Average Error: 0.0 → 0.0
Time: 2.6s
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 r9890 = x;
        double r9891 = y;
        double r9892 = r9891 - r9890;
        double r9893 = z;
        double r9894 = r9892 / r9893;
        double r9895 = r9890 + r9894;
        return r9895;
}
↓
double f(double x, double y, double z) {
        double r9896 = x;
        double r9897 = y;
        double r9898 = z;
        double r9899 = r9897 / r9898;
        double r9900 = r9896 / r9898;
        double r9901 = r9899 - r9900;
        double r9902 = r9896 + r9901;
        return r9902;
}

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 2019354 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))