Average Error: 0.1 → 0.1
Time: 4.1s
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 r177668 = 1.0;
        double r177669 = 2.0;
        double r177670 = r177668 / r177669;
        double r177671 = x;
        double r177672 = y;
        double r177673 = z;
        double r177674 = sqrt(r177673);
        double r177675 = r177672 * r177674;
        double r177676 = r177671 + r177675;
        double r177677 = r177670 * r177676;
        return r177677;
}
↓
double f(double x, double y, double z) {
        double r177678 = 1.0;
        double r177679 = 2.0;
        double r177680 = r177678 / r177679;
        double r177681 = x;
        double r177682 = y;
        double r177683 = z;
        double r177684 = sqrt(r177683);
        double r177685 = r177682 * r177684;
        double r177686 = r177681 + r177685;
        double r177687 = r177680 * r177686;
        return r177687;
}

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 2020020 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))