Average Error: 0.2 → 0.2
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 r190602 = 1.0;
        double r190603 = 2.0;
        double r190604 = r190602 / r190603;
        double r190605 = x;
        double r190606 = y;
        double r190607 = z;
        double r190608 = sqrt(r190607);
        double r190609 = r190606 * r190608;
        double r190610 = r190605 + r190609;
        double r190611 = r190604 * r190610;
        return r190611;
}
↓
double f(double x, double y, double z) {
        double r190612 = 1.0;
        double r190613 = x;
        double r190614 = z;
        double r190615 = sqrt(r190614);
        double r190616 = y;
        double r190617 = r190615 * r190616;
        double r190618 = r190613 + r190617;
        double r190619 = r190612 * r190618;
        double r190620 = 2.0;
        double r190621 = r190619 / r190620;
        return r190621;
}

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. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))