Average Error: 0.2 → 0.2
Time: 4.9s
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 r274678 = 1.0;
        double r274679 = 2.0;
        double r274680 = r274678 / r274679;
        double r274681 = x;
        double r274682 = y;
        double r274683 = z;
        double r274684 = sqrt(r274683);
        double r274685 = r274682 * r274684;
        double r274686 = r274681 + r274685;
        double r274687 = r274680 * r274686;
        return r274687;
}
↓
double f(double x, double y, double z) {
        double r274688 = 1.0;
        double r274689 = 2.0;
        double r274690 = r274688 / r274689;
        double r274691 = x;
        double r274692 = y;
        double r274693 = z;
        double r274694 = sqrt(r274693);
        double r274695 = r274692 * r274694;
        double r274696 = r274691 + r274695;
        double r274697 = r274690 * r274696;
        return r274697;
}

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 2020083 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))