Average Error: 0.0 → 0.0
Time: 12.2s
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 r14801 = x;
        double r14802 = y;
        double r14803 = r14802 - r14801;
        double r14804 = z;
        double r14805 = r14803 / r14804;
        double r14806 = r14801 + r14805;
        return r14806;
}
↓
double f(double x, double y, double z) {
        double r14807 = x;
        double r14808 = y;
        double r14809 = z;
        double r14810 = r14808 / r14809;
        double r14811 = r14807 + r14810;
        double r14812 = r14807 / r14809;
        double r14813 = r14811 - r14812;
        return r14813;
}

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 2019326 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))