Average Error: 0.2 → 0.2
Time: 4.7s
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 r269566 = 1.0;
        double r269567 = 2.0;
        double r269568 = r269566 / r269567;
        double r269569 = x;
        double r269570 = y;
        double r269571 = z;
        double r269572 = sqrt(r269571);
        double r269573 = r269570 * r269572;
        double r269574 = r269569 + r269573;
        double r269575 = r269568 * r269574;
        return r269575;
}
↓
double f(double x, double y, double z) {
        double r269576 = 1.0;
        double r269577 = 2.0;
        double r269578 = r269576 / r269577;
        double r269579 = x;
        double r269580 = y;
        double r269581 = z;
        double r269582 = sqrt(r269581);
        double r269583 = r269580 * r269582;
        double r269584 = r269579 + r269583;
        double r269585 = r269578 * r269584;
        return r269585;
}

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 2020083 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))