Average Error: 0.1 → 0.1
Time: 4.3s
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 r214759 = 1.0;
        double r214760 = 2.0;
        double r214761 = r214759 / r214760;
        double r214762 = x;
        double r214763 = y;
        double r214764 = z;
        double r214765 = sqrt(r214764);
        double r214766 = r214763 * r214765;
        double r214767 = r214762 + r214766;
        double r214768 = r214761 * r214767;
        return r214768;
}
↓
double f(double x, double y, double z) {
        double r214769 = 1.0;
        double r214770 = 2.0;
        double r214771 = r214769 / r214770;
        double r214772 = x;
        double r214773 = y;
        double r214774 = z;
        double r214775 = sqrt(r214774);
        double r214776 = r214773 * r214775;
        double r214777 = r214772 + r214776;
        double r214778 = r214771 * r214777;
        return r214778;
}

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 2020001 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))