Average Error: 0.0 → 0.0
Time: 10.7s
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 r13420 = x;
        double r13421 = y;
        double r13422 = r13421 - r13420;
        double r13423 = z;
        double r13424 = r13422 / r13423;
        double r13425 = r13420 + r13424;
        return r13425;
}
↓
double f(double x, double y, double z) {
        double r13426 = x;
        double r13427 = y;
        double r13428 = z;
        double r13429 = r13427 / r13428;
        double r13430 = r13426 / r13428;
        double r13431 = r13429 - r13430;
        double r13432 = r13426 + r13431;
        return r13432;
}

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 2019325 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))