Average Error: 0.1 → 0.1
Time: 21.7s
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 r208199 = 1.0;
        double r208200 = 2.0;
        double r208201 = r208199 / r208200;
        double r208202 = x;
        double r208203 = y;
        double r208204 = z;
        double r208205 = sqrt(r208204);
        double r208206 = r208203 * r208205;
        double r208207 = r208202 + r208206;
        double r208208 = r208201 * r208207;
        return r208208;
}
↓
double f(double x, double y, double z) {
        double r208209 = 1.0;
        double r208210 = 2.0;
        double r208211 = r208209 / r208210;
        double r208212 = x;
        double r208213 = y;
        double r208214 = z;
        double r208215 = sqrt(r208214);
        double r208216 = r208213 * r208215;
        double r208217 = r208212 + r208216;
        double r208218 = r208211 * r208217;
        return r208218;
}

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 2019199 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  (* (/ 1.0 2.0) (+ x (* y (sqrt z)))))