Average Error: 0.0 → 0.0
Time: 5.0s
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 r6354 = x;
        double r6355 = y;
        double r6356 = r6355 - r6354;
        double r6357 = z;
        double r6358 = r6356 / r6357;
        double r6359 = r6354 + r6358;
        return r6359;
}
↓
double f(double x, double y, double z) {
        double r6360 = x;
        double r6361 = y;
        double r6362 = z;
        double r6363 = r6361 / r6362;
        double r6364 = r6360 / r6362;
        double r6365 = r6363 - r6364;
        double r6366 = r6360 + r6365;
        return r6366;
}

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 2020047 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))