Average Error: 0.2 → 0.2
Time: 11.8s
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 r181927 = 1.0;
        double r181928 = 2.0;
        double r181929 = r181927 / r181928;
        double r181930 = x;
        double r181931 = y;
        double r181932 = z;
        double r181933 = sqrt(r181932);
        double r181934 = r181931 * r181933;
        double r181935 = r181930 + r181934;
        double r181936 = r181929 * r181935;
        return r181936;
}
↓
double f(double x, double y, double z) {
        double r181937 = 1.0;
        double r181938 = 2.0;
        double r181939 = r181937 / r181938;
        double r181940 = x;
        double r181941 = y;
        double r181942 = z;
        double r181943 = sqrt(r181942);
        double r181944 = r181941 * r181943;
        double r181945 = r181940 + r181944;
        double r181946 = r181939 * r181945;
        return r181946;
}

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 2019297 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))