Average Error: 0.2 → 0.2
Time: 5.3s
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 r248256 = 1.0;
        double r248257 = 2.0;
        double r248258 = r248256 / r248257;
        double r248259 = x;
        double r248260 = y;
        double r248261 = z;
        double r248262 = sqrt(r248261);
        double r248263 = r248260 * r248262;
        double r248264 = r248259 + r248263;
        double r248265 = r248258 * r248264;
        return r248265;
}
↓
double f(double x, double y, double z) {
        double r248266 = 1.0;
        double r248267 = 2.0;
        double r248268 = r248266 / r248267;
        double r248269 = x;
        double r248270 = y;
        double r248271 = z;
        double r248272 = sqrt(r248271);
        double r248273 = r248270 * r248272;
        double r248274 = r248269 + r248273;
        double r248275 = r248268 * r248274;
        return r248275;
}

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)))))