Average Error: 0.0 → 0.0
Time: 4.9s
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 r5911 = x;
        double r5912 = y;
        double r5913 = r5912 - r5911;
        double r5914 = z;
        double r5915 = r5913 / r5914;
        double r5916 = r5911 + r5915;
        return r5916;
}
↓
double f(double x, double y, double z) {
        double r5917 = x;
        double r5918 = y;
        double r5919 = z;
        double r5920 = r5918 / r5919;
        double r5921 = r5917 / r5919;
        double r5922 = r5920 - r5921;
        double r5923 = r5917 + r5922;
        return r5923;
}

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 2020047 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))