Average Error: 0.0 → 0.0
Time: 8.1s
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 r12917 = x;
        double r12918 = y;
        double r12919 = r12918 - r12917;
        double r12920 = z;
        double r12921 = r12919 / r12920;
        double r12922 = r12917 + r12921;
        return r12922;
}
↓
double f(double x, double y, double z) {
        double r12923 = x;
        double r12924 = y;
        double r12925 = z;
        double r12926 = r12924 / r12925;
        double r12927 = r12923 / r12925;
        double r12928 = r12926 - r12927;
        double r12929 = r12923 + r12928;
        return r12929;
}

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 2019323 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))