Average Error: 0.2 → 0.2
Time: 8.6s
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 r271990 = 1.0;
        double r271991 = 2.0;
        double r271992 = r271990 / r271991;
        double r271993 = x;
        double r271994 = y;
        double r271995 = z;
        double r271996 = sqrt(r271995);
        double r271997 = r271994 * r271996;
        double r271998 = r271993 + r271997;
        double r271999 = r271992 * r271998;
        return r271999;
}
↓
double f(double x, double y, double z) {
        double r272000 = 1.0;
        double r272001 = 2.0;
        double r272002 = r272000 / r272001;
        double r272003 = x;
        double r272004 = y;
        double r272005 = z;
        double r272006 = sqrt(r272005);
        double r272007 = r272004 * r272006;
        double r272008 = r272003 + r272007;
        double r272009 = r272002 * r272008;
        return r272009;
}

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 2020047 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))