Average Error: 0.0 → 0.0
Time: 3.7s
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 r14871 = x;
        double r14872 = y;
        double r14873 = r14872 - r14871;
        double r14874 = z;
        double r14875 = r14873 / r14874;
        double r14876 = r14871 + r14875;
        return r14876;
}
↓
double f(double x, double y, double z) {
        double r14877 = x;
        double r14878 = y;
        double r14879 = z;
        double r14880 = r14878 / r14879;
        double r14881 = r14877 + r14880;
        double r14882 = r14877 / r14879;
        double r14883 = r14881 - r14882;
        return r14883;
}

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 2020025 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))