Average Error: 0.1 → 0.1
Time: 4.9s
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 r271947 = 1.0;
        double r271948 = 2.0;
        double r271949 = r271947 / r271948;
        double r271950 = x;
        double r271951 = y;
        double r271952 = z;
        double r271953 = sqrt(r271952);
        double r271954 = r271951 * r271953;
        double r271955 = r271950 + r271954;
        double r271956 = r271949 * r271955;
        return r271956;
}
↓
double f(double x, double y, double z) {
        double r271957 = 1.0;
        double r271958 = 2.0;
        double r271959 = r271957 / r271958;
        double r271960 = x;
        double r271961 = y;
        double r271962 = z;
        double r271963 = sqrt(r271962);
        double r271964 = r271961 * r271963;
        double r271965 = r271960 + r271964;
        double r271966 = r271959 * r271965;
        return r271966;
}

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 2019354 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))