;
}

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 2019322 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))