Average Error: 0.1 → 0.1
Time: 5.8s
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 r257075 = 1.0;
        double r257076 = 2.0;
        double r257077 = r257075 / r257076;
        double r257078 = x;
        double r257079 = y;
        double r257080 = z;
        double r257081 = sqrt(r257080);
        double r257082 = r257079 * r257081;
        double r257083 = r257078 + r257082;
        double r257084 = r257077 * r257083;
        return r257084;
}
↓
double f(double x, double y, double z) {
        double r257085 = 1.0;
        double r257086 = 2.0;
        double r257087 = r257085 / r257086;
        double r257088 = x;
        double r257089 = y;
        double r257090 = z;
        double r257091 = sqrt(r257090);
        double r257092 = r257089 * r257091;
        double r257093 = r257088 + r257092;
        double r257094 = r257087 * r257093;
        return r257094;
}

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 2019322 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, B"
  :precision binary64
  (* (/ 1 2) (+ x (* y (sqrt z)))))