Average Error: 0.0 → 0.0
Time: 1.3s
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 r6968 = x;
        double r6969 = y;
        double r6970 = r6969 - r6968;
        double r6971 = z;
        double r6972 = r6970 / r6971;
        double r6973 = r6968 + r6972;
        return r6973;
}
↓
double f(double x, double y, double z) {
        double r6974 = x;
        double r6975 = y;
        double r6976 = z;
        double r6977 = r6975 / r6976;
        double r6978 = r6974 / r6976;
        double r6979 = r6977 - r6978;
        double r6980 = r6974 + r6979;
        return r6980;
}

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 2020020 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))