Average Error: 0.0 → 0.0
Time: 12.3s
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 r11094 = x;
        double r11095 = y;
        double r11096 = r11095 - r11094;
        double r11097 = z;
        double r11098 = r11096 / r11097;
        double r11099 = r11094 + r11098;
        return r11099;
}
↓
double f(double x, double y, double z) {
        double r11100 = x;
        double r11101 = y;
        double r11102 = z;
        double r11103 = r11101 / r11102;
        double r11104 = r11100 / r11102;
        double r11105 = r11103 - r11104;
        double r11106 = r11100 + r11105;
        return r11106;
}

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 2019304 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))