Average Error: 0.2 → 0.2
Time: 4.7s
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 r248211 = 1.0;
        double r248212 = 2.0;
        double r248213 = r248211 / r248212;
        double r248214 = x;
        double r248215 = y;
        double r248216 = z;
        double r248217 = sqrt(r248216);
        double r248218 = r248215 * r248217;
        double r248219 = r248214 + r248218;
        double r248220 = r248213 * r248219;
        return r248220;
}
↓
double f(double x, double y, double z) {
        double r248221 = 1.0;
        double r248222 = 2.0;
        double r248223 = r248221 / r248222;
        double r248224 = x;
        double r248225 = y;
        double r248226 = z;
        double r248227 = sqrt(r248226);
        double r248228 = r248225 * r248227;
        double r248229 = r248224 + r248228;
        double r248230 = r248223 * r248229;
        return r248230;
}

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 2020036 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))