Average Error: 0.1 → 0.1
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 r243799 = 1.0;
        double r243800 = 2.0;
        double r243801 = r243799 / r243800;
        double r243802 = x;
        double r243803 = y;
        double r243804 = z;
        double r243805 = sqrt(r243804);
        double r243806 = r243803 * r243805;
        double r243807 = r243802 + r243806;
        double r243808 = r243801 * r243807;
        return r243808;
}
↓
double f(double x, double y, double z) {
        double r243809 = 1.0;
        double r243810 = 2.0;
        double r243811 = r243809 / r243810;
        double r243812 = x;
        double r243813 = y;
        double r243814 = z;
        double r243815 = sqrt(r243814);
        double r243816 = r243813 * r243815;
        double r243817 = r243812 + r243816;
        double r243818 = r243811 * r243817;
        return r243818;
}

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 2019356 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))