Average Error: 0.0 → 0.0
Time: 14.8s
Precision: 64
\[x + \frac{y - x}{z}\]
↓
\[\left(\frac{y}{z} + x\right) - \frac{x}{z}\]
x + \frac{y - x}{z}
↓
\left(\frac{y}{z} + x\right) - \frac{x}{z}
double f(double x, double y, double z) {
        double r732461 = x;
        double r732462 = y;
        double r732463 = r732462 - r732461;
        double r732464 = z;
        double r732465 = r732463 / r732464;
        double r732466 = r732461 + r732465;
        return r732466;
}
↓
double f(double x, double y, double z) {
        double r732467 = y;
        double r732468 = z;
        double r732469 = r732467 / r732468;
        double r732470 = x;
        double r732471 = r732469 + r732470;
        double r732472 = r732470 / r732468;
        double r732473 = r732471 - r732472;
        return r732473;
}

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

    \[\leadsto \left(\frac{y}{z} + x\right) - \frac{x}{z}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))