Average Error: 0.1 → 0.1
Time: 17.2s
Precision: 64
\[\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1}{2} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1}{2} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r12193708 = 1.0;
        double r12193709 = 2.0;
        double r12193710 = r12193708 / r12193709;
        double r12193711 = x;
        double r12193712 = y;
        double r12193713 = z;
        double r12193714 = sqrt(r12193713);
        double r12193715 = r12193712 * r12193714;
        double r12193716 = r12193711 + r12193715;
        double r12193717 = r12193710 * r12193716;
        return r12193717;
}
↓
double f(double x, double y, double z) {
        double r12193718 = 1.0;
        double r12193719 = 2.0;
        double r12193720 = r12193718 / r12193719;
        double r12193721 = x;
        double r12193722 = z;
        double r12193723 = sqrt(r12193722);
        double r12193724 = y;
        double r12193725 = r12193723 * r12193724;
        double r12193726 = r12193721 + r12193725;
        double r12193727 = r12193720 * r12193726;
        return r12193727;
}

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

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))