Average Error: 0.1 → 0.1
Time: 4.3s
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 r202720 = 1.0;
        double r202721 = 2.0;
        double r202722 = r202720 / r202721;
        double r202723 = x;
        double r202724 = y;
        double r202725 = z;
        double r202726 = sqrt(r202725);
        double r202727 = r202724 * r202726;
        double r202728 = r202723 + r202727;
        double r202729 = r202722 * r202728;
        return r202729;
}
↓
double f(double x, double y, double z) {
        double r202730 = 1.0;
        double r202731 = 2.0;
        double r202732 = r202730 / r202731;
        double r202733 = x;
        double r202734 = y;
        double r202735 = z;
        double r202736 = sqrt(r202735);
        double r202737 = r202734 * r202736;
        double r202738 = r202733 + r202737;
        double r202739 = r202732 * r202738;
        return r202739;
}

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 2020001 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))