Average Error: 0.0 → 0.0
Time: 3.2s
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 r2268 = x;
        double r2269 = y;
        double r2270 = r2269 - r2268;
        double r2271 = z;
        double r2272 = r2270 / r2271;
        double r2273 = r2268 + r2272;
        return r2273;
}
↓
double f(double x, double y, double z) {
        double r2274 = x;
        double r2275 = y;
        double r2276 = z;
        double r2277 = r2275 / r2276;
        double r2278 = r2274 / r2276;
        double r2279 = r2277 - r2278;
        double r2280 = r2274 + r2279;
        return r2280;
}

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 2020045 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))