Average Error: 0.1 → 0.1
Time: 4.8s
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 r249598 = 1.0;
        double r249599 = 2.0;
        double r249600 = r249598 / r249599;
        double r249601 = x;
        double r249602 = y;
        double r249603 = z;
        double r249604 = sqrt(r249603);
        double r249605 = r249602 * r249604;
        double r249606 = r249601 + r249605;
        double r249607 = r249600 * r249606;
        return r249607;
}
↓
double f(double x, double y, double z) {
        double r249608 = 1.0;
        double r249609 = 2.0;
        double r249610 = r249608 / r249609;
        double r249611 = x;
        double r249612 = y;
        double r249613 = z;
        double r249614 = sqrt(r249613);
        double r249615 = r249612 * r249614;
        double r249616 = r249611 + r249615;
        double r249617 = r249610 * r249616;
        return r249617;
}

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 2020039 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))