Average Error: 0.0 → 0.0
Time: 2.5s
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 r13871 = x;
        double r13872 = y;
        double r13873 = r13872 - r13871;
        double r13874 = z;
        double r13875 = r13873 / r13874;
        double r13876 = r13871 + r13875;
        return r13876;
}
↓
double f(double x, double y, double z) {
        double r13877 = x;
        double r13878 = y;
        double r13879 = z;
        double r13880 = r13878 / r13879;
        double r13881 = r13877 / r13879;
        double r13882 = r13880 - r13881;
        double r13883 = r13877 + r13882;
        return r13883;
}

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 2020060 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))