Average Error: 0.0 → 0.0
Time: 2.2s
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 r10737 = x;
        double r10738 = y;
        double r10739 = r10738 - r10737;
        double r10740 = z;
        double r10741 = r10739 / r10740;
        double r10742 = r10737 + r10741;
        return r10742;
}
↓
double f(double x, double y, double z) {
        double r10743 = x;
        double r10744 = y;
        double r10745 = z;
        double r10746 = r10744 / r10745;
        double r10747 = r10743 / r10745;
        double r10748 = r10746 - r10747;
        double r10749 = r10743 + r10748;
        return r10749;
}

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 2020100 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))