Average Error: 0.0 → 0.0
Time: 4.4s
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 r6184 = x;
        double r6185 = y;
        double r6186 = r6185 - r6184;
        double r6187 = z;
        double r6188 = r6186 / r6187;
        double r6189 = r6184 + r6188;
        return r6189;
}
↓
double f(double x, double y, double z) {
        double r6190 = x;
        double r6191 = y;
        double r6192 = z;
        double r6193 = r6191 / r6192;
        double r6194 = r6190 + r6193;
        double r6195 = r6190 / r6192;
        double r6196 = r6194 - r6195;
        return r6196;
}

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 2020047 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))