Average Error: 0.0 → 0.0
Time: 3.4s
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 r3617 = x;
        double r3618 = y;
        double r3619 = r3618 - r3617;
        double r3620 = z;
        double r3621 = r3619 / r3620;
        double r3622 = r3617 + r3621;
        return r3622;
}
↓
double f(double x, double y, double z) {
        double r3623 = x;
        double r3624 = y;
        double r3625 = z;
        double r3626 = r3624 / r3625;
        double r3627 = r3623 / r3625;
        double r3628 = r3626 - r3627;
        double r3629 = r3623 + r3628;
        return r3629;
}

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 2020045 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))