Average Error: 0.0 → 0.0
Time: 1.2s
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 r3414 = x;
        double r3415 = y;
        double r3416 = r3415 - r3414;
        double r3417 = z;
        double r3418 = r3416 / r3417;
        double r3419 = r3414 + r3418;
        return r3419;
}
↓
double f(double x, double y, double z) {
        double r3420 = x;
        double r3421 = y;
        double r3422 = z;
        double r3423 = r3421 / r3422;
        double r3424 = r3420 / r3422;
        double r3425 = r3423 - r3424;
        double r3426 = r3420 + r3425;
        return r3426;
}

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 2020036 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))