Average Error: 0.1 → 0.1
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 r273695 = 1.0;
        double r273696 = 2.0;
        double r273697 = r273695 / r273696;
        double r273698 = x;
        double r273699 = y;
        double r273700 = z;
        double r273701 = sqrt(r273700);
        double r273702 = r273699 * r273701;
        double r273703 = r273698 + r273702;
        double r273704 = r273697 * r273703;
        return r273704;
}
↓
double f(double x, double y, double z) {
        double r273705 = 1.0;
        double r273706 = 2.0;
        double r273707 = r273705 / r273706;
        double r273708 = x;
        double r273709 = y;
        double r273710 = z;
        double r273711 = sqrt(r273710);
        double r273712 = r273709 * r273711;
        double r273713 = r273708 + r273712;
        double r273714 = r273707 * r273713;
        return r273714;
}

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 2020021 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))