Average Error: 0.1 → 0.1
Time: 4.1s
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 r229924 = 1.0;
        double r229925 = 2.0;
        double r229926 = r229924 / r229925;
        double r229927 = x;
        double r229928 = y;
        double r229929 = z;
        double r229930 = sqrt(r229929);
        double r229931 = r229928 * r229930;
        double r229932 = r229927 + r229931;
        double r229933 = r229926 * r229932;
        return r229933;
}
↓
double f(double x, double y, double z) {
        double r229934 = 1.0;
        double r229935 = 2.0;
        double r229936 = r229934 / r229935;
        double r229937 = x;
        double r229938 = y;
        double r229939 = z;
        double r229940 = sqrt(r229939);
        double r229941 = r229938 * r229940;
        double r229942 = r229937 + r229941;
        double r229943 = r229936 * r229942;
        return r229943;
}

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 2020021 +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)))))