Average Error: 0.1 → 0.1
Time: 18.6s
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 r154698 = 1.0;
        double r154699 = 2.0;
        double r154700 = r154698 / r154699;
        double r154701 = x;
        double r154702 = y;
        double r154703 = z;
        double r154704 = sqrt(r154703);
        double r154705 = r154702 * r154704;
        double r154706 = r154701 + r154705;
        double r154707 = r154700 * r154706;
        return r154707;
}
↓
double f(double x, double y, double z) {
        double r154708 = 1.0;
        double r154709 = 2.0;
        double r154710 = r154708 / r154709;
        double r154711 = x;
        double r154712 = y;
        double r154713 = z;
        double r154714 = sqrt(r154713);
        double r154715 = r154712 * r154714;
        double r154716 = r154711 + r154715;
        double r154717 = r154710 * r154716;
        return r154717;
}

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 2019323 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))