Average Error: 0.1 → 0.1
Time: 15.0s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1 \cdot \left(x + \sqrt{z} \cdot y\right)}{2}\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1 \cdot \left(x + \sqrt{z} \cdot y\right)}{2}
double f(double x, double y, double z) {
        double r189453 = 1.0;
        double r189454 = 2.0;
        double r189455 = r189453 / r189454;
        double r189456 = x;
        double r189457 = y;
        double r189458 = z;
        double r189459 = sqrt(r189458);
        double r189460 = r189457 * r189459;
        double r189461 = r189456 + r189460;
        double r189462 = r189455 * r189461;
        return r189462;
}
↓
double f(double x, double y, double z) {
        double r189463 = 1.0;
        double r189464 = x;
        double r189465 = z;
        double r189466 = sqrt(r189465);
        double r189467 = y;
        double r189468 = r189466 * r189467;
        double r189469 = r189464 + r189468;
        double r189470 = r189463 * r189469;
        double r189471 = 2.0;
        double r189472 = r189470 / r189471;
        return r189472;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{1 \cdot \left(x + \sqrt{z} \cdot y\right)}{2}}\]

  3. Final simplification0.1

    \[\leadsto \frac{1 \cdot \left(x + \sqrt{z} \cdot y\right)}{2}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))