Average Error: 0.0 → 0.0
Time: 8.1s
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 r17742 = x;
        double r17743 = y;
        double r17744 = r17743 - r17742;
        double r17745 = z;
        double r17746 = r17744 / r17745;
        double r17747 = r17742 + r17746;
        return r17747;
}
↓
double f(double x, double y, double z) {
        double r17748 = x;
        double r17749 = y;
        double r17750 = z;
        double r17751 = r17749 / r17750;
        double r17752 = r17748 / r17750;
        double r17753 = r17751 - r17752;
        double r17754 = r17748 + r17753;
        return r17754;
}

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 2019298 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))