Average Error: 0.2 → 0.2
Time: 12.7s
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 r139690 = 1.0;
        double r139691 = 2.0;
        double r139692 = r139690 / r139691;
        double r139693 = x;
        double r139694 = y;
        double r139695 = z;
        double r139696 = sqrt(r139695);
        double r139697 = r139694 * r139696;
        double r139698 = r139693 + r139697;
        double r139699 = r139692 * r139698;
        return r139699;
}
↓
double f(double x, double y, double z) {
        double r139700 = 1.0;
        double r139701 = 2.0;
        double r139702 = r139700 / r139701;
        double r139703 = x;
        double r139704 = y;
        double r139705 = z;
        double r139706 = sqrt(r139705);
        double r139707 = r139704 * r139706;
        double r139708 = r139703 + r139707;
        double r139709 = r139702 * r139708;
        return r139709;
}

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 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))