Average Error: 0.0 → 0.0
Time: 2.4s
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 r15519 = x;
        double r15520 = y;
        double r15521 = r15520 - r15519;
        double r15522 = z;
        double r15523 = r15521 / r15522;
        double r15524 = r15519 + r15523;
        return r15524;
}
↓
double f(double x, double y, double z) {
        double r15525 = x;
        double r15526 = y;
        double r15527 = z;
        double r15528 = r15526 / r15527;
        double r15529 = r15525 + r15528;
        double r15530 = r15525 / r15527;
        double r15531 = r15529 - r15530;
        return r15531;
}

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 2020056 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))