Average Error: 0.1 → 0.1
Time: 4.9s
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 r264101 = 1.0;
        double r264102 = 2.0;
        double r264103 = r264101 / r264102;
        double r264104 = x;
        double r264105 = y;
        double r264106 = z;
        double r264107 = sqrt(r264106);
        double r264108 = r264105 * r264107;
        double r264109 = r264104 + r264108;
        double r264110 = r264103 * r264109;
        return r264110;
}
↓
double f(double x, double y, double z) {
        double r264111 = 1.0;
        double r264112 = 2.0;
        double r264113 = r264111 / r264112;
        double r264114 = x;
        double r264115 = y;
        double r264116 = z;
        double r264117 = sqrt(r264116);
        double r264118 = r264115 * r264117;
        double r264119 = r264114 + r264118;
        double r264120 = r264113 * r264119;
        return r264120;
}

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 2020089 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))