Average Error: 0.1 → 0.1
Time: 10.3s
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 r207179 = 1.0;
        double r207180 = 2.0;
        double r207181 = r207179 / r207180;
        double r207182 = x;
        double r207183 = y;
        double r207184 = z;
        double r207185 = sqrt(r207184);
        double r207186 = r207183 * r207185;
        double r207187 = r207182 + r207186;
        double r207188 = r207181 * r207187;
        return r207188;
}
↓
double f(double x, double y, double z) {
        double r207189 = 1.0;
        double r207190 = 2.0;
        double r207191 = r207189 / r207190;
        double r207192 = x;
        double r207193 = y;
        double r207194 = z;
        double r207195 = sqrt(r207194);
        double r207196 = r207193 * r207195;
        double r207197 = r207192 + r207196;
        double r207198 = r207191 * r207197;
        return r207198;
}

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 2020045 +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)))))