Average Error: 0.1 → 0.1
Time: 4.6s
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 r171747 = 1.0;
        double r171748 = 2.0;
        double r171749 = r171747 / r171748;
        double r171750 = x;
        double r171751 = y;
        double r171752 = z;
        double r171753 = sqrt(r171752);
        double r171754 = r171751 * r171753;
        double r171755 = r171750 + r171754;
        double r171756 = r171749 * r171755;
        return r171756;
}
↓
double f(double x, double y, double z) {
        double r171757 = 1.0;
        double r171758 = 2.0;
        double r171759 = r171757 / r171758;
        double r171760 = x;
        double r171761 = y;
        double r171762 = z;
        double r171763 = sqrt(r171762);
        double r171764 = r171761 * r171763;
        double r171765 = r171760 + r171764;
        double r171766 = r171759 * r171765;
        return r171766;
}

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 2020027 +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)))))