Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[x + \frac{y - x}{z}\]
↓
\[\left(x + \frac{y}{z}\right) - \frac{x}{z}\]
x + \frac{y - x}{z}
↓
\left(x + \frac{y}{z}\right) - \frac{x}{z}
double f(double x, double y, double z) {
        double r8661 = x;
        double r8662 = y;
        double r8663 = r8662 - r8661;
        double r8664 = z;
        double r8665 = r8663 / r8664;
        double r8666 = r8661 + r8665;
        return r8666;
}
↓
double f(double x, double y, double z) {
        double r8667 = x;
        double r8668 = y;
        double r8669 = z;
        double r8670 = r8668 / r8669;
        double r8671 = r8667 + r8670;
        double r8672 = r8667 / r8669;
        double r8673 = r8671 - r8672;
        return r8673;
}

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. Applied associate-+r-0.0

    \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}}\]

  5. Final simplification0.0

    \[\leadsto \left(x + \frac{y}{z}\right) - \frac{x}{z}\]

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))