Average Error: 0.0 → 0.0
Time: 7.8s
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 r9719 = x;
        double r9720 = y;
        double r9721 = r9720 - r9719;
        double r9722 = z;
        double r9723 = r9721 / r9722;
        double r9724 = r9719 + r9723;
        return r9724;
}
↓
double f(double x, double y, double z) {
        double r9725 = x;
        double r9726 = y;
        double r9727 = z;
        double r9728 = r9726 / r9727;
        double r9729 = r9725 / r9727;
        double r9730 = r9728 - r9729;
        double r9731 = r9725 + r9730;
        return r9731;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\frac{y - x}{z} + x}\]
  3. Using strategy rm

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))