Average Error: 0.0 → 0.0
Time: 9.6s
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 r16582 = x;
        double r16583 = y;
        double r16584 = r16583 - r16582;
        double r16585 = z;
        double r16586 = r16584 / r16585;
        double r16587 = r16582 + r16586;
        return r16587;
}
↓
double f(double x, double y, double z) {
        double r16588 = x;
        double r16589 = y;
        double r16590 = z;
        double r16591 = r16589 / r16590;
        double r16592 = r16588 / r16590;
        double r16593 = r16591 - r16592;
        double r16594 = r16588 + r16593;
        return r16594;
}

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 2019291 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))