Average Error: 0.0 → 0.0
Time: 2.0s
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 r10037 = x;
        double r10038 = y;
        double r10039 = r10038 - r10037;
        double r10040 = z;
        double r10041 = r10039 / r10040;
        double r10042 = r10037 + r10041;
        return r10042;
}
↓
double f(double x, double y, double z) {
        double r10043 = x;
        double r10044 = y;
        double r10045 = z;
        double r10046 = r10044 / r10045;
        double r10047 = r10043 / r10045;
        double r10048 = r10046 - r10047;
        double r10049 = r10043 + r10048;
        return r10049;
}

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 2020020 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))