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 r14171 = x;
        double r14172 = y;
        double r14173 = r14172 - r14171;
        double r14174 = z;
        double r14175 = r14173 / r14174;
        double r14176 = r14171 + r14175;
        return r14176;
}
↓
double f(double x, double y, double z) {
        double r14177 = x;
        double r14178 = y;
        double r14179 = z;
        double r14180 = r14178 / r14179;
        double r14181 = r14177 / r14179;
        double r14182 = r14180 - r14181;
        double r14183 = r14177 + r14182;
        return r14183;
}

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 2020060 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))