Average Error: 0.2 → 0.2
Time: 4.0s
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 r289666 = 1.0;
        double r289667 = 2.0;
        double r289668 = r289666 / r289667;
        double r289669 = x;
        double r289670 = y;
        double r289671 = z;
        double r289672 = sqrt(r289671);
        double r289673 = r289670 * r289672;
        double r289674 = r289669 + r289673;
        double r289675 = r289668 * r289674;
        return r289675;
}
↓
double f(double x, double y, double z) {
        double r289676 = 1.0;
        double r289677 = 2.0;
        double r289678 = r289676 / r289677;
        double r289679 = x;
        double r289680 = y;
        double r289681 = z;
        double r289682 = sqrt(r289681);
        double r289683 = r289680 * r289682;
        double r289684 = r289679 + r289683;
        double r289685 = r289678 * r289684;
        return r289685;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))