Average Error: 0.1 → 0.1
Time: 7.5s
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 r171752 = 1.0;
        double r171753 = 2.0;
        double r171754 = r171752 / r171753;
        double r171755 = x;
        double r171756 = y;
        double r171757 = z;
        double r171758 = sqrt(r171757);
        double r171759 = r171756 * r171758;
        double r171760 = r171755 + r171759;
        double r171761 = r171754 * r171760;
        return r171761;
}
↓
double f(double x, double y, double z) {
        double r171762 = 1.0;
        double r171763 = 2.0;
        double r171764 = r171762 / r171763;
        double r171765 = x;
        double r171766 = y;
        double r171767 = z;
        double r171768 = sqrt(r171767);
        double r171769 = r171766 * r171768;
        double r171770 = r171765 + r171769;
        double r171771 = r171764 * r171770;
        return r171771;
}

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 1978988140 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))