Average Error: 0.0 → 0.0
Time: 15.7s
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 r16946 = x;
        double r16947 = y;
        double r16948 = r16947 - r16946;
        double r16949 = z;
        double r16950 = r16948 / r16949;
        double r16951 = r16946 + r16950;
        return r16951;
}
↓
double f(double x, double y, double z) {
        double r16952 = x;
        double r16953 = y;
        double r16954 = z;
        double r16955 = r16953 / r16954;
        double r16956 = r16952 / r16954;
        double r16957 = r16955 - r16956;
        double r16958 = r16952 + r16957;
        return r16958;
}

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 2019325 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))