Average Error: 0.1 → 0.1
Time: 11.4s
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 r208690 = 1.0;
        double r208691 = 2.0;
        double r208692 = r208690 / r208691;
        double r208693 = x;
        double r208694 = y;
        double r208695 = z;
        double r208696 = sqrt(r208695);
        double r208697 = r208694 * r208696;
        double r208698 = r208693 + r208697;
        double r208699 = r208692 * r208698;
        return r208699;
}
↓
double f(double x, double y, double z) {
        double r208700 = 1.0;
        double r208701 = 2.0;
        double r208702 = r208700 / r208701;
        double r208703 = x;
        double r208704 = y;
        double r208705 = z;
        double r208706 = sqrt(r208705);
        double r208707 = r208704 * r208706;
        double r208708 = r208703 + r208707;
        double r208709 = r208702 * r208708;
        return r208709;
}

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 2019294 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))