Average Error: 0.1 → 0.1
Time: 5.0s
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 r285238 = 1.0;
        double r285239 = 2.0;
        double r285240 = r285238 / r285239;
        double r285241 = x;
        double r285242 = y;
        double r285243 = z;
        double r285244 = sqrt(r285243);
        double r285245 = r285242 * r285244;
        double r285246 = r285241 + r285245;
        double r285247 = r285240 * r285246;
        return r285247;
}
↓
double f(double x, double y, double z) {
        double r285248 = 1.0;
        double r285249 = 2.0;
        double r285250 = r285248 / r285249;
        double r285251 = x;
        double r285252 = y;
        double r285253 = z;
        double r285254 = sqrt(r285253);
        double r285255 = r285252 * r285254;
        double r285256 = r285251 + r285255;
        double r285257 = r285250 * r285256;
        return r285257;
}

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 2020034 +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)))))