Average Error: 0.0 → 0.0
Time: 2.5s
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 r11132 = x;
        double r11133 = y;
        double r11134 = r11133 - r11132;
        double r11135 = z;
        double r11136 = r11134 / r11135;
        double r11137 = r11132 + r11136;
        return r11137;
}
↓
double f(double x, double y, double z) {
        double r11138 = x;
        double r11139 = y;
        double r11140 = z;
        double r11141 = r11139 / r11140;
        double r11142 = r11138 / r11140;
        double r11143 = r11141 - r11142;
        double r11144 = r11138 + r11143;
        return r11144;
}

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