Average Error: 0.0 → 0.0
Time: 1.2s
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 r4628 = x;
        double r4629 = y;
        double r4630 = r4629 - r4628;
        double r4631 = z;
        double r4632 = r4630 / r4631;
        double r4633 = r4628 + r4632;
        return r4633;
}
↓
double f(double x, double y, double z) {
        double r4634 = x;
        double r4635 = y;
        double r4636 = z;
        double r4637 = r4635 / r4636;
        double r4638 = r4634 / r4636;
        double r4639 = r4637 - r4638;
        double r4640 = r4634 + r4639;
        return r4640;
}

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 2019353 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))