Average Error: 0.2 → 0.2
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 r191842 = 1.0;
        double r191843 = 2.0;
        double r191844 = r191842 / r191843;
        double r191845 = x;
        double r191846 = y;
        double r191847 = z;
        double r191848 = sqrt(r191847);
        double r191849 = r191846 * r191848;
        double r191850 = r191845 + r191849;
        double r191851 = r191844 * r191850;
        return r191851;
}
↓
double f(double x, double y, double z) {
        double r191852 = 1.0;
        double r191853 = 2.0;
        double r191854 = r191852 / r191853;
        double r191855 = x;
        double r191856 = y;
        double r191857 = z;
        double r191858 = sqrt(r191857);
        double r191859 = r191856 * r191858;
        double r191860 = r191855 + r191859;
        double r191861 = r191854 * r191860;
        return r191861;
}

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 2020002 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))