Average Error: 0.0 → 0.0
Time: 14.2s
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 r20274 = x;
        double r20275 = y;
        double r20276 = r20275 - r20274;
        double r20277 = z;
        double r20278 = r20276 / r20277;
        double r20279 = r20274 + r20278;
        return r20279;
}
↓
double f(double x, double y, double z) {
        double r20280 = x;
        double r20281 = y;
        double r20282 = z;
        double r20283 = r20281 / r20282;
        double r20284 = r20280 / r20282;
        double r20285 = r20283 - r20284;
        double r20286 = r20280 + r20285;
        return r20286;
}

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 2019198 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  (+ x (/ (- y x) z)))