Average Error: 0.0 → 0.0
Time: 8.8s
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 r9184 = x;
        double r9185 = y;
        double r9186 = r9185 - r9184;
        double r9187 = z;
        double r9188 = r9186 / r9187;
        double r9189 = r9184 + r9188;
        return r9189;
}
↓
double f(double x, double y, double z) {
        double r9190 = x;
        double r9191 = y;
        double r9192 = z;
        double r9193 = r9191 / r9192;
        double r9194 = r9190 / r9192;
        double r9195 = r9193 - r9194;
        double r9196 = r9190 + r9195;
        return r9196;
}

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 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))