Average Error: 0.1 → 0.1
Time: 4.7s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
double f(double x, double y, double z) {
        double r291885 = 1.0;
        double r291886 = 2.0;
        double r291887 = r291885 / r291886;
        double r291888 = x;
        double r291889 = y;
        double r291890 = z;
        double r291891 = sqrt(r291890);
        double r291892 = r291889 * r291891;
        double r291893 = r291888 + r291892;
        double r291894 = r291887 * r291893;
        return r291894;
}
↓
double f(double x, double y, double z) {
        double r291895 = 1.0;
        double r291896 = 2.0;
        double r291897 = r291895 / r291896;
        double r291898 = x;
        double r291899 = y;
        double r291900 = z;
        double r291901 = sqrt(r291900);
        double r291902 = r291899 * r291901;
        double r291903 = r291898 + r291902;
        double r291904 = r291897 * r291903;
        return r291904;
}

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 0.1

    \[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.1

    \[\leadsto \frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))