Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[x + \frac{y - x}{z}\]
↓
\[\left(x + \frac{y}{z}\right) - \frac{x}{z}\]
x + \frac{y - x}{z}
↓
\left(x + \frac{y}{z}\right) - \frac{x}{z}
double f(double x, double y, double z) {
        double r15421 = x;
        double r15422 = y;
        double r15423 = r15422 - r15421;
        double r15424 = z;
        double r15425 = r15423 / r15424;
        double r15426 = r15421 + r15425;
        return r15426;
}
↓
double f(double x, double y, double z) {
        double r15427 = x;
        double r15428 = y;
        double r15429 = z;
        double r15430 = r15428 / r15429;
        double r15431 = r15427 + r15430;
        double r15432 = r15427 / r15429;
        double r15433 = r15431 - r15432;
        return r15433;
}

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. Applied associate-+r-0.0

    \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}}\]

  5. Final simplification0.0

    \[\leadsto \left(x + \frac{y}{z}\right) - \frac{x}{z}\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))