Average Error: 0.0 → 0.0
Time: 4.3s
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 r4776 = x;
        double r4777 = y;
        double r4778 = r4777 - r4776;
        double r4779 = z;
        double r4780 = r4778 / r4779;
        double r4781 = r4776 + r4780;
        return r4781;
}
↓
double f(double x, double y, double z) {
        double r4782 = x;
        double r4783 = y;
        double r4784 = z;
        double r4785 = r4783 / r4784;
        double r4786 = r4782 / r4784;
        double r4787 = r4785 - r4786;
        double r4788 = r4782 + r4787;
        return r4788;
}

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 2020045 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))