Average Error: 0.0 → 0.0
Time: 11.3s
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 r15917 = x;
        double r15918 = y;
        double r15919 = r15918 - r15917;
        double r15920 = z;
        double r15921 = r15919 / r15920;
        double r15922 = r15917 + r15921;
        return r15922;
}
↓
double f(double x, double y, double z) {
        double r15923 = x;
        double r15924 = y;
        double r15925 = z;
        double r15926 = r15924 / r15925;
        double r15927 = r15923 / r15925;
        double r15928 = r15926 - r15927;
        double r15929 = r15923 + r15928;
        return r15929;
}

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