Average Error: 0.2 → 0.2
Time: 5.2s
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 r323651 = 1.0;
        double r323652 = 2.0;
        double r323653 = r323651 / r323652;
        double r323654 = x;
        double r323655 = y;
        double r323656 = z;
        double r323657 = sqrt(r323656);
        double r323658 = r323655 * r323657;
        double r323659 = r323654 + r323658;
        double r323660 = r323653 * r323659;
        return r323660;
}
↓
double f(double x, double y, double z) {
        double r323661 = 1.0;
        double r323662 = 2.0;
        double r323663 = r323661 / r323662;
        double r323664 = x;
        double r323665 = y;
        double r323666 = z;
        double r323667 = sqrt(r323666);
        double r323668 = r323665 * r323667;
        double r323669 = r323664 + r323668;
        double r323670 = r323663 * r323669;
        return r323670;
}

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 2020046 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))