Average Error: 0.1 → 0.1
Time: 11.6s
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 r201838 = 1.0;
        double r201839 = 2.0;
        double r201840 = r201838 / r201839;
        double r201841 = x;
        double r201842 = y;
        double r201843 = z;
        double r201844 = sqrt(r201843);
        double r201845 = r201842 * r201844;
        double r201846 = r201841 + r201845;
        double r201847 = r201840 * r201846;
        return r201847;
}
↓
double f(double x, double y, double z) {
        double r201848 = 1.0;
        double r201849 = 2.0;
        double r201850 = r201848 / r201849;
        double r201851 = x;
        double r201852 = y;
        double r201853 = z;
        double r201854 = sqrt(r201853);
        double r201855 = r201852 * r201854;
        double r201856 = r201851 + r201855;
        double r201857 = r201850 * r201856;
        return r201857;
}

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 2019303 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))