Average Error: 0.1 → 0.1
Time: 17.7s
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 r165216 = 1.0;
        double r165217 = 2.0;
        double r165218 = r165216 / r165217;
        double r165219 = x;
        double r165220 = y;
        double r165221 = z;
        double r165222 = sqrt(r165221);
        double r165223 = r165220 * r165222;
        double r165224 = r165219 + r165223;
        double r165225 = r165218 * r165224;
        return r165225;
}
↓
double f(double x, double y, double z) {
        double r165226 = 1.0;
        double r165227 = 2.0;
        double r165228 = r165226 / r165227;
        double r165229 = x;
        double r165230 = y;
        double r165231 = z;
        double r165232 = sqrt(r165231);
        double r165233 = r165230 * r165232;
        double r165234 = r165229 + r165233;
        double r165235 = r165228 * r165234;
        return r165235;
}

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 2019322 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))