Average Error: 0.2 → 0.2
Time: 15.2s
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 r200099 = 1.0;
        double r200100 = 2.0;
        double r200101 = r200099 / r200100;
        double r200102 = x;
        double r200103 = y;
        double r200104 = z;
        double r200105 = sqrt(r200104);
        double r200106 = r200103 * r200105;
        double r200107 = r200102 + r200106;
        double r200108 = r200101 * r200107;
        return r200108;
}
↓
double f(double x, double y, double z) {
        double r200109 = 1.0;
        double r200110 = 2.0;
        double r200111 = r200109 / r200110;
        double r200112 = x;
        double r200113 = y;
        double r200114 = z;
        double r200115 = sqrt(r200114);
        double r200116 = r200113 * r200115;
        double r200117 = r200112 + r200116;
        double r200118 = r200111 * r200117;
        return r200118;
}

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 2019209 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))