Average Error: 0.0 → 0.0
Time: 2.4s
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 r10463 = x;
        double r10464 = y;
        double r10465 = r10464 - r10463;
        double r10466 = z;
        double r10467 = r10465 / r10466;
        double r10468 = r10463 + r10467;
        return r10468;
}
↓
double f(double x, double y, double z) {
        double r10469 = x;
        double r10470 = y;
        double r10471 = z;
        double r10472 = r10470 / r10471;
        double r10473 = r10469 / r10471;
        double r10474 = r10472 - r10473;
        double r10475 = r10469 + r10474;
        return r10475;
}

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 2020002 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))