Average Error: 0.0 → 0.0
Time: 7.6s
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 r98 = x;
        double r99 = y;
        double r100 = r99 - r98;
        double r101 = z;
        double r102 = r100 / r101;
        double r103 = r98 + r102;
        return r103;
}
↓
double f(double x, double y, double z) {
        double r104 = x;
        double r105 = y;
        double r106 = z;
        double r107 = r105 / r106;
        double r108 = r104 / r106;
        double r109 = r107 - r108;
        double r110 = r104 + r109;
        return r110;
}

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 2020025 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))