Average Error: 0.0 → 0.0
Time: 7.5s
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 r17116 = x;
        double r17117 = y;
        double r17118 = r17117 - r17116;
        double r17119 = z;
        double r17120 = r17118 / r17119;
        double r17121 = r17116 + r17120;
        return r17121;
}
↓
double f(double x, double y, double z) {
        double r17122 = x;
        double r17123 = y;
        double r17124 = z;
        double r17125 = r17123 / r17124;
        double r17126 = r17122 / r17124;
        double r17127 = r17125 - r17126;
        double r17128 = r17122 + r17127;
        return r17128;
}

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 2019297 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))