Average Error: 0.0 → 0.0
Time: 1.7s
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 r8818 = x;
        double r8819 = y;
        double r8820 = r8819 - r8818;
        double r8821 = z;
        double r8822 = r8820 / r8821;
        double r8823 = r8818 + r8822;
        return r8823;
}
↓
double f(double x, double y, double z) {
        double r8824 = x;
        double r8825 = y;
        double r8826 = z;
        double r8827 = r8825 / r8826;
        double r8828 = r8824 + r8827;
        double r8829 = r8824 / r8826;
        double r8830 = r8828 - r8829;
        return r8830;
}

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 2020057 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))