Average Error: 0.1 → 0.1
Time: 4.0s
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 r229701 = 1.0;
        double r229702 = 2.0;
        double r229703 = r229701 / r229702;
        double r229704 = x;
        double r229705 = y;
        double r229706 = z;
        double r229707 = sqrt(r229706);
        double r229708 = r229705 * r229707;
        double r229709 = r229704 + r229708;
        double r229710 = r229703 * r229709;
        return r229710;
}
↓
double f(double x, double y, double z) {
        double r229711 = 1.0;
        double r229712 = 2.0;
        double r229713 = r229711 / r229712;
        double r229714 = x;
        double r229715 = y;
        double r229716 = z;
        double r229717 = sqrt(r229716);
        double r229718 = r229715 * r229717;
        double r229719 = r229714 + r229718;
        double r229720 = r229713 * r229719;
        return r229720;
}

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 2020049 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))