Average Error: 0.1 → 0.1
Time: 4.6s
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 r282972 = 1.0;
        double r282973 = 2.0;
        double r282974 = r282972 / r282973;
        double r282975 = x;
        double r282976 = y;
        double r282977 = z;
        double r282978 = sqrt(r282977);
        double r282979 = r282976 * r282978;
        double r282980 = r282975 + r282979;
        double r282981 = r282974 * r282980;
        return r282981;
}
↓
double f(double x, double y, double z) {
        double r282982 = 1.0;
        double r282983 = 2.0;
        double r282984 = r282982 / r282983;
        double r282985 = x;
        double r282986 = y;
        double r282987 = z;
        double r282988 = sqrt(r282987);
        double r282989 = r282986 * r282988;
        double r282990 = r282985 + r282989;
        double r282991 = r282984 * r282990;
        return r282991;
}

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 2020003 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))