Average Error: 0.0 → 0.0
Time: 9.0s
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 r22985 = x;
        double r22986 = y;
        double r22987 = r22986 - r22985;
        double r22988 = z;
        double r22989 = r22987 / r22988;
        double r22990 = r22985 + r22989;
        return r22990;
}
↓
double f(double x, double y, double z) {
        double r22991 = x;
        double r22992 = y;
        double r22993 = z;
        double r22994 = r22992 / r22993;
        double r22995 = r22991 + r22994;
        double r22996 = r22991 / r22993;
        double r22997 = r22995 - r22996;
        return r22997;
}

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 2019303 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))