Average Error: 0.2 → 0.2
Time: 15.2s
Precision: 64
\[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]
↓
\[\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]
\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)
↓
\frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)
double f(double x, double y, double z) {
        double r13380799 = 1.0;
        double r13380800 = 2.0;
        double r13380801 = r13380799 / r13380800;
        double r13380802 = x;
        double r13380803 = y;
        double r13380804 = z;
        double r13380805 = sqrt(r13380804);
        double r13380806 = r13380803 * r13380805;
        double r13380807 = r13380802 + r13380806;
        double r13380808 = r13380801 * r13380807;
        return r13380808;
}
↓
double f(double x, double y, double z) {
        double r13380809 = 1.0;
        double r13380810 = 2.0;
        double r13380811 = r13380809 / r13380810;
        double r13380812 = x;
        double r13380813 = z;
        double r13380814 = sqrt(r13380813);
        double r13380815 = y;
        double r13380816 = r13380814 * r13380815;
        double r13380817 = r13380812 + r13380816;
        double r13380818 = r13380811 * r13380817;
        return r13380818;
}

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

    \[\frac{1.0}{2.0} \cdot \left(x + y \cdot \sqrt{z}\right)\]

  2. Final simplification0.2

    \[\leadsto \frac{1.0}{2.0} \cdot \left(x + \sqrt{z} \cdot y\right)\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))